Daily Papers

Clinical reasoning demands multi-step interactions -- gathering patient history, ordering tests, interpreting results, and making safe treatment decisions -- yet a unified training environment provides the breadth of clinical domains and specialized tools to train generalizable medical AI agents through reinforcement learning remains elusive. We present a comprehensive empirical study of multi-turn agentic RL for medical AI, built on , a gymnasium-compatible environment spanning 10 clinical domains with 3.6K+ tasks, 135 domain-specific tools, and a knowledge base of 828K medical passages. Our analysis reveals that agentic multi-turn structure degrades into verbose single-turn monologues, characterized by monotonic length explosion and a simultaneous erosion of tool-use frequency. We characterize how this collapse, alongside distillation instability, stems from the misalignment of sparse terminal rewards with sequential clinical trajectories. We find that vanilla GRPO achieves strong final accuracy on some benchmarks but suffers from training instability, evidenced by significant oscillations in response length and prolonged convergence periods. To improve training efficiency and stability, we propose Turn-level Truncated On-Policy Distillation (TT-OPD), a self-distillation framework where a gradient-free EMA teacher leverages outcome-privileged information to provide dense, outcome-aware KL regularization at every conversation turn. TT-OPD achieves the best performance on 10 of 18 benchmarks with an average +3.9~pp improvement over the non-RL baseline with faster early convergence, controlled response length, and sustained multi-turn tool use.

On-policy distillation (OPD) is appealing for large language model (LLM) post-training because it evaluates teacher feedback on student-generated rollouts rather than fixed teacher traces. In long-horizon settings, however, the common sampled-token variant is fragile: it reduces distribution matching to a one-token signal and becomes increasingly unreliable as rollouts drift away from prefixes the teacher commonly visits. We revisit OPD from the estimator and implementation sides. Theoretically, token-level OPD is biased relative to sequence-level reverse-KL, but it has a much tighter worst-case variance bound; our toy study shows the same tradeoff empirically, with stronger future-reward coupling producing higher gradient variance and less stable learning. Empirically, we identify three failure modes of sampled-token OPD: an imbalanced one-token signal, unreliable teacher guidance on student-generated prefixes, and distortions caused by tokenizer or special-token mismatch. We address these issues with teacher top-K local support matching, implemented as truncated reverse-KL with top-p rollout sampling and special-token masking. Across single-task math reasoning and multi-task agentic-plus-math training, this objective yields more stable optimization and better downstream performance than sampled-token OPD.

On-policy distillation (OPD) trains student models under their own induced distribution while leveraging supervision from stronger teachers. We identify a failure mode of OPD: as training progresses, on-policy rollouts can undergo abrupt length inflation, causing truncated trajectories to dominate the training data. This truncation collapse coincides with abrupt repetition saturation and induces biased gradient signals, leading to severe training instability and sharp degradation in validation performance. We attribute this problem to the interaction between student-induced data collection and the distillation objective, which implicitly favors long and repetitive rollouts. To address this issue, we propose StableOPD, a stabilized OPD framework that combines a reference-based divergence constraint with rollout mixture distillation. These together mitigate repetition-induced length inflation and further stabilize OPD training. Across multiple math reasoning datasets, our approach prevents truncation collapse, stabilizes training dynamics, and improves performance by 7.2% on average.

On-policy distillation is pivotal for transferring reasoning capabilities to capacity-constrained models, yet remains prone to instability and negative transfer. We show that on-policy distillation can be interpreted, both theoretically and empirically, as a form of policy optimization, where the teacher-student log-likelihood ratio acts as a token reward. From this insight, we introduce REOPOLD (Relaxed On-Policy Distillation) a framework that stabilizes optimization by relaxing the strict imitation constraints of standard on-policy distillation. Specifically, REOPOLD temperately and selectively leverages rewards from the teacher through mixture-based reward clipping, entropy-based token-level dynamic sampling, and a unified exploration-to-refinement training strategy. Empirically, REOPOLD surpasses its baselines with superior sample efficiency during training and enhanced test-time scaling at inference, across mathematical, visual, and agentic tool-use reasoning tasks. Specifically, REOPOLD outperforms recent RL approaches achieving 6.7~12x greater sample efficiency and enables a 7B student to match a 32B teacher in visual reasoning with a ~3.32x inference speedup.

On-policy distillation (OPD), which samples trajectories from the student model and supervises them with a teacher at the token level, avoids relying solely on verifiable terminal rewards and can yield better generalization than off-policy distillation. However, OPD requires expensive on-the-fly sampling of the student policy during training, which substantially increases training cost, especially for long responses. Our initial analysis shows that, during OPD, training signals are often concentrated in the prefix of each output, and that even a short teacher-generated prefix can significantly help the student produce the correct answer. Motivated by these observations, we propose a simple yet effective modification of OPD: we apply the distillation objective only to prefixes of student-generated outputs and terminate each sampling early during distillation. Experiments on a suite of AI-for-Math and out-of-domain benchmarks show that on-policy prefix distillation matches the performance of full OPD while reducing training FLOP by 2x-47x.

On-policy distillation is a promising approach for transferring knowledge between language models, where a student learns from dense token-level signals along its own trajectories. This framework typically uses reverse KL divergence, encouraging the student to match the teacher's high-confidence predictions. However, we show that the mode-seeking property of reverse KL reduces generation diversity and yields unstable learning signals when the teacher distribution has high entropy. To address this, we introduce Entropy-Aware On-Policy Distillation. Our key idea is augmenting the standard reverse KL objective with forward KL when teacher entropy is high, capturing the full range of plausible outputs while retaining precise imitation elsewhere. It balances mode-seeking precision with mode-covering robustness without sacrificing on-policy training efficiency. Experiments show that our method maintains generation diversity (sustained token-level entropy) and improves student-teacher alignment (lower forward KL on high-entropy tokens). Across six math reasoning benchmarks, this yields Pass@8 accuracy gains of +1.37 for Qwen3-0.6B-Base, +2.39 for Qwen3-1.7B-Base, and +5.05 for Qwen3-4B-Base compared to baseline on-policy distillation methods. These results demonstrate that accounting for teacher uncertainty is essential for maintaining diversity and achieving effective knowledge transfer.

Knowledge distillation improves large language model (LLM) reasoning by compressing the knowledge of a teacher LLM to train smaller LLMs. On-policy distillation advances this approach by having the student sample its own trajectories while a teacher LLM provides dense token-level supervision, addressing the distribution mismatch between training and inference in off-policy distillation methods. However, on-policy distillation typically requires a separate, often larger, teacher LLM and does not explicitly leverage ground-truth solutions available in reasoning datasets. Inspired by the intuition that a sufficiently capable LLM can rationalize external privileged reasoning traces and teach its weaker self (i.e., the version without access to privileged information), we introduce On-Policy Self-Distillation (OPSD), a framework where a single model acts as both teacher and student by conditioning on different contexts. The teacher policy conditions on privileged information (e.g., verified reasoning traces) while the student policy sees only the question; training minimizes the per-token divergence between these distributions over the student's own rollouts. We demonstrate the efficacy of our method on multiple mathematical reasoning benchmarks, achieving 4-8x token efficiency compared to reinforcement learning methods such as GRPO and superior performance over off-policy distillation methods.

Knowledge distillation has become a primary mechanism for transferring reasoning and domain expertise from frontier Large Language Models (LLMs) to smaller, deployable students. However, the dominant paradigm remains off-policy: students train on static teacher-generated data and never encounter their own errors during learning. This train--test mismatch, an instance of exposure bias, causes prediction errors to compound autoregressively at inference time. On-Policy Distillation (OPD) addresses this by letting the student generate its own trajectories and receive teacher feedback on these self-generated outputs, grounding distillation in the theory of interactive imitation learning. Despite rapid growth spanning divergence minimization, reward-guided learning, and self-play, the OPD literature remains fragmented with no unified treatment. This survey provides the first comprehensive overview of OPD for LLMs. We introduce a unified f-divergence framework over on-policy samples and organize the landscape along three orthogonal dimensions: feedback signal (logit-based, outcome-based, or self-play), teacher access (white-box, black-box, or teacher-free), and loss granularity (token-level, sequence-level, or hybrid). We systematically analyze representative methods, examine industrial deployments, and identify open problems including distillation scaling laws, uncertainty-aware feedback, and agent-level distillation.

Knowledge distillation (KD) is a powerful paradigm for compressing large language models (LLMs), whose effectiveness depends on intertwined choices of divergence direction, optimization strategy, and data regime. We break down the design of existing KD methods and present a unified view that establishes connections between them, reformulating KD as a reweighted log-likelihood objective at the token level. We further propose Hybrid Policy Distillation (HPD), which integrates the complementary advantages of forward and reverse KL to balance mode coverage and mode-seeking, and combines off-policy data with lightweight, approximate on-policy sampling. We validate HPD on long-generation math reasoning as well as short-generation dialogue and code tasks, demonstrating improved optimization stability, computational efficiency, and final performance across diverse model families and scales. The code related to this work is available at https://github.com/zwhong714/Hybrid-Policy-Distillation.

On-policy distillation (OPD), which aligns the student with the teacher's logit distribution on student-generated trajectories, has demonstrated strong empirical gains in improving student performance and often outperforms off-policy distillation and reinforcement learning (RL) paradigms. In this work, we first theoretically show that OPD is a special case of dense KL-constrained RL where the reward function and the KL regularization are always weighted equally and the reference model can by any model. Then, we propose the Generalized On-Policy Distillation (G-OPD) framework, which extends the standard OPD objective by introducing a flexible reference model and a reward scaling factor that controls the relative weight of the reward term against the KL regularization. Through comprehensive experiments on math reasoning and code generation tasks, we derive two novel insights: (1) Setting the reward scaling factor to be greater than 1 (i.e., reward extrapolation), which we term ExOPD, consistently improves over standard OPD across a range of teacher-student size pairings. In particular, in the setting where we merge the knowledge from different domain experts, obtained by applying domain-specific RL to the same student model, back into the original student, ExOPD enables the student to even surpass the teacher's performance boundary and outperform the domain teachers. (2) Building on ExOPD, we further find that in the strong-to-weak distillation setting (i.e., distilling a smaller student from a larger teacher), performing reward correction by choosing the reference model as the teacher's base model before RL yields a more accurate reward signal and further improves distillation performance. However, this choice assumes access to the teacher's pre-RL variant and incurs more computational overhead. We hope our work offers new insights for future research on OPD.

Black-box knowledge distillation for large language models presents a strict trade-off. Simple off-policy methods (e.g., sequence-level knowledge distillation) struggle to correct the student's inherent errors. Fully on-policy methods (e.g., Generative Adversarial Distillation) solve this via adversarial training but introduce well-known training instability and crippling computational overhead. To address this dilemma, we propose SODA (Semi On-policy Distillation with Alignment), a highly efficient alternative motivated by the inherent capability gap between frontier teachers and much smaller base models. Because a compact student model's natural, zero-shot responses are almost strictly inferior to the powerful teacher's targets, we can construct a highly effective contrastive signal simply by pairing the teacher's optimal response with a one-time static snapshot of the student's outputs. This demonstrates that exposing the small student to its own static inferior behaviors is sufficient for high-quality distribution alignment, eliminating the need for costly dynamic rollouts and fragile adversarial balancing. Extensive evaluations across four compact Qwen2.5 and Llama-3 models validate this semi on-policy paradigm. SODA matches or outperforms the state-of-the-art methods on 15 out of 16 benchmark results. More importantly, it achieves this superior distillation quality while training 10 times faster, consuming 27% less peak GPU memory, and completely eliminating adversarial instability.

Context distillation enables language models to internalize in-context knowledge into their parameters. In our work, we propose On-Policy Context Distillation (OPCD), a framework that bridges on-policy distillation with context distillation by training a student model on its own generated trajectories while minimizing reverse Kullback-Leibler divergence against a context-conditioned teacher. We demonstrate the effectiveness of OPCD on two important applications: experiential knowledge distillation, where models extract and consolidate transferable knowledge from their historical solution traces, and system prompt distillation, where models internalize beneficial behaviors encoded in optimized prompts. Across mathematical reasoning, text-based games, and domain-specific tasks, OPCD consistently outperforms baseline methods, achieving higher task accuracy while better preserving out-of-distribution capabilities. We further show that OPCD enables effective cross-size distillation, where smaller student models can internalize experiential knowledge from larger teachers.

Reinforcement learning (RL) has been widely used to train LLM agents for multi-turn interactive tasks, but its sample efficiency is severely limited by sparse rewards and long horizons. On-policy self-distillation (OPSD) alleviates this by providing dense token-level supervision from a privileged teacher that has access to ground-truth answers. However, such fixed privileged information cannot capture the diverse valid strategies in agent tasks, and naively combining OPSD with RL often leads to training collapse. To address these limitations, we introduce Skill-SD, a framework that turns the agent's own trajectories into dynamic training-only supervision. Completed trajectories are summarized into compact natural language skills that describe successful behaviors, mistakes, and workflows. These skills serve as dynamic privileged information conditioning only the teacher, while the student always acts under the plain task prompt and learns to internalize the guidance through distillation. To stabilize the training, we derive an importance-weighted reverse-KL loss to provide gradient-correct token-level distillation, and dynamically synchronize the teacher with the improving student. Experimental results on agentic benchmarks demonstrate that Skill-SD substantially outperforms the standard RL baseline, improving both vanilla GRPO (+14.0%/+10.9% on AppWorld/Sokoban) and vanilla OPD (+42.1%/+40.6%). Project page: https://k1xe.github.io/skill-sd/

Large language models trained with reinforcement learning (RL) for mathematical reasoning face a fundamental challenge: on problems the model cannot solve at all - "cliff" prompts - the RL gradient vanishes entirely, preventing any learning signal from reaching these failure modes. We introduce Hybrid Distillation Policy Optimization (HDPO), which augments standard RL with privileged self-distillation targeting cliff prompts. On each training step, HDPO identifies prompts where all rollouts fail, generates privileged rollouts by providing the model with ground-truth information, filters for correct solutions, and distills the teacher's token-level distribution into the student. Because teacher and student share the same weights - differing only in their input - the realizability gap is provably bounded, unlike cross-model distillation. We prove that R=1 filtered privileged generation recovers the optimal KL-regularized RL policy in the hard-threshold limit. Experiments on OpenMathInstruct-2 with Qwen2.5-Math-1.5B-Instruct show that HDPO consistently improves coverage metrics (pass@4 by +0.8-1.1%, pass@8 by +0.4-1.7%) while maintaining greedy accuracy, with the distillation weight lambda providing direct control over the exploration-exploitation tradeoff.

On-policy distillation (OPD) has become a popular training paradigm in the LLM community. This paradigm selects a larger model as the teacher to provide dense, fine-grained signals for each sampled trajectory, in contrast to reinforcement learning with verifiable rewards (RLVR), which only obtains sparse signals from verifiable outcomes in the environment. Recently, the community has explored on-policy self-distillation (OPSD), where the same model serves as both teacher and student, with the teacher receiving additional privileged information such as reference answers to enable self-evolution. This paper demonstrates that learning signals solely derived from the privileged teacher result in severe information leakage and unstable long-term training. Accordingly, we identify the optimal niche for self-distillation and propose RLSD (RLVR with Self-Distillation). Specifically, we leverage self-distillation to obtain token-level policy differences for determining fine-grained update magnitudes, while continuing to use RLVR to derive reliable update directions from environmental feedback (e.g., response correctness). This enables RLSD to simultaneously harness the strengths of both RLVR and OPSD, achieving a higher convergence ceiling and superior training stability.

On-policy reinforcement learning has become the dominant paradigm for reasoning alignment in large language models, yet its sparse, outcome-level rewards make token-level credit assignment notoriously difficult. On-Policy Distillation (OPD) alleviates this by introducing dense, token-level KL supervision from a teacher model, but typically applies this supervision uniformly across all rollouts, ignoring fundamental differences in signal quality. We propose Signal-Calibrated On-Policy Distillation Enhancement (SCOPE), a dual-path adaptive training framework that routes on-policy rollouts by correctness into two complementary supervision paths. For incorrect trajectories, SCOPE performs teacher-perplexity-weighted KL distillation to prioritize instances where the teacher demonstrates genuine corrective capability, while down-weighting unreliable guidance. For correct trajectories, it applies student-perplexity-weighted MLE to concentrate reinforcement on low-confidence samples at the capability boundary rather than over-reinforcing already mastered ones. Both paths employ a group-level normalization to adaptively calibrate weight distributions, accounting for the intrinsic difficulty variance across prompts. Extensive experiments on six reasoning benchmarks show that SCOPE achieves an average relative improvement of 11.42% in Avg@32 and 7.30% in Pass@32 over competitive baselines, demonstrating its consistent effectiveness.

On-policy distillation (OPD) has emerged as an efficient post-training paradigm for large language models. However, standard OPD requires a live teacher inference server throughout training, resulting in substantial infrastructure overhead. In this work, we investigate whether on-policy distillation can be performed offline. A natural approach is to precompute teacher log-probabilities once over SFT rollouts and reuse them during training. In practice, however, this offline variant fails to reliably match the performance of standard OPD. To understand this discrepancy, we identify a previously overlooked condition that is critical for any OPD pipeline, which we term teacher consistency. This condition requires that the same teacher model be used for both supervised fine-tuning and OPD. We show that violating teacher consistency introduces an irreducible gradient bias, causing both offline and online OPD to converge to a suboptimal fixed point regardless of training duration. Building on this insight, we propose Lightning OPD, an offline on-policy distillation framework that enforces teacher consistency by precomputing teacher log-probabilities over SFT rollouts. This design eliminates the need for a live teacher server entirely. We further show that, under teacher consistency, Lightning OPD shares the same optimum as standard OPD, with bounded gradient discrepancy and an implicit regularization effect that helps prevent policy drift. Extensive experiments on mathematical reasoning and code generation demonstrate that Lightning OPD achieves state-of-the-art performance with significantly improved efficiency. Starting from an SFT-initialized Qwen3-8B-Base model, Lightning OPD reaches 69.9% on AIME 2024 in just 30 GPU hours, achieving a 4.0x speedup over standard OPD and substantially lowering the barrier to entry for academic research on LLM post-training.

On-policy distillation (OPD) is an increasingly important paradigm for post-training language models. However, we identify a pervasive Scaling Law of Miscalibration: while OPD effectively improves task accuracy, it systematically traps models in severe overconfidence. We trace this failure to an information mismatch: teacher supervision is formed under privileged context available during training, whereas the deployed model must report confidence using only deployment-time information. We formalize this perspective theoretically, showing that teacher-conditioned success is generally not a valid target for deployment-time confidence and that helpful privileged context induces entropy collapse and a systematic optimism bias. To address this, we propose a calibration-aware OPD framework, CaOPD, that estimates empirical confidence from model rollouts, replaces self-reported confidence with this student-grounded target, and distills the revised response through the same self-distillation pipeline. Experiments across various models and domains show that CaOPD achieves Pareto-optimal calibration while maintaining competitive capability, generalizing robustly under out-of-distribution and continual learning. Our findings highlight that capability distillation does not imply calibrated confidence, and that confidence should be treated as an essential objective in post-training. Code: https://github.com/SalesforceAIResearch/CaOPD

Knowledge distillation offers a promising path to transfer reasoning capabilities from large teacher models to efficient student models; however, existing token-level on-policy distillation methods require token-level alignment between the student and teacher models, which restricts the student model's exploration ability, prevent effective use of interactive environment feedback, and suffer from severe memory bottlenecks in reinforcement learning. We introduce On-policy Verbal Distillation (OVD), a memory-efficient framework that replaces token-level probability matching with trajectory matching using discrete verbal scores (0--9) from teacher models. OVD dramatically reduces memory consumption while enabling on-policy distillation from teacher models with verbal feedback, and avoids token-level alignment, allowing the student model to freely explore the output space. Extensive experiments on Web question answering and mathematical reasoning tasks show that OVD substantially outperforms existing methods, delivering up to +12.9% absolute improvement in average EM on Web Q&A tasks and a up to +25.7% gain on math benchmarks (when trained with only one random samples), while also exhibiting superior training efficiency. Our project page is available at https://OVD.github.io

On-policy distillation (OPD) has become a core technique in the post-training of large language models, yet its training dynamics remain poorly understood. This paper provides a systematic investigation of OPD dynamics and mechanisms. We first identify that two conditions govern whether OPD succeeds or fails: (i) the student and teacher should share compatible thinking patterns; and (ii) even with consistent thinking patterns and higher scores, the teacher must offer genuinely new capabilities beyond what the student has seen during training. We validate these findings through weak-to-strong reverse distillation, showing that same-family 1.5B and 7B teachers are distributionally indistinguishable from the student's perspective. Probing into the token-level mechanism, we show that successful OPD is characterized by progressive alignment on high-probability tokens at student-visited states, a small shared token set that concentrates most of the probability mass (97%-99%). We further propose two practical strategies to recover failing OPD: off-policy cold start and teacher-aligned prompt selection. Finally, we show that OPD's apparent free lunch of dense token-level reward comes at a cost, raising the question of whether OPD can scale to long-horizon distillation.

Training-time privileged information (PI) can enable language models to succeed on tasks they would otherwise fail, making it a powerful tool for reinforcement learning in hard, long-horizon settings. However, transferring capabilities learned with PI to policies that must act without it at inference time remains a fundamental challenge. We study this problem in the context of distilling frontier models for multi-turn agentic environments, where closed-source systems typically hide their internal reasoning and expose only action trajectories. This breaks standard distillation pipelines, since successful behavior is observable but the reasoning process is not. For this, we introduce π-Distill, a joint teacher-student objective that trains a PI-conditioned teacher and an unconditioned student simultaneously using the same model. Additionally, we also introduce On-Policy Self-Distillation (OPSD), an alternative approach that trains using Reinforcement Learning (RL) with a reverse KL-penalty between the student and the PI-conditioned teacher. We show that both of these algorithms effectively distill frontier agents using action-only PI. Specifically we find that π-Distill and in some cases OPSD, outperform industry standard practices (Supervised finetuning followed by RL) that assume access to full Chain-of-Thought supervision across multiple agentic benchmarks, models, and forms of PI. We complement our results with extensive analysis that characterizes the factors enabling effective learning with PI, focusing primarily on π-Distill and characterizing when OPSD is competitive.

We introduce a novel approach to large language model (LLM) distillation by formulating it as a constrained reinforcement learning problem. While recent work has begun exploring the integration of task-specific rewards into distillation processes, existing methods typically rely on ad-hoc reward weighting. We propose a principled optimization framework that maximizes task-specific rewards while constraining the divergence from the teacher model to remain below a specified threshold. Our approach adapts constrained state augmented reinforcement learning to the distillation setting, introducing a modified reward function that maintains theoretical guarantees of constraint satisfaction without requiring state augmentation or teacher model access during deployment and without the computational overhead of the dual Lagrangian methods. Through extensive experiments on mathematical reasoning tasks, we demonstrate that our method achieves better constraint satisfaction rates and better reasoning compared to the soft Lagrangian relaxation baselines while maintaining competitive task performance. Our framework provides a theoretically grounded and practically efficient solution for reward-aware distillation in resource-constrained settings.

Reinforcement learning (RL) post-training has recently driven major gains in long chain-of-thought reasoning large language models (LLMs), but the high inference cost of such models motivates distillation into smaller students. Most existing knowledge distillation (KD) methods are designed for supervised fine-tuning (SFT), relying on fixed teacher traces or teacher-student Kullback-Leibler (KL) divergence-based regularization. When combined with RL, these approaches often suffer from distribution mismatch and objective interference: teacher supervision may not align with the student's evolving rollout distribution, and the KL regularizer can compete with reward maximization and require careful loss balancing. To address these issues, we propose RL-aware distillation (RLAD), which performs selective imitation during RL -- guiding the student toward the teacher only when it improves the current policy update. Our core component, Trust Region Ratio Distillation (TRRD), replaces the teacher-student KL regularizer with a PPO/GRPO-style likelihood-ratio objective anchored to a teacher--old-policy mixture, yielding advantage-aware, trust-region-bounded distillation on student rollouts and naturally balancing exploration, exploitation, and imitation. Across diverse logic reasoning and math benchmarks, RLAD consistently outperforms offline distillation, standard GRPO, and KL-based on-policy teacher-student knowledge distillation.

Graphical User Interface (GUI) grounding maps natural language instructions to the visual coordinates of target elements and serves as a core capability for autonomous GUI agents. Recent reinforcement learning methods (e.g., GRPO) have achieved strong performance, but they rely on expensive multiple rollouts and suffer from sparse signals on hard samples. These limitations make on-policy self-distillation (OPSD), which provides dense token-level supervision from a single rollout, a promising alternative. However, its applicability to GUI grounding remains unexplored. In this paper, we present GUI-SD, the first OPSD framework tailored for GUI grounding. First, it constructs a visually enriched privileged context for the teacher using a target bounding box and a Gaussian soft mask, providing informative guidance without leaking exact coordinates. Second, it employs entropy-guided distillation, which adaptively weights tokens based on digit significance and teacher confidence, concentrating optimization on the most impactful and reliable positions. Extensive experiments on six representative GUI grounding benchmarks show that GUI-SD consistently outperforms GRPO-based methods and naive OPSD in both accuracy and training efficiency. Code and training data are available at https://zhangyan-ucas.github.io/GUI-SD/.

On-policy distillation (OPD) has shown strong potential for transferring reasoning ability from frontier or domain-specific models to smaller students. While effective on static single-turn tasks, its behavior in multi-turn agent settings remains underexplored. In this work, we identify a key limitation of vanilla OPD in such settings, which we term Trajectory-Level KL Instability. Specifically, we observe that KL divergence increases together with a drop in success rate, and even after convergence, the KL remains high, leading to unstable training. This instability arises from inter-turn error compounding: as errors accumulate, the student is driven beyond the teacher's effective support, rendering the supervision signal unreliable. To address this, we propose TCOD (Temporal Curriculum On-Policy Distillation), a simple yet effective framework that controls the trajectory depth exposed to the student and progressively expands it from short to long with a curriculum schedule.Experimental results across four student-teacher pairs on three multi-turn agent benchmarks (ALFWorld, WebShop, ScienceWorld) show that TCOD mitigates KL escalation and enhances KL stability throughout training, improving agent performance by up to 18 points over vanilla OPD. Further evaluations show that TCOD can even surpass the teacher's performance and generalize to tasks on which the teacher fails.

Many existing studies have achieved significant improvements in the reasoning capabilities of large language models (LLMs) through reinforcement learning with verifiable rewards (RLVR), while the enhancement of reasoning abilities in small language models (SLMs) has not yet been sufficiently explored. Combining distilled data from larger models with RLVR on small models themselves is a natural approach, but it still faces various challenges and issues. Therefore, we propose \underline{R}ecall-\underline{E}xtend \underline{D}ynamics(RED): Enhancing Small Language Models through Controlled Exploration and Refined Offline Integration. In this paper, we explore the perspective of varying exploration spaces, balancing offline distillation with online reinforcement learning. Simultaneously, we specifically design and optimize for the insertion problem within offline data. By monitoring the ratio of entropy changes in the model concerning offline and online data, we regulate the weight of offline-SFT, thereby addressing the issues of insufficient exploration space in small models and the redundancy and complexity during the distillation process. Furthermore, to tackle the distribution discrepancies between offline data and the current policy, we design a sample-accuracy-based policy shift mechanism that dynamically chooses between imitating offline distilled data and learning from its own policy.

Reasoning-oriented language models achieve strong performance by generating long chain-of-thought traces at inference time. However, this capability comes with substantial and often excessive computational cost, which can materialize in redundant or inefficient reasoning. We study this setting and introduce Truncated-Reasoning Self-Distillation (TRSD), a lightweight post-training procedure that encourages models to produce correct predictions from partial reasoning traces. In TRSD, a frozen teacher model first generates a full reasoning trace and evaluates the corresponding answer distribution conditioned on the prompt and the complete reasoning to construct a synthetic training target. A student model with the same architecture is then trained to match the teacher's answer distribution while being conditioned only on a truncated prefix of its reasoning trace. Across multiple reasoning benchmarks and token budgets, we demonstrate that TRSD improves robustness to truncated inference, with far reduced accuracy tradeoffs when applied to a diverse set of reasoning models. Moreover, although never explicitly regularized for shorter generation during training, we also find that TRSD-trained models inherently output shorter reasoning traces without truncation, significantly reducing inference-time costs even without artificial interventions.

Recently, test-time scaling Large Language Models (LLMs) have demonstrated exceptional reasoning capabilities across scientific and professional tasks by generating long chains-of-thought (CoT). As a crucial component for developing these reasoning models, reinforcement learning (RL), exemplified by Proximal Policy Optimization (PPO) and its variants, allows models to learn through trial and error. However, PPO can be time-consuming due to its inherent on-policy nature, which is further exacerbated by increasing response lengths. In this work, we propose Truncated Proximal Policy Optimization (T-PPO), a novel extension to PPO that improves training efficiency by streamlining policy update and length-restricted response generation. T-PPO mitigates the issue of low hardware utilization, an inherent drawback of fully synchronized long-generation procedures, where resources often sit idle during the waiting periods for complete rollouts. Our contributions are two-folds. First, we propose Extended Generalized Advantage Estimation (EGAE) for advantage estimation derived from incomplete responses while maintaining the integrity of policy learning. Second, we devise a computationally optimized mechanism that allows for the independent optimization of the policy and value models. By selectively filtering prompt and truncated tokens, this mechanism reduces redundant computations and accelerates the training process without sacrificing convergence performance. We demonstrate the effectiveness and efficacy of T-PPO on AIME 2024 with a 32B base model. The experimental results show that T-PPO improves the training efficiency of reasoning LLMs by up to 2.5x and outperforms its existing competitors.

The landscape of high-performance image generation models is currently shifting from the inefficient multi-step ones to the efficient few-step counterparts (e.g, Z-Image-Turbo and FLUX.2-klein). However, these models present significant challenges for directly continuous supervised fine-tuning. For example, applying the commonly used fine-tuning technique would compromises their inherent few-step inference capability. To address this, we propose D-OPSD, a novel training paradigm for step-distilled diffusion models that enables on-policy learning during supervised fine-tuning. We first find that the modern diffusion model where the LLM/VLM serves as the encoder can inherit its encoder's in-context capabilities. This enables us to make the training as an on-policy self-distillation process. Specifically, during training, we make the model acts as both the teacher and the student with different contexts, where the student is conditioned only on the text feature, while the teacher is conditioned on the multimodal feature of both the text prompt and the target image. Training minimizes the two predicted distributions over the student's own roll-outs. By optimized on the model's own trajectory and under it's own supervision, D-OPSD enables the model to learn new concept, style, etc. without sacrificing the original few-step capacity.

Causal language models have demonstrated remarkable capabilities, but their size poses significant challenges for deployment in resource-constrained environments. Knowledge distillation, a widely-used technique for transferring knowledge from a large teacher model to a small student model, presents a promising approach for model compression. A significant remaining issue lies in the major differences between teacher and student models, namely the substantial capacity gap, mode averaging, and mode collapse, which pose barriers during distillation. To address these issues, we introduce Temporally Adaptive Interpolated Distillation (TAID), a novel knowledge distillation approach that dynamically interpolates student and teacher distributions through an adaptive intermediate distribution, gradually shifting from the student's initial distribution towards the teacher's distribution. We provide a theoretical analysis demonstrating TAID's ability to prevent mode collapse and empirically show its effectiveness in addressing the capacity gap while balancing mode averaging and mode collapse. Our comprehensive experiments demonstrate TAID's superior performance across various model sizes and architectures in both instruction tuning and pre-training scenarios. Furthermore, we showcase TAID's practical impact by developing two state-of-the-art compact foundation models: TAID-LLM-1.5B for language tasks and TAID-VLM-2B for vision-language tasks. These results demonstrate TAID's effectiveness in creating high-performing and efficient models, advancing the development of more accessible AI technologies.

Distilling knowledge from a large teacher model to a lightweight one is a widely successful approach for generating compact, powerful models in the semi-supervised learning setting where a limited amount of labeled data is available. In large-scale applications, however, the teacher tends to provide a large number of incorrect soft-labels that impairs student performance. The sheer size of the teacher additionally constrains the number of soft-labels that can be queried due to prohibitive computational and/or financial costs. The difficulty in achieving simultaneous efficiency (i.e., minimizing soft-label queries) and robustness (i.e., avoiding student inaccuracies due to incorrect labels) hurts the widespread application of knowledge distillation to many modern tasks. In this paper, we present a parameter-free approach with provable guarantees to query the soft-labels of points that are simultaneously informative and correctly labeled by the teacher. At the core of our work lies a game-theoretic formulation that explicitly considers the inherent trade-off between the informativeness and correctness of input instances. We establish bounds on the expected performance of our approach that hold even in worst-case distillation instances. We present empirical evaluations on popular benchmarks that demonstrate the improved distillation performance enabled by our work relative to that of state-of-the-art active learning and active distillation methods.

Real-time video generation via diffusion is essential for building general-purpose multimodal interactive AI systems. However, the simultaneous denoising of all video frames with bidirectional attention via an iterative process in diffusion models prevents real-time interaction. While existing distillation methods can make the model autoregressive and reduce sampling steps to mitigate this, they focus primarily on text-to-video generation, leaving the human-AI interaction unnatural and less efficient. This paper targets real-time interactive video diffusion conditioned on a multimodal context, including text, image, and audio, to bridge the gap. Given the observation that the leading on-policy distillation approach Self Forcing encounters challenges (visual artifacts like flickering, black frames, and quality degradation) with multimodal conditioning, we investigate an improved distillation recipe with emphasis on the quality of condition inputs as well as the initialization and schedule for the on-policy optimization. On benchmarks for multimodal-conditioned (audio, image, and text) avatar video generation including HDTF, AVSpeech, and CelebV-HQ, our distilled model matches the visual quality of the full-step, bidirectional baselines of similar or larger size with 20x less inference cost and latency. Further, we integrate our model with audio language models and long-form video inference technique Anchor-Heavy Identity Sinks to build LiveTalk, a real-time multimodal interactive avatar system. System-level evaluation on our curated multi-turn interaction benchmark shows LiveTalk outperforms state-of-the-art models (Sora2, Veo3) in multi-turn video coherence and content quality, while reducing response latency from 1 to 2 minutes to real-time generation, enabling seamless human-AI multimodal interaction.

Knowledge distillation (KD) is widely used for compressing a teacher model to a smaller student model, reducing its inference cost and memory footprint while preserving model capabilities. However, current KD methods for auto-regressive sequence models (e.g., large language models) suffer from missing a standardized objective function. Moreover, the recent use of student-generated outputs to address training-inference mismatches has significantly escalated computational costs. To tackle these issues, we introduce DistiLLM, a more effective and efficient KD framework for auto-regressive language models. DistiLLM comprises two components: (1) a novel skew Kullback-Leibler divergence loss, where we unveil and leverage its theoretical properties, and (2) an adaptive off-policy approach designed to enhance the efficiency in utilizing student-generated outputs. Extensive experiments, including instruction-following tasks, demonstrate the effectiveness of DistiLLM in building high-performing student models while achieving up to 4.3times speedup compared to recent KD methods.

Large language models (LLMs) demonstrate remarkable reasoning capabilities in tasks such as algorithmic coding and mathematical problem-solving. Recent methods have improved reasoning through expanded corpus and multistage training combining reinforcement learning and supervised fine-tuning. Although some methods suggest that small but targeted dataset can incentivize reasoning via only distillation, a reasoning scaling laws is still taking shape, increasing computational costs. To address this, we propose a data-efficient distillation framework (DED) that optimizes the Pareto frontier of reasoning distillation. Inspired by the on-policy learning and diverse roll-out strategies of reinforcement learning, the key idea of our approach is threefold: (1) We identify that benchmark scores alone do not determine an effective teacher model. Through comprehensive comparisons of leading reasoning LLMs, we develop a method to select an optimal teacher model. (2) While scaling distillation can enhance reasoning, it often degrades out-of-domain performance. A carefully curated, smaller corpus achieves a balanced trade-off between in-domain and out-of-domain capabilities. (3) Diverse reasoning trajectories encourage the student model to develop robust reasoning skills. We validate our method through evaluations on mathematical reasoning (AIME 2024/2025, MATH-500) and code generation (LiveCodeBench), achieving state-of-the-art results with only 0.8k carefully curated examples, bypassing the need for extensive scaling. Our systematic analysis demonstrates that DED outperforms existing methods by considering factors beyond superficial hardness, token length, or teacher model capability. This work offers a practical and efficient pathway to advanced reasoning while preserving general capabilities.

Standard Knowledge Distillation (KD) compresses Large Language Models (LLMs) by optimizing final outputs, yet it typically treats the teacher's intermediate layer's thought process as a black box. While feature-based distillation attempts to bridge this gap, existing methods (e.g., MSE and asymmetric KL divergence) ignore the rich uncertainty profiles required for the final output. In this paper, we introduce DistillLens, a framework that symmetrically aligns the evolving thought processes of student and teacher models. By projecting intermediate hidden states into the vocabulary space via the Logit Lens, we enforce structural alignment using a symmetric divergence objective. Our analysis proves that this constraint imposes a dual-sided penalty, preventing both overconfidence and underconfidence while preserving the high-entropy information conduits essential for final deduction. Extensive experiments on GPT-2 and Llama architectures demonstrate that DistillLens consistently outperforms standard KD and feature-transfer baselines on diverse instruction-following benchmarks. The code is available at https://github.com/manishdhakal/DistillLens.

Few-step diffusion or flow-based generative models typically distill a velocity-predicting teacher into a student that predicts a shortcut towards denoised data. This format mismatch has led to complex distillation procedures that often suffer from a quality-diversity trade-off. To address this, we propose policy-based flow models (pi-Flow). pi-Flow modifies the output layer of a student flow model to predict a network-free policy at one timestep. The policy then produces dynamic flow velocities at future substeps with negligible overhead, enabling fast and accurate ODE integration on these substeps without extra network evaluations. To match the policy's ODE trajectory to the teacher's, we introduce a novel imitation distillation approach, which matches the policy's velocity to the teacher's along the policy's trajectory using a standard ell_2 flow matching loss. By simply mimicking the teacher's behavior, pi-Flow enables stable and scalable training and avoids the quality-diversity trade-off. On ImageNet 256^2, it attains a 1-NFE FID of 2.85, outperforming MeanFlow of the same DiT architecture. On FLUX.1-12B and Qwen-Image-20B at 4 NFEs, pi-Flow achieves substantially better diversity than state-of-the-art few-step methods, while maintaining teacher-level quality.

On-policy knowledge distillation (OPD) trains a student on its own rollouts under token-level supervision from a teacher. Not all token positions matter equally, but existing views of token importance are incomplete. We ask a direct question: which tokens carry the most useful learning signal in OPD? Our answer is that informative tokens come from two regions: positions with high student entropy, and positions with low student entropy plus high teacher--student divergence, where the student is overconfident and wrong. Empirically, student entropy is a strong first-order proxy: retaining 50% of tokens with entropy-based sampling matches or exceeds all-token training while reducing peak memory by up to 47%. But entropy alone misses a second important region. When we isolate low-entropy, high-divergence tokens, training on fewer than 10% of all tokens nearly matches full-token baselines, showing that overconfident tokens carry dense corrective signal despite being nearly invisible to entropy-only rules. We organize these findings with TIP (Token Importance in on-Policy distillation), a two-axis taxonomy over student entropy and teacher--student divergence, and give a theoretical explanation for why entropy is useful yet structurally incomplete. This view motivates type-aware token selection rules that combine uncertainty and disagreement. We validate this picture across three teacher--student pairs spanning Qwen3, Llama, and Qwen2.5 on MATH-500 and AIME 2024/2025, and on the DeepPlanning benchmark for long-horizon agentic planning, where Q3-only training on <20% of tokens surpasses full-token OPD. Our experiments are implemented by extending the OPD repository https://github.com/HJSang/OPSD_OnPolicyDistillation, which supports memory-efficient distillation of larger models under limited GPU budgets.

Diffusion Policies have demonstrated impressive performance in robotic manipulation tasks. However, their long inference time, resulting from an extensive iterative denoising process, and the need to execute an action chunk before the next prediction to maintain consistent actions limit their applicability to latency-critical tasks or simple tasks with a short cycle time. While recent methods explored distillation or alternative policy structures to accelerate inference, these often demand additional training, which can be resource-intensive for large robotic models. In this paper, we introduce a novel approach inspired by the Real-Time Iteration (RTI) Scheme, a method from optimal control that accelerates optimization by leveraging solutions from previous time steps as initial guesses for subsequent iterations. We explore the application of this scheme in diffusion inference and propose a scaling-based method to effectively handle discrete actions, such as grasping, in robotic manipulation. The proposed scheme significantly reduces runtime computational costs without the need for distillation or policy redesign. This enables a seamless integration into many pre-trained diffusion-based models, in particular, to resource-demanding large models. We also provide theoretical conditions for the contractivity which could be useful for estimating the initial denoising step. Quantitative results from extensive simulation experiments show a substantial reduction in inference time, with comparable overall performance compared with Diffusion Policy using full-step denoising. Our project page with additional resources is available at: https://rti-dp.github.io/.

Reinforcement learning (RL) has emerged as a promising paradigm for inducing explicit reasoning behaviors in large language and vision-language models. However, reasoning-oriented RL post-training remains fundamentally challenging due to sparse trajectory-level rewards, leading to ambiguous credit assignment and severe exploration failures that can trap the policy in a ``learning cliff.'' Recent on-policy distillation methods introduce dense teacher supervision to stabilize optimization, but apply it uniformly across all generated trajectories. We argue that such uniform distillation is ill-suited for reasoning-intensive tasks, as low-quality on-policy trajectories often originate from early logical errors, and distillation under flawed contexts injects noisy and misaligned gradients. To address these challenges, we propose Knowledge-Enhanced Preference Optimization (KEPO), a unified post-training framework that integrates: (i) a quality-gated on-policy distillation objective that selectively applies dense teacher guidance only to high-quality trajectories, and (ii) a knowledge-enhanced exploration strategy that leverages hints learned from a teacher model to rejectively sample reward-positive on-policy trajectories for RL, thereby mitigating exploration collapse. Evaluated on a challenging medical visual question answering benchmark under single-source generalization, KEPO demonstrates improved training stability, more coherent reasoning behaviors, and superior out-of-distribution performance over reinforcement learning and on-policy distillation baselines.

Deploying large language models (LLMs) of several billion parameters can be impractical in most industrial use cases due to constraints such as cost, latency limitations, and hardware accessibility. Knowledge distillation (KD) offers a solution by compressing knowledge from resource-intensive large models to smaller ones. Various strategies exist, some relying on the text generated by the teacher model and optionally utilizing his logits to enhance learning. However, these methods based on logits often require both teacher and student models to share the same tokenizer, limiting their applicability across different LLM families. In this paper, we introduce Universal Logit Distillation (ULD) loss, grounded in optimal transport, to address this limitation. Our experimental results demonstrate the effectiveness of ULD loss in enabling distillation across models with different architectures and tokenizers, paving the way to a more widespread use of distillation techniques.

Knowledge distillation (KD) is a widely adopted technique for transferring knowledge from large language models to smaller student models; however, conventional supervised KD often suffers from a distribution mismatch between training and inference. While on-policy KD approaches attempt to mitigate this issue by learning directly from student-generated outputs, they frequently encounter training instabilities because the distributional gap between the novice student and the expert teacher is often too wide to bridge directly. These challenges manifest as pathological gradients in forward KL objectives or diversity collapse in reverse KL regimes. To address these limitations, we propose Veto, an objective-level reformulation that constructs a geometric bridge in the logit space. Unlike prior methods that mix data samples, Veto creates an intermediate target distribution that promotes alignment between the teacher and the student. By introducing a tunable parameter beta, Veto serves as an Adaptive Gradient Veto that stabilizes optimization by suppressing harmful gradients on low-confidence tokens, while simultaneously acting as a Decisiveness Knob to balance reward-driven performance with output diversity. Extensive experiments across various reasoning and generation tasks demonstrate that Veto consistently outperforms supervised fine-tuning and existing on-policy baselines.

Multimodal dataset distillation aims to construct compact synthetic datasets that enable efficient compression and knowledge transfer from large-scale image-text data. However, existing approaches often fail to capture the complex, dynamically evolving knowledge embedded in the later training stages of teacher models. This limitation leads to degraded student performance and compromises the quality of the distilled data. To address critical challenges such as pronounced cross-stage performance gaps and unstable teacher trajectories, we propose Phased Teacher Model with Shortcut Trajectory (PTM-ST) -- a novel phased distillation framework. PTM-ST leverages stage-aware teacher modeling and a shortcut-based trajectory construction strategy to accurately fit the teacher's learning dynamics across distinct training phases. This enhances both the stability and expressiveness of the distillation process. Through theoretical analysis and comprehensive experiments, we show that PTM-ST significantly mitigates optimization oscillations and inter-phase knowledge gaps, while also reducing storage overhead. Our method consistently surpasses state-of-the-art baselines on Flickr30k and COCO, achieving up to 13.5% absolute improvement and an average gain of 9.53% on Flickr30k. Code: https://github.com/Previsior/PTM-ST.

Knowledge distillation trains a smaller student model to match the output distribution of a larger teacher to maximize the end-task performance under computational constraints. However, existing literature on language model distillation primarily focuses on compressing encoder-only models that are then specialized by task-specific supervised finetuning. We need to rethink this setup for more recent large language models with tens to hundreds of billions of parameters. Task-specific finetuning is impractical at this scale, and model performance is often measured using zero/few-shot prompting. Thus, in this work, we advocate for task-agnostic zero-shot evaluated distillation for large language models without access to end-task finetuning data. We propose a teacher-free task-agnostic distillation method, which uses a truncated version of the larger model for initialization, and continues pretraining this model using a language modeling objective. Our teacher-free method shines in a distillation regime where it is infeasible to fit both the student and teacher into the GPU memory. Despite its simplicity, our method can effectively reduce the model size by 50\%, matching or outperforming the vanilla distillation method on perplexity and accuracy on 13 zero-shot end-tasks while being 1.5x computationally efficient.

Reinforcement learning with verifiable rewards has emerged as a promising paradigm for enhancing the reasoning capabilities of large language models particularly in mathematics. Current approaches in this domain present a clear trade-off: PPO-style methods (e.g., GRPO/DAPO) offer training stability but exhibit slow learning trajectories due to their trust-region constraints on policy updates, while REINFORCE-style approaches (e.g., CISPO) demonstrate improved learning efficiency but suffer from performance instability as they clip importance sampling weights while still permitting non-zero gradients outside the trust-region. To address these limitations, we introduce DISPO, a simple yet effective REINFORCE-style algorithm that decouples the up-clipping and down-clipping of importance sampling weights for correct and incorrect responses, yielding four controllable policy update regimes. Through targeted ablations, we uncover how each regime impacts training: for correct responses, weights >1 increase the average token entropy (i.e., exploration) while weights <1 decrease it (i.e., distillation) -- both beneficial but causing gradual performance degradation when excessive. For incorrect responses, overly restrictive clipping triggers sudden performance collapse through repetitive outputs (when weights >1) or vanishing response lengths (when weights <1). By separately tuning these four clipping parameters, DISPO maintains the exploration-distillation balance while preventing catastrophic failures, achieving 61.04% on AIME'24 (vs. 55.42% CISPO and 50.21% DAPO) with similar gains across various benchmarks and models.

Diffusion distillation models effectively accelerate reverse sampling by compressing the process into fewer steps. However, these models still exhibit a performance gap compared to their pre-trained diffusion model counterparts, exacerbated by distribution shifts and accumulated errors during multi-step sampling. To address this, we introduce Distillation++, a novel inference-time distillation framework that reduces this gap by incorporating teacher-guided refinement during sampling. Inspired by recent advances in conditional sampling, our approach recasts student model sampling as a proximal optimization problem with a score distillation sampling loss (SDS). To this end, we integrate distillation optimization during reverse sampling, which can be viewed as teacher guidance that drives student sampling trajectory towards the clean manifold using pre-trained diffusion models. Thus, Distillation++ improves the denoising process in real-time without additional source data or fine-tuning. Distillation++ demonstrates substantial improvements over state-of-the-art distillation baselines, particularly in early sampling stages, positioning itself as a robust guided sampling process crafted for diffusion distillation models. Code: https://github.com/geonyeong-park/inference_distillation.

We propose Algorithm Distillation (AD), a method for distilling reinforcement learning (RL) algorithms into neural networks by modeling their training histories with a causal sequence model. Algorithm Distillation treats learning to reinforcement learn as an across-episode sequential prediction problem. A dataset of learning histories is generated by a source RL algorithm, and then a causal transformer is trained by autoregressively predicting actions given their preceding learning histories as context. Unlike sequential policy prediction architectures that distill post-learning or expert sequences, AD is able to improve its policy entirely in-context without updating its network parameters. We demonstrate that AD can reinforcement learn in-context in a variety of environments with sparse rewards, combinatorial task structure, and pixel-based observations, and find that AD learns a more data-efficient RL algorithm than the one that generated the source data.

Training a large and state-of-the-art machine learning model typically necessitates the use of large-scale datasets, which, in turn, makes the training and parameter-tuning process expensive and time-consuming. Some researchers opt to distil information from real-world datasets into tiny and compact synthetic datasets while maintaining their ability to train a well-performing model, hence proposing a data-efficient method known as Dataset Distillation (DD). Despite recent progress in this field, existing methods still underperform and cannot effectively replace large datasets. In this paper, unlike previous methods that focus solely on improving the efficacy of student distillation, we are the first to recognize the important interplay between expert and student. We argue the significant impact of expert smoothness when employing more potent expert trajectories in subsequent dataset distillation. Based on this, we introduce the integration of clipping loss and gradient penalty to regulate the rate of parameter changes in expert trajectories. Furthermore, in response to the sensitivity exhibited towards randomly initialized variables during distillation, we propose representative initialization for synthetic dataset and balanced inner-loop loss. Finally, we present two enhancement strategies, namely intermediate matching loss and weight perturbation, to mitigate the potential occurrence of cumulative errors. We conduct extensive experiments on datasets of different scales, sizes, and resolutions. The results demonstrate that the proposed method significantly outperforms prior methods.

We introduce ORPO-Distill, a general-purpose method for cross-architecture LLM distillation that formulates the problem as a preference optimization task. Unlike standard CoT distillation, the approach transfers knowledge through diverse reasoning traces. It employs an Odds-Ratio Preference Optimization objective that contrasts teacher and student traces for more effective learning, and adopts a mixed-policy strategy for utilizing student-generated outputs, outperforming both off- and on-policy alternatives. Experiments on five datasets and multiple student models show consistent improvements over conventional black-box KD baselines.

Distribution Matching Distillation (DMD) distills a pre-trained multi-step diffusion model to a few-step one to improve inference efficiency. However, the performance of the latter is often capped by the former. To circumvent this dilemma, we propose DMDR, a novel framework that combines Reinforcement Learning (RL) techniques into the distillation process. We show that for the RL of the few-step generator, the DMD loss itself is a more effective regularization compared to the traditional ones. In turn, RL can help to guide the mode coverage process in DMD more effectively. These allow us to unlock the capacity of the few-step generator by conducting distillation and RL simultaneously. Meanwhile, we design the dynamic distribution guidance and dynamic renoise sampling training strategies to improve the initial distillation process. The experiments demonstrate that DMDR can achieve leading visual quality, prompt coherence among few-step methods, and even exhibit performance that exceeds the multi-step teacher.

The growing size of neural language models has led to increased attention in model compression. The two predominant approaches are pruning, which gradually removes weights from a pre-trained model, and distillation, which trains a smaller compact model to match a larger one. Pruning methods can significantly reduce the model size but hardly achieve large speedups as distillation. However, distillation methods require large amounts of unlabeled data and are expensive to train. In this work, we propose a task-specific structured pruning method CoFi (Coarse- and Fine-grained Pruning), which delivers highly parallelizable subnetworks and matches the distillation methods in both accuracy and latency, without resorting to any unlabeled data. Our key insight is to jointly prune coarse-grained (e.g., layers) and fine-grained (e.g., heads and hidden units) modules, which controls the pruning decision of each parameter with masks of different granularity. We also devise a layerwise distillation strategy to transfer knowledge from unpruned to pruned models during optimization. Our experiments on GLUE and SQuAD datasets show that CoFi yields models with over 10x speedups with a small accuracy drop, showing its effectiveness and efficiency compared to previous pruning and distillation approaches.

Reasoning models think out loud, but much of what they say is noise. We introduce OPSDC (On-Policy Self-Distillation for Reasoning Compression), a method that teaches models to reason more concisely by distilling their own concise behavior back into themselves. The entire approach reduces to one idea: condition the same model on a "be concise" instruction to obtain teacher logits, and minimize per-token reverse KL on the student's own rollouts. No ground-truth answers, no token budgets, no difficulty estimators. Just self-distillation. Yet this simplicity belies surprising sophistication: OPSDC automatically compresses easy problems aggressively while preserving the deliberation needed for hard ones. On Qwen3-8B and Qwen3-14B, we achieve 57-59% token reduction on MATH-500 while improving accuracy by 9-16 points absolute. On AIME 2024, the 14B model gains 10 points with 41% compression. The secret? Much of what reasoning models produce is not just redundant-it is actively harmful, compounding errors with every unnecessary token.

Direct Preference Optimization (DPO) has emerged as a simple alternative to reinforcement learning from human feedback (RLHF) for aligning language models, but its reliance on hard pairwise labels makes it brittle under noise; our experiments show performance degrading by up to 93 percent in noisy settings. We introduce Anchored Direct Preference Optimization (ADPO), a unified framework that addresses this fragility through reference anchoring. By minimizing KL(q || softmax((l - l_ref) / tau_anc)), where l_ref are reference policy log probabilities, ADPO provides three key advantages: (1) it unifies major learning paradigms, including supervised fine-tuning, knowledge distillation, maximum-entropy reinforcement learning, and DPO, as special cases through different choices of target distribution q, anchor policy pi_ref, and temperature tau_anc; (2) it induces an implicit trust region governed by the softmax Fisher metric with curvature scaling as 1 / tau_anc^2, providing geometric regularization absent in standard methods; and (3) it enables flexible anchor strategies tailored to different learning contexts. Empirically, ADPO consistently outperforms standard DPO by 12 to 93 percent across twelve noisy scenarios, with listwise variants achieving top performance in eleven of twelve cases. In offline distillation, ADPO reduces student-teacher KL by 4 to 49 times while achieving superior returns (for example, 279.3 vs -309.0 for knowledge distillation on HalfCheetah). We further uncover a task-dependent tradeoff: dynamic anchors excel at online exploration in noisy environments (plus 5 to 11 percent), while fixed anchors enable stable offline distillation. Our work establishes anchoring as a general principle for robust policy optimization, with clear practical guidance for anchor selection across diverse learning scenarios.

Continual learning, enabling models to acquire new skills and knowledge without degrading existing capabilities, remains a fundamental challenge for foundation models. While on-policy reinforcement learning can reduce forgetting, it requires explicit reward functions that are often unavailable. Learning from expert demonstrations, the primary alternative, is dominated by supervised fine-tuning (SFT), which is inherently off-policy. We introduce Self-Distillation Fine-Tuning (SDFT), a simple method that enables on-policy learning directly from demonstrations. SDFT leverages in-context learning by using a demonstration-conditioned model as its own teacher, generating on-policy training signals that preserve prior capabilities while acquiring new skills. Across skill learning and knowledge acquisition tasks, SDFT consistently outperforms SFT, achieving higher new-task accuracy while substantially reducing catastrophic forgetting. In sequential learning experiments, SDFT enables a single model to accumulate multiple skills over time without performance regression, establishing on-policy distillation as a practical path to continual learning from demonstrations.

Recently, a series of diffusion-aware distillation algorithms have emerged to alleviate the computational overhead associated with the multi-step inference process of Diffusion Models (DMs). Current distillation techniques often dichotomize into two distinct aspects: i) ODE Trajectory Preservation; and ii) ODE Trajectory Reformulation. However, these approaches suffer from severe performance degradation or domain shifts. To address these limitations, we propose Hyper-SD, a novel framework that synergistically amalgamates the advantages of ODE Trajectory Preservation and Reformulation, while maintaining near-lossless performance during step compression. Firstly, we introduce Trajectory Segmented Consistency Distillation to progressively perform consistent distillation within pre-defined time-step segments, which facilitates the preservation of the original ODE trajectory from a higher-order perspective. Secondly, we incorporate human feedback learning to boost the performance of the model in a low-step regime and mitigate the performance loss incurred by the distillation process. Thirdly, we integrate score distillation to further improve the low-step generation capability of the model and offer the first attempt to leverage a unified LoRA to support the inference process at all steps. Extensive experiments and user studies demonstrate that Hyper-SD achieves SOTA performance from 1 to 8 inference steps for both SDXL and SD1.5. For example, Hyper-SDXL surpasses SDXL-Lightning by +0.68 in CLIP Score and +0.51 in Aes Score in the 1-step inference.

Recent large reasoning models such as DeepSeek-R1 exhibit strong complex problems solving abilities by generating long chain-of-thought (CoT) reasoning steps. It is challenging to directly train small language models (SLMs) to emerge long CoT. Thus, distillation becomes a practical method to enable SLMs for such reasoning ability. However, the long CoT often contains a lot of redundant contents (e.g., overthinking steps) which may make SLMs hard to learn considering their relatively poor capacity and generalization. To address this issue, we propose a simple-yet-effective method to prune unnecessary steps in long CoT, and then employ an on-policy method for the SLM itself to curate valid and useful long CoT training data. In this way, SLMs can effectively learn efficient long CoT reasoning and preserve competitive performance at the same time. Experimental results across a series of mathematical reasoning benchmarks demonstrate the effectiveness of the proposed method in distilling long CoT reasoning ability into SLMs which maintains the competitive performance but significantly reduces generating redundant reasoning steps.

Recent advances in knowledge distillation (KD) have enabled smaller student models to approach the performance of larger teacher models. However, popular methods such as supervised KD and on-policy KD, are adversely impacted by the knowledge gaps between teacher-student in practical scenarios. Supervised KD suffers from a distribution mismatch between training with a static dataset and inference over final student-generated outputs. Conversely, on-policy KD, which uses student-generated samples for training, can suffer from low-quality training examples with which teacher models are not familiar, resulting in inaccurate teacher feedback. To address these limitations, we introduce Speculative Knowledge Distillation (SKD), a novel approach that leverages cooperation between student and teacher models to generate high-quality training data on-the-fly while aligning with the student's inference-time distribution. In SKD, the student proposes tokens, and the teacher replaces poorly ranked ones based on its own distribution, transferring high-quality knowledge adaptively. We evaluate SKD on various text generation tasks, including translation, summarization, math, and instruction following, and show that SKD consistently outperforms existing KD methods across different domains, data sizes, and model initialization strategies.

Recent advances in Large Language Models (LLMs) show that extending the length of reasoning chains significantly improves performance on complex tasks. While revealing these reasoning traces helps users better follow, verify, and learn from the model's problem-solving process, it also makes them highly vulnerable to unauthorized distillation. To mitigate this risk, proprietary model providers often adopt aggressive protection strategies, such as replacing detailed reasoning with brief summaries, which deprive users of valuable intermediate information. To address this trade-off, we propose PART, an information-preserving antidistillation reformulation of reasoning traces. Motivated by the difference between how humans understand reasoning traces and how LLMs exploit them for supervised fine-tuning, we design a simple but effective two-step reformulation: removing self-talk behaviors and reordering sub-conclusions. A small auxiliary model is trained to perform this reformulation, incurring minimal computational overhead. Extensive experiments demonstrate that PART consistently disrupts distillation across student models of different sizes and types on various reasoning benchmarks. For instance, when training on reformulated traces, even the performance of a large 32B student model decreases from 54.17 to 46.88 on AIME 2024, corresponding to a 13.5% degradation.

Knowledge distillation has emerged as an effective strategy for compressing large language models' (LLMs) knowledge into smaller, more efficient student models. However, standard one-shot distillation methods often produce suboptimal results due to a mismatch between teacher-generated rationales and the student's specific learning requirements. In this paper, we introduce the UNDO: UNderstanding Distillation as Optimization framework, designed to bridge this gap by iteratively identifying the student's errors and prompting the teacher to refine its explanations accordingly. Each iteration directly targets the student's learning deficiencies, motivating the teacher to provide tailored and enhanced rationales that specifically address these weaknesses. Empirical evaluations on various challenging mathematical and commonsense reasoning tasks demonstrate that our iterative distillation method, UNDO, significantly outperforms standard one-step distillation methods, achieving performance gains of up to 20%. Additionally, we show that teacher-generated data refined through our iterative process remains effective even when applied to different student models, underscoring the broad applicability of our approach. Our work fundamentally reframes knowledge distillation as an iterative teacher-student interaction, effectively leveraging dynamic refinement by the teacher for better knowledge distillation.

Recent work on distilling Whisper's knowledge into small models using pseudo-labels shows promising performance while reducing the size by up to 50\%. This results in small, efficient, and dedicated models. However, a critical step of distillation from pseudo-labels involves filtering high-quality predictions and using only those during training. This step requires ground truth labels to compare and filter low-quality examples making the whole process supervised. In addition to that, the distillation process requires a large amount of data thereby limiting the ability to distill models in low-resource settings. To address this challenge, we propose a distillation framework that does not require any labeled data. Through experimentation, we show that our best distilled models outperform the teacher model by 5-7 points in terms of WER compared to those without filtering and are on par with or perform better than similar supervised data filtering setups. When we scale the data, our models significantly outperform all zero-shot and supervised models. We demonstrate that it is possible to distill large Whisper models into relatively small ones without using any labeled data. Our distilled models are also 25-50\% more compute- and memory-efficient while maintaining performance equal to or better than that of the teacher model.

Diffusion models have seen rapid adoption in robotic imitation learning, enabling autonomous execution of complex dexterous tasks. However, action synthesis is often slow, requiring many steps of iterative denoising, limiting the extent to which models can be used in tasks that require fast reactive policies. To sidestep this, recent works have explored how the distillation of the diffusion process can be used to accelerate policy synthesis. However, distillation is computationally expensive and can hurt both the accuracy and diversity of synthesized actions. We propose SDP (Streaming Diffusion Policy), an alternative method to accelerate policy synthesis, leveraging the insight that generating a partially denoised action trajectory is substantially faster than a full output action trajectory. At each observation, our approach outputs a partially denoised action trajectory with variable levels of noise corruption, where the immediate action to execute is noise-free, with subsequent actions having increasing levels of noise and uncertainty. The partially denoised action trajectory for a new observation can then be quickly generated by applying a few steps of denoising to the previously predicted noisy action trajectory (rolled over by one timestep). We illustrate the efficacy of this approach, dramatically speeding up policy synthesis while preserving performance across both simulated and real-world settings.

Due to constraints on privacy, cost, and latency, on-premise deployment of small models is increasingly common. However, most practical pipelines stop at supervised fine-tuning (SFT) and fail to reach the reinforcement learning (RL) alignment stage. The main reason is that RL alignment typically requires either expensive human preference annotation or heavy reliance on high-quality reward models with large-scale API usage and ongoing engineering maintenance, both of which are ill-suited to on-premise settings. To bridge this gap, we propose a positive-unlabeled (PU) RL distillation method for on-premise small-model deployment. Without human-labeled preferences or a reward model, our method distills the teacher's preference-optimization capability from black-box generations into a locally trainable student. For each prompt, we query the teacher once to obtain an anchor response, locally sample multiple student candidates, and perform anchor-conditioned self-ranking to induce pairwise or listwise preferences, enabling a fully local training loop via direct preference optimization or group relative policy optimization. Theoretical analysis justifies that the induced preference signal by our method is order-consistent and concentrates on near-optimal candidates, supporting its stability for preference optimization. Experiments demonstrate that our method achieves consistently strong performance under a low-cost setting.

Vision-Language-Action Models (VLAs) have demonstrated remarkable generalization capabilities in real-world experiments. However, their success rates are often not on par with expert policies, and they require fine-tuning when the setup changes. In this work, we introduce Refined Policy Distillation (RPD), a novel Reinforcement Learning (RL)-based policy refinement method that bridges this performance gap through a combination of on-policy RL with behavioral cloning. The core idea of RPD is to distill and refine VLAs into compact, high-performing expert policies by guiding the student policy during RL exploration using the actions of a teacher VLA, resulting in increased sample efficiency and faster convergence. We complement our method by fine-tuned versions of Octo and OpenVLA for ManiSkill3 to evaluate RPD in simulation. While this is a key requirement for applying RL, it also yields new insights beyond existing studies on VLA performance in real-world settings. Our experimental results across various manipulation tasks show that RPD enables the RL student to learn expert policies that outperform the VLA teacher in both dense and sparse reward settings, while also achieving faster convergence than the RL baseline. Our approach is even robust to changes in camera perspective and can generalize to task variations that the underlying VLA cannot solve. Our code, dataset, VLA checkpoints, and videos are available at https://refined-policy-distillation.github.io

Reinforcement learning with verifiable rewards (RLVR) has become a standard paradigm for post-training large language models. While Group Relative Policy Optimization (GRPO) is widely adopted, its coarse credit assignment uniformly penalizes failed rollouts, lacking the token-level focus needed to efficiently address specific deviations. Self-Distillation Policy Optimization (SDPO) addresses this by providing denser, more targeted logit-level supervision that facilitates rapid early improvement, yet it frequently collapses during prolonged training. We trace this late-stage instability to two intrinsic flaws: self-distillation on already-correct samples introduces optimization ambiguity, and the self-teacher's signal reliability progressively degrades. To resolve these issues, we propose Sample-Routed Policy Optimization (SRPO), a unified on-policy framework that routes correct samples to GRPO's reward-aligned reinforcement and failed samples to SDPO's targeted logit-level correction. SRPO further incorporates an entropy-aware dynamic weighting mechanism to suppress high-entropy, unreliable distillation targets while emphasizing confident ones. Evaluated across five benchmarks and two model scales, SRPO achieves both the rapid early improvement of SDPO and the long-horizon stability of GRPO. It consistently surpasses the peak performance of both baselines, raising the five-benchmark average on Qwen3-8B by 3.4% over GRPO and 6.3% over SDPO, while simultaneously yielding moderate response lengths and lowering per-step compute cost by up to 17.2%.

Black-box distillation creates student large language models (LLMs) by learning from a proprietary teacher model's text outputs alone, without access to its internal logits or parameters. In this work, we introduce Generative Adversarial Distillation (GAD), which enables on-policy and black-box distillation. GAD frames the student LLM as a generator and trains a discriminator to distinguish its responses from the teacher LLM's, creating a minimax game. The discriminator acts as an on-policy reward model that co-evolves with the student, providing stable, adaptive feedback. Experimental results show that GAD consistently surpasses the commonly used sequence-level knowledge distillation. In particular, Qwen2.5-14B-Instruct (student) trained with GAD becomes comparable to its teacher, GPT-5-Chat, on the LMSYS-Chat automatic evaluation. The results establish GAD as a promising and effective paradigm for black-box LLM distillation.

Knowledge distillation establishes a learning paradigm that leverages both data supervision and teacher guidance. However, determining the optimal balance between learning from data and learning from the teacher is challenging, as some samples may be noisy while others are subject to teacher uncertainty. This motivates the need for adaptively balancing data and teacher supervision. We propose Beta-weighted Knowledge Distillation (Beta-KD), an uncertainty-aware distillation framework that adaptively modulates how much the student relies on teacher guidance. Specifically, we formulate teacher--student learning from a unified Bayesian perspective and interpret teacher supervision as a Gibbs prior over student activations. This yields a closed-form, uncertainty-aware weighting mechanism and supports arbitrary distillation objectives and their combinations. Extensive experiments on multimodal VQA benchmarks demonstrate that distilling student Vision-Language Models from a large teacher VLM consistently improves performance. The results show that Beta-KD outperforms existing knowledge distillation methods. The code is available at https://github.com/Jingchensun/beta-kd.

Knowledge distillation (KD) has been shown to be highly effective in guiding a student model with a larger teacher model and achieving practical benefits in improving the computational and memory efficiency for large language models (LLMs). State-of-the-art KD methods for LLMs mostly rely on minimizing explicit distribution distance between teacher and student probability predictions. Instead of optimizing these mandatory behaviour cloning objectives, we explore an imitation learning strategy for KD of LLMs. In particular, we minimize the imitation gap by matching the action-value moments of the teacher's behavior from both on- and off-policy perspectives. To achieve this action-value moment-matching goal, we propose an adversarial training algorithm to jointly estimate the moment-matching distance and optimize the student policy to minimize it. Results from both task-agnostic instruction-following experiments and task-specific experiments demonstrate the effectiveness of our method and achieve new state-of-the-art performance.

We present Ring-lite, a Mixture-of-Experts (MoE)-based large language model optimized via reinforcement learning (RL) to achieve efficient and robust reasoning capabilities. Built upon the publicly available Ling-lite model, a 16.8 billion parameter model with 2.75 billion activated parameters, our approach matches the performance of state-of-the-art (SOTA) small-scale reasoning models on challenging benchmarks (e.g., AIME, LiveCodeBench, GPQA-Diamond) while activating only one-third of the parameters required by comparable models. To accomplish this, we introduce a joint training pipeline integrating distillation with RL, revealing undocumented challenges in MoE RL training. First, we identify optimization instability during RL training, and we propose Constrained Contextual Computation Policy Optimization(C3PO), a novel approach that enhances training stability and improves computational throughput via algorithm-system co-design methodology. Second, we empirically demonstrate that selecting distillation checkpoints based on entropy loss for RL training, rather than validation metrics, yields superior performance-efficiency trade-offs in subsequent RL training. Finally, we develop a two-stage training paradigm to harmonize multi-domain data integration, addressing domain conflicts that arise in training with mixed dataset. We will release the model, dataset, and code.

Masked diffusion language models (MDLMs) offer the potential for parallel token generation, but most open-source MDLMs decode fewer than 5 tokens per model forward pass even with sophisticated sampling strategies. As a result, their sampling speeds are often comparable to AR + speculative decoding schemes, limiting their advantage over mainstream autoregressive approaches. Existing distillation-based accelerators (dParallel, d3LLM) finetune MDLMs on trajectories generated by a base model, which can become off-policy during finetuning and restrict performance to the quality of the base model's samples. We propose dUltra, an on-policy reinforcement learning framework based on Group Relative Policy Optimization (GRPO) that learns unmasking strategies for efficient parallel decoding. dUltra introduces an unmasking planner head that predicts per-token unmasking likelihoods under independent Bernoulli distributions. We jointly optimize the base diffusion LLM and the unmasking order planner using reward signals combining verifiable reward, distillation reward, and the number of unmasking steps. Across mathematical reasoning and code generation tasks, dUltra improves the accuracy--efficiency trade-off over state-of-the-art heuristic and distillation baselines, moving towards achieving ``diffusion supremacy'' over autoregressive models.

There have been numerous attempts to distill quadratic attention-based large language models (LLMs) into sub-quadratic linearized architectures. However, despite extensive research, such distilled models often fail to match the performance of their teacher LLMs on various downstream tasks. We set out the goal of lossless distillation, which we define in terms of tolerance-corrected Win-and-Tie rates between student and teacher on sets of tasks. To this end, we introduce an effective distillation pipeline for xLSTM-based students. We propose an additional merging stage, where individually linearized experts are combined into a single model. We show the effectiveness of this pipeline by distilling base and instruction-tuned models from the Llama, Qwen, and Olmo families. In many settings, our xLSTM-based students recover most of the teacher's performance, and even exceed it on some downstream tasks. Our contributions are an important step towards more energy-efficient and cost-effective replacements for transformer-based LLMs.

Diffusion Models have emerged as a leading class of generative models, yet their iterative sampling process remains computationally expensive. Timestep distillation is a promising technique to accelerate generation, but it often requires extensive training and leads to image quality degradation. Furthermore, fine-tuning these distilled models for specific objectives, such as aesthetic appeal or user preference, using Reinforcement Learning (RL) is notoriously unstable and easily falls into reward hacking. In this work, we introduce Flash-DMD, a novel framework that enables fast convergence with distillation and joint RL-based refinement. Specifically, we first propose an efficient timestep-aware distillation strategy that significantly reduces training cost with enhanced realism, outperforming DMD2 with only 2.1% its training cost. Second, we introduce a joint training scheme where the model is fine-tuned with an RL objective while the timestep distillation training continues simultaneously. We demonstrate that the stable, well-defined loss from the ongoing distillation acts as a powerful regularizer, effectively stabilizing the RL training process and preventing policy collapse. Extensive experiments on score-based and flow matching models show that our proposed Flash-DMD not only converges significantly faster but also achieves state-of-the-art generation quality in the few-step sampling regime, outperforming existing methods in visual quality, human preference, and text-image alignment metrics. Our work presents an effective paradigm for training efficient, high-fidelity, and stable generative models. Codes are coming soon.

Knowledge Distillation (KD) in general and feature distillation in particular are promising techniques for reducing the high computational demand of large language models (LLMs). However, traditional feature KD methods typically assume that the teacher and the student share the same hidden size, limiting the flexibility of the student's architecture. A common solution to this problem involves training a linear projector to align their feature spaces, but this introduces additional parameters that must be learned from scratch and often degrades performance on downstream tasks, especially in generative settings. To address this issue, in this work, we propose a novel task-based feature distillation method that enables knowledge transfer between teacher and student models with different hidden layer dimensions, without introducing any new parameters. Leveraging the insight that only a subset of LLM components contribute significantly to a specific downstream task, our approach identifies the most task-relevant hidden units in the teacher and directly distills their activations to the student. Our method is flexible and easily integrates with other distillation frameworks. Empirical results show consistent improvements over prior approaches across diverse tasks, including classification, instruction-following, and summarization, achieving up to a 3\% performance gain over the linear projection baseline.

Proactive agents must decide not only what to say but also whether and when to intervene. Many current systems rely on brittle heuristics or indiscriminate long reasoning, which offers little control over the benefit-burden tradeoff. We formulate the problem as cost-sensitive selective intervention and present PRISM, a novel framework that couples a decision-theoretic gate with a dual-process reasoning architecture. At inference time, the agent intervenes only when a calibrated probability of user acceptance exceeds a threshold derived from asymmetric costs of missed help and false alarms. Inspired by festina lente (Latin: "make haste slowly"), we gate by an acceptance-calibrated, cost-derived threshold and invoke a resource-intensive Slow mode with counterfactual checks only near the decision boundary, concentrating computation on ambiguous and high-stakes cases. Training uses gate-aligned, schema-locked distillation: a teacher running the full PRISM pipeline provides dense, executable supervision on unlabeled interaction traces, while the student learns a response policy that is explicitly decoupled from the intervention gate to enable tunable and auditable control. On ProactiveBench, PRISM reduces false alarms by 22.78% and improves F1 by 20.14% over strong baselines. These results show that principled decision-theoretic gating, paired with selective slow reasoning and aligned distillation, yields proactive agents that are precise, computationally efficient, and controllable. To facilitate reproducibility, we release our code, models, and resources at https://prism-festinalente.github.io/; all experiments use the open-source ProactiveBench benchmark.

Diffusion models produce high-quality text-to-image results, but their iterative denoising is computationally expensive.Distribution Matching Distillation (DMD) emerges as a promising path to few-step distillation, but suffers from diversity collapse and fidelity degradation when reduced to two steps or fewer. We present 1.x-Distill, the first fractional-step distillation framework that breaks the integer-step constraint of prior few-step methods and establishes 1.x-step generation as a practical regime for distilled diffusion models.Specifically, we first analyze the overlooked role of teacher CFG in DMD and introduce a simple yet effective modification to suppress mode collapse. Then, to improve performance under extreme steps, we introduce Stagewise Focused Distillation, a two-stage strategy that learns coarse structure through diversity-preserving distribution matching and refines details with inference-consistent adversarial distillation. Furthermore, we design a lightweight compensation module for Distill--Cache co-Training, which naturally incorporates block-level caching into our distillation pipeline.Experiments on SD3-Medium and SD3.5-Large show that 1.x-Distill surpasses prior few-step methods, achieving better quality and diversity at 1.67 and 1.74 effective NFEs, respectively, with up to 33x speedup over original 28x2 NFE sampling.

Recent years have witnessed remarkable progress in world models, which primarily aim to capture the spatio-temporal correlations between an agent's actions and the evolving environment. However, existing approaches often suffer from tight runtime coupling or depend on offline reward signals, resulting in substantial inference overhead or hindering end-to-end optimization. To overcome these limitations, we introduce WPT, a World-to-Policy Transfer training paradigm that enables online distillation under the guidance of an end-to-end world model. Specifically, we develop a trainable reward model that infuses world knowledge into a teacher policy by aligning candidate trajectories with the future dynamics predicted by the world model. Subsequently, we propose policy distillation and world reward distillation to transfer the teacher's reasoning ability into a lightweight student policy, enhancing planning performance while preserving real-time deployability. Extensive experiments on both open-loop and closed-loop benchmarks show that our WPT achieves state-of-the-art performance with a simple policy architecture: it attains a 0.11 collision rate (open-loop) and achieves a 79.23 driving score (closed-loop) surpassing both world-model-based and imitation-learning methods in accuracy and safety. Moreover, the student sustains up to 4.9x faster inference, while retaining most of the gains.

Recent work in probability-domain knowledge distillation has established axiomatic frameworks for temperature scaling, multi-teacher aggregation, and bias-variance trade-offs in single-stage settings. However, the mathematical behavior of recursive or multi-generation distillation remains poorly understood, with prior approaches relying primarily on empirical heuristics. In this work, we introduce an axiomatic and operator-theoretic framework for recursive meta-distillation, formalizing iterative knowledge distillation as a sequence of probability-distribution operators with explicit anchoring to base teachers. We define structural axioms for valid meta-teacher construction and prove the existence of non-trivial operator families satisfying these axioms without specifying particular algorithms or loss functions. Under mild realizability and convexity assumptions, we show that anchored recursive distillation induces contraction in KL divergence, yielding geometric convergence to base teacher distributions and a unique, globally attractive fixed point. The contribution is foundational rather than algorithmic: the framework characterizes when recursive distillation is mathematically well-posed and convergent rather than error-accumulating, independent of model architecture, optimization details, or specific operator instantiations. These results provide a theoretical basis for understanding stability, bias-variance behavior, and failure modes in iterative and multi-teacher distillation under capacity constraints.

Large language models (LLMs) are increasingly adapted to proprietary and domain-specific corpora that contain sensitive information, creating a tension between formal privacy guarantees and efficient deployment through model compression. Differential privacy (DP), typically enforced via DP-SGD, provides record-level protection but often incurs substantial utility loss in autoregressive generation, where optimization noise can amplify exposure bias and compounding errors along long rollouts. Existing approaches to private distillation either apply DP-SGD to both teacher and student, worsening computation and the privacy--utility tradeoff, or rely on DP synthetic text generation from a DP-trained teacher, avoiding DP on the student at the cost of DP-optimizing a large teacher and introducing an offline generation pipeline. We propose Differentially Private On-Policy Distillation (DP-OPD), a synthesis-free framework that enforces privacy solely through DP-SGD on the student while leveraging a frozen teacher to provide dense token-level targets on student-generated trajectories. DP-OPD instantiates this idea via private generalized knowledge distillation on continuation tokens. Under a strict privacy budget (varepsilon=2.0), DP-OPD improves perplexity over DP fine-tuning and off-policy DP distillation, and outperforms synthesis-based DP distillation (Yelp: 44.15rightarrow41.68; BigPatent: 32.43rightarrow30.63), while substantially simplifying the training pipeline. In particular, DP-OPD collapses private compression into a single DP student-training loop by eliminating DP teacher training and offline synthetic text generation. Code will be released upon publication at https://github.com/khademfatemeh/dp_opd.

Knowledge distillation is an effective method for training small and efficient deep learning models. However, the efficacy of a single method can degenerate when transferring to other tasks, modalities, or even other architectures. To address this limitation, we propose a novel constrained feature distillation method. This method is derived from a small set of core principles, which results in two emerging components: an orthogonal projection and a task-specific normalisation. Equipped with both of these components, our transformer models can outperform all previous methods on ImageNet and reach up to a 4.4% relative improvement over the previous state-of-the-art methods. To further demonstrate the generality of our method, we apply it to object detection and image generation, whereby we obtain consistent and substantial performance improvements over state-of-the-art. Code and models are publicly available: https://github.com/roymiles/vkd

While the shift from cascaded dialogue systems to end-to-end (E2E) speech Large Language Models (LLMs) improves latency and paralinguistic modeling, E2E models often exhibit a significant performance degradation compared to their text-based counterparts. The standard Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL) training methods fail to close this gap. To address this, we propose X-OPD, a novel Cross-Modal On-Policy Distillation framework designed to systematically align the capabilities of Speech LLMs to their text-based counterparts. X-OPD enables the Speech LLM to explore its own distribution via on-policy rollouts, where a text-based teacher model evaluates these trajectories and provides token-level feedback, effectively distilling teacher's capabilities into student's multi-modal representations. Extensive experiments across multiple benchmarks demonstrate that X-OPD significantly narrows the gap in complex tasks while preserving the model's inherent capabilities.

Current post-training methods in verifiable settings fall into two categories. Reinforcement learning (RLVR) relies on binary rewards, which are broadly applicable and powerful, but provide only sparse supervision during training. Distillation provides dense token-level supervision, typically obtained from an external teacher or using high-quality demonstrations. Collecting such supervision can be costly or unavailable. We propose Self-Distillation Zero (SD-Zero), a method that is substantially more training sample-efficient than RL and does not require an external teacher or high-quality demonstrations. SD-Zero trains a single model to play two roles: a Generator, which produces an initial response, and a Reviser, which conditions on that response and its binary reward to produce an improved response. We then perform on-policy self-distillation to distill the reviser into the generator, using the reviser's token distributions conditioned on the generator's response and its reward as supervision. In effect, SD-Zero trains the model to transform binary rewards into dense token-level self-supervision. On math and code reasoning benchmarks with Qwen3-4B-Instruct and Olmo-3-7B-Instruct, SD-Zero improves performance by at least 10% over the base models and outperforms strong baselines, including Rejection Fine-Tuning (RFT), GRPO, and Self-Distillation Fine-Tuning (SDFT), under the same question set and training sample budget. Extensive ablation studies show two novel characteristics of our proposed algorithm: (a) token-level self-localization, where the reviser can identify the key tokens that need to be revised in the generator's response based on reward, and (b) iterative self-evolution, where the improving ability to revise answers can be distilled back into generation performance with regular teacher synchronization.

Reinforcement learning (RL) approaches for Large Language Models (LLMs) frequently use on-policy algorithms, such as PPO or GRPO. However, policy lag from distributed training architectures and differences between the training and inference policies break this assumption, making the data off-policy by design. To rectify this, prior work has focused on making this off-policy data appear more on-policy, either via importance sampling (IS), or by more closely aligning the training and inference policies by explicitly modifying the inference engine. In this work, we embrace off-policyness and propose a novel off-policy RL algorithm that does not require these modifications: Optimal Advantage-based Policy Optimization with Lagged Inference policy (OAPL). We show that OAPL outperforms GRPO with importance sampling on competition math benchmarks, and can match the performance of a publicly available coding model, DeepCoder, on LiveCodeBench, while using 3x fewer generations during training. We further empirically demonstrate that models trained via OAPL have improved test time scaling under the Pass@k metric. OAPL allows for efficient, effective post-training even with lags of more than 400 gradient steps between the training and inference policies, 100x more off-policy than prior approaches.

We develop a unified theoretical framework for sparse knowledge distillation based on probability-domain softening operators. While the equivalence p^{1/T} propto softmax(z/T) is well known, our contribution is an operator-level analytical framework built on this foundation rather than the equivalence itself. The framework comprises four core components: (i) operator-agnostic bias--variance decompositions that characterize when sparse students outperform dense teachers, (ii) a homotopy path formalization of multi-stage pruning in function space explaining why iterative compression succeeds where one-shot pruning fails, (iii) convergence guarantees establishing O(1/n) rates for n-stage distillation with explicit parameter dependence, and (iv) equivalence class characterizations identifying distinct probability-domain operators that yield identical student models under capacity constraints. We introduce an axiomatic definition of probability-domain softening operators based on ranking preservation, continuity, entropy monotonicity, identity, and boundary behavior, and show that multiple non-equivalent operator families satisfy these axioms. All learning-theoretic guarantees are shown to hold uniformly across this operator class, independent of implementation details. These results provide theoretical grounding for black-box teacher distillation, partial-access settings such as top-k truncation and text-only outputs, and privacy-preserving model compression.

Knowledge distillation is a model compression technique in which a compact "student" network is trained to replicate the predictive behavior of a larger "teacher" network. In logit-based knowledge distillation, it has become the de facto approach to augment cross-entropy with a distillation term. Typically, this term is either a KL divergence that matches marginal probabilities or a correlation-based loss that captures intra- and inter-class relationships. In every case, it acts as an additional term to cross-entropy. This term has its own weight, which must be carefully tuned. In this paper, we adopt a choice-theoretic perspective and recast knowledge distillation under the Plackett-Luce model by interpreting teacher logits as "worth" scores. We introduce "Plackett-Luce Distillation (PLD)", a weighted list-wise ranking loss. In PLD, the teacher model transfers knowledge of its full ranking of classes, weighting each ranked choice by its own confidence. PLD directly optimizes a single "teacher-optimal" ranking. The true label is placed first, followed by the remaining classes in descending teacher confidence. This process yields a convex and translation-invariant surrogate that subsumes weighted cross-entropy. Empirically, across CIFAR-100, ImageNet-1K, and MS-COCO, PLD achieves consistent gains across diverse architectures and distillation objectives, including divergence-based, correlation-based, and feature-based methods, in both homogeneous and heterogeneous teacher-student pairs.

Reinforcement learning from human feedback (RLHF) is a key driver of quality and safety in state-of-the-art large language models. Yet, a surprisingly simple and strong inference-time strategy is Best-of-N sampling that selects the best generation among N candidates. In this paper, we propose Best-of-N Distillation (BOND), a novel RLHF algorithm that seeks to emulate Best-of-N but without its significant computational overhead at inference time. Specifically, BOND is a distribution matching algorithm that forces the distribution of generations from the policy to get closer to the Best-of-N distribution. We use the Jeffreys divergence (a linear combination of forward and backward KL) to balance between mode-covering and mode-seeking behavior, and derive an iterative formulation that utilizes a moving anchor for efficiency. We demonstrate the effectiveness of our approach and several design choices through experiments on abstractive summarization and Gemma models. Aligning Gemma policies with BOND outperforms other RLHF algorithms by improving results on several benchmarks.

While classifier-free guidance (CFG) is essential for conditional diffusion models, it doubles the number of neural function evaluations (NFEs) per inference step. To mitigate this inefficiency, we introduce adapter guidance distillation (AGD), a novel approach that simulates CFG in a single forward pass. AGD leverages lightweight adapters to approximate CFG, effectively doubling the sampling speed while maintaining or even improving sample quality. Unlike prior guidance distillation methods that tune the entire model, AGD keeps the base model frozen and only trains minimal additional parameters (sim2%) to significantly reduce the resource requirement of the distillation phase. Additionally, this approach preserves the original model weights and enables the adapters to be seamlessly combined with other checkpoints derived from the same base model. We also address a key mismatch between training and inference in existing guidance distillation methods by training on CFG-guided trajectories instead of standard diffusion trajectories. Through extensive experiments, we show that AGD achieves comparable or superior FID to CFG across multiple architectures with only half the NFEs. Notably, our method enables the distillation of large models (sim2.6B parameters) on a single consumer GPU with 24 GB of VRAM, making it more accessible than previous approaches that require multiple high-end GPUs. We will publicly release the implementation of our method.

Reinforcement Learning has emerged as a post-training approach to elicit agentic RAG behaviors such as search and planning from language models. However, compact language models (e.g., 0.5B parameters) struggle due to poor reasoning ability, resulting in sparse rewards and unstable training. To overcome these difficulties, we propose Distillation-Guided Policy Optimization (DGPO), which addresses the challenges through cold-start initialization from teacher demonstrations and continuous teacher guidance during policy optimization. To systematically evaluate our approach, we introduce Agentic RAG Capabilities (ARC), a fine-grained metric analyzing reasoning, search coordination, and response synthesis. Comprehensive experiments demonstrate that DGPO enables compact models to achieve sophisticated agentic search behaviors, even outperforming the larger teacher model in some cases. DGPO makes agentic RAG feasible in computing resource-constrained environments.

On-policy reinforcement learning (RL) methods widely used for language model post-training, like Group Relative Policy Optimization (GRPO), often suffer from limited exploration and early saturation due to low sampling diversity. While off-policy data can help, current approaches that mix entire trajectories cause significant policy mismatch and instability. In this work, we propose the Single-sample Mix-pOlicy Unified Paradigm (SOUP), a framework that unifies off- and on-policy learning within individual samples at the token level. It confines off-policy influence to the prefix of a generated sequence sampled from historical policies, while the continuation is generated on-policy. Through token-level importance ratios, SOUP effectively leverages off-policy information while preserving training stability. Extensive experiments demonstrate that SOUP consistently outperforms standard on-policy training and existing off-policy extensions. Our further analysis clarifies how our fine-grained, single-sample mix-policy training can improve both exploration and final performance in LLM RL.

R1-style Reinforcement Learning (RL) significantly enhances Large Language Models' reasoning capabilities, yet the mechanism behind rule-based RL remains unclear. We found that small-scale SFT has significant influence on RL but shows poor efficiency. To explain our observations, we propose an analytical framework and compare the efficiency of SFT and RL by measuring sample effect. Hypothetical analysis show that SFT efficiency is limited by training data. Guided by our analysis, we propose Re-distillation, a technique that fine-tunes pretrain model through small-scale distillation from the RL-trained policy. Experiments on Knight & Knave and MATH datasets demonstrate re-distillation's surprising efficiency: re-distilled models match RL performance with far fewer samples and less computation. Empirical verification shows that sample effect is a good indicator of performance improvements. As a result, on K&K dataset, our re-distilled Qwen2.5-1.5B model surpasses DeepSeek-V3-0324 with only 1K SFT samples. On MATH, Qwen2.5-1.5B fine-tuned with re-distilled 500 samples matches its instruct-tuned variant without RL. Our work explains several interesting phenomena in R1-style RL, shedding light on the mechanisms behind its empirical success. Code is available at: https://github.com/on1262/deep-reasoning

Knowledge distillation with multiple teachers is increasingly used to improve robustness, efficiency, and safety, yet existing approaches rely largely on heuristic or implementation-specific weighting schemes. This paper develops an operator-agnostic axiomatic framework for adaptive weighting in multi-teacher knowledge distillation across three complementary scales: token, task, and context. We formalize structural conditions under which adaptive weighting operators are well-defined, admit multiple non-equivalent implementations, and can be hierarchically composed via product-structure normalization. Within this framework, we establish existence and non-uniqueness of conforming operators, characterize convergence of gradient-based optimization under standard assumptions, analyze stability and perturbation robustness, and provide an abstract formulation of safety-constrained distillation. The results decouple theoretical guarantees from specific weighting formulas, enabling principled analysis of adaptive distillation methods under heterogeneity, distribution shift, and safety constraints.

Knowledge Distillation (KD) has emerged as a promising approach for transferring knowledge from a larger, more complex teacher model to a smaller student model. Traditionally, KD involves training the student to mimic the teacher's output probabilities, while more advanced techniques have explored guiding the student to adopt the teacher's internal representations. Despite its widespread success, the performance of KD in binary classification and few-class problems has been less satisfactory. This is because the information about the teacher model's generalization patterns scales directly with the number of classes. Moreover, several sophisticated distillation methods may not be universally applicable or effective for data types beyond Computer Vision. Consequently, effective distillation techniques remain elusive for a range of key real-world applications, such as sentiment analysis, search query understanding, and advertisement-query relevance assessment. Taking these observations into account, we introduce a novel method for distilling knowledge from the teacher's model representations, which we term Learning Embedding Linear Projections (LELP). Inspired by recent findings about the structure of final-layer representations, LELP works by identifying informative linear subspaces in the teacher's embedding space, and splitting them into pseudo-subclasses. The student model is then trained to replicate these pseudo-classes. Our experimental evaluation on large-scale NLP benchmarks like Amazon Reviews and Sentiment140 demonstrate the LELP is consistently competitive with, and typically superior to, existing state-of-the-art distillation algorithms for binary and few-class problems, where most KD methods suffer.

Diffusion models achieve remarkable generation quality but suffer from computational intensive sampling due to suboptimal step discretization. While existing works focus on optimizing denoising directions, we address the principled design of stepsize schedules. This paper proposes Optimal Stepsize Distillation, a dynamic programming framework that extracts theoretically optimal schedules by distilling knowledge from reference trajectories. By reformulating stepsize optimization as recursive error minimization, our method guarantees global discretization bounds through optimal substructure exploitation. Crucially, the distilled schedules demonstrate strong robustness across architectures, ODE solvers, and noise schedules. Experiments show 10x accelerated text-to-image generation while preserving 99.4% performance on GenEval. Our code is available at https://github.com/bebebe666/OptimalSteps.

Post-training of language models (LMs) increasingly relies on the following two stages: (i) knowledge distillation, where the LM is trained to imitate a larger teacher LM, and (ii) reinforcement learning from human feedback (RLHF), where the LM is aligned by optimizing a reward model. In the second RLHF stage, a well-known challenge is reward hacking, where the LM over-optimizes the reward model. Such phenomenon is in line with Goodhart's law and can lead to degraded performance on the true objective. In this paper, we investigate whether a similar phenomenon, that we call teacher hacking, can occur during knowledge distillation. This could arise because the teacher LM is itself an imperfect approximation of the true distribution. To study this, we propose a controlled experimental setup involving: (i) an oracle LM representing the ground-truth distribution, (ii) a teacher LM distilled from the oracle, and (iii) a student LM distilled from the teacher. Our experiments reveal the following insights. When using a fixed offline dataset for distillation, teacher hacking occurs; moreover, we can detect it by observing when the optimization process deviates from polynomial convergence laws. In contrast, employing online data generation techniques effectively mitigates teacher hacking. More precisely, we identify data diversity as the key factor in preventing hacking. Overall, our findings provide a deeper understanding of the benefits and limitations of distillation for building robust and efficient LMs.

Speculative decoding (SD) accelerates large language model inference by employing a faster draft model for generating multiple tokens, which are then verified in parallel by the larger target model, resulting in the text generated according to the target model distribution. However, identifying a compact draft model that is well-aligned with the target model is challenging. To tackle this issue, we propose DistillSpec that uses knowledge distillation to better align the draft model with the target model, before applying SD. DistillSpec makes two key design choices, which we demonstrate via systematic study to be crucial to improving the draft and target alignment: utilizing on-policy data generation from the draft model, and tailoring the divergence function to the task and decoding strategy. Notably, DistillSpec yields impressive 10 - 45% speedups over standard SD on a range of standard benchmarks, using both greedy and non-greedy sampling. Furthermore, we combine DistillSpec with lossy SD to achieve fine-grained control over the latency vs. task performance trade-off. Finally, in practical scenarios with models of varying sizes, first using distillation to boost the performance of the target model and then applying DistillSpec to train a well-aligned draft model can reduce decoding latency by 6-10x with minimal performance drop, compared to standard decoding without distillation.

Despite the advanced intelligence abilities of large language models (LLMs) in various applications, they still face significant computational and storage demands. Knowledge Distillation (KD) has emerged as an effective strategy to improve the performance of a smaller LLM (i.e., the student model) by transferring knowledge from a high-performing LLM (i.e., the teacher model). Prevailing techniques in LLM distillation typically use a black-box model API to generate high-quality pretrained and aligned datasets, or utilize white-box distillation by altering the loss function to better transfer knowledge from the teacher LLM. However, these methods ignore the knowledge differences between the student and teacher LLMs across domains. This results in excessive focus on domains with minimal performance gaps and insufficient attention to domains with large gaps, reducing overall performance. In this paper, we introduce a new LLM distillation framework called DDK, which dynamically adjusts the composition of the distillation dataset in a smooth manner according to the domain performance differences between the teacher and student models, making the distillation process more stable and effective. Extensive evaluations show that DDK significantly improves the performance of student models, outperforming both continuously pretrained baselines and existing knowledge distillation methods by a large margin.

Language model (LM) distillation is a trending area that aims to distil the knowledge resided in a large teacher LM to a small student one. While various methods have been proposed to push the distillation to its limits, it is still a pain distilling LMs when a large capacity gap is exhibited between the teacher and the student LMs. The pain is mainly resulted by the curse of capacity gap, which describes that a larger teacher LM cannot always lead to a better student LM than one distilled from a smaller teacher LM due to the affect of capacity gap increment. That is, there is likely an optimal point yielding the best student LM along the scaling course of the teacher LM. Even worse, the curse of capacity gap can be only partly yet not fully lifted as indicated in previous studies. However, the tale is not ever one-sided. Although a larger teacher LM has better performance than a smaller teacher LM, it is much more resource-demanding especially in the context of recent large LMs (LLMs). Consequently, instead of sticking to lifting the curse, leaving the curse as is should be arguably fine. Even better, in this paper, we reveal that the optimal capacity gap is almost consistent across different student scales and architectures, fortunately turning the curse into the law of capacity gap. The law later guides us to distil a 3B student LM (termed MiniMA) from a 7B teacher LM (adapted LLaMA2-7B). MiniMA is demonstrated to yield a new compute-performance pareto frontier among existing 3B LMs on commonly used benchmarks, and its instruction-tuned version (termed MiniChat) outperforms a wide range of 3B competitors in GPT4 evaluation and could even compete with several 7B chat models.

While long Chain-of-Thought (CoT) distillation effectively transfers reasoning capability to smaller language models, the reasoning process often remains redundant and computational budget uncontrollable, leading to inefficient resource usage. To address this limitation, we propose Budget-Aware Reasoning Distillation (BARD), a novel framework that simultaneously distills reasoning capability and enables fine-grained control over the reasoning length. BARD uses the thinking budget as a user-specified control signal, allowing the model to dynamically balance reasoning performance and computational efficiency. To achieve this concept, BARD introduces a two-phase training regimen. The first phase, Supervised Fine-Tuning (SFT) on teacher-generated long CoT data compressed to various budget levels, bootstrapping the model's understanding of budget constraints. The second phase leverages Reinforcement Learning (RL) from a reward signal in consideration of reasoning performance and budget fidelity simultaneously. Incorporating the two-phase regimen is crucial to avoiding policy degradation and ensuring that both objectives are optimized jointly. Extensive experiments demonstrate that our method empowers an 8B student model to achieve strong performance on challenging reasoning benchmarks (AIME24, AIME25, GPQA) while providing precise and adaptive control over its reasoning length across a wide range of budgets.

Deep neural networks (DNNs) continue to make significant advances, solving tasks from image classification to translation or reinforcement learning. One aspect of the field receiving considerable attention is efficiently executing deep models in resource-constrained environments, such as mobile or embedded devices. This paper focuses on this problem, and proposes two new compression methods, which jointly leverage weight quantization and distillation of larger teacher networks into smaller student networks. The first method we propose is called quantized distillation and leverages distillation during the training process, by incorporating distillation loss, expressed with respect to the teacher, into the training of a student network whose weights are quantized to a limited set of levels. The second method, differentiable quantization, optimizes the location of quantization points through stochastic gradient descent, to better fit the behavior of the teacher model. We validate both methods through experiments on convolutional and recurrent architectures. We show that quantized shallow students can reach similar accuracy levels to full-precision teacher models, while providing order of magnitude compression, and inference speedup that is linear in the depth reduction. In sum, our results enable DNNs for resource-constrained environments to leverage architecture and accuracy advances developed on more powerful devices.

Most existing distillation methods ignore the flexible role of the temperature in the loss function and fix it as a hyper-parameter that can be decided by an inefficient grid search. In general, the temperature controls the discrepancy between two distributions and can faithfully determine the difficulty level of the distillation task. Keeping a constant temperature, i.e., a fixed level of task difficulty, is usually sub-optimal for a growing student during its progressive learning stages. In this paper, we propose a simple curriculum-based technique, termed Curriculum Temperature for Knowledge Distillation (CTKD), which controls the task difficulty level during the student's learning career through a dynamic and learnable temperature. Specifically, following an easy-to-hard curriculum, we gradually increase the distillation loss w.r.t. the temperature, leading to increased distillation difficulty in an adversarial manner. As an easy-to-use plug-in technique, CTKD can be seamlessly integrated into existing knowledge distillation frameworks and brings general improvements at a negligible additional computation cost. Extensive experiments on CIFAR-100, ImageNet-2012, and MS-COCO demonstrate the effectiveness of our method. Our code is available at https://github.com/zhengli97/CTKD.

Despite recent progress in large-scale reinforcement learning (RL) for reasoning, the training recipe for building high-performing reasoning models remains elusive. Key implementation details of frontier models, such as DeepSeek-R1, including data curation strategies and RL training recipe, are often omitted. Moreover, recent research indicates distillation remains more effective than RL for smaller models. In this work, we demonstrate that large-scale RL can significantly enhance the reasoning capabilities of strong, small- and mid-sized models, achieving results that surpass those of state-of-the-art distillation-based models. We systematically study the RL training process through extensive ablations and propose a simple yet effective approach: first training on math-only prompts, then on code-only prompts. Notably, we find that math-only RL not only significantly enhances the performance of strong distilled models on math benchmarks (e.g., +14.6% / +17.2% on AIME 2025 for the 7B / 14B models), but also code reasoning tasks (e.g., +6.8% / +5.8% on LiveCodeBench for the 7B / 14B models). In addition, extended code-only RL iterations further improve performance on code benchmarks with minimal or no degradation in math results. We develop a robust data curation pipeline to collect challenging prompts with high-quality, verifiable answers and test cases to enable verification-based RL across both domains. Finally, we identify key experimental insights, including curriculum learning with progressively increasing response lengths and the stabilizing effect of on-policy parameter updates. We find that RL not only elicits the foundational reasoning capabilities acquired during pretraining and supervised fine-tuning (e.g., distillation), but also pushes the limits of the model's reasoning ability, enabling it to solve problems that were previously unsolvable.

Growing efforts to improve knowledge distillation (KD) in large language models (LLMs) replace dense teacher supervision with selective distillation, which uses a subset of token positions, vocabulary classes, or training samples for supervision. However, it remains unclear which importance signals, selection policies, and their interplay are most effective. In this work, we revisit where and how to distill in autoregressive LLMs. We disentangle selective KD along the position, class, and sample axes and systematically compare importance signals and selection policies. Then, guided by this analysis, we identify underexplored opportunities and introduce student-entropy-guided position selection (SE-KD). Across a suite of benchmarks, SE-KD often improves accuracy, downstream task adherence, and memory efficiency over dense distillation. Extending this approach across the class and sample axes (SE-KD 3X) yields complementary efficiency gains that make offline teacher caching feasible. In practice, this reduces wall time by 70% and peak memory by 18%, while cutting storage usage by 80% over prior methods without sacrificing performance.

Distilled diffusion models suffer from a critical limitation: reduced sample diversity compared to their base counterparts. In this work, we uncover that despite this diversity loss, distilled models retain the fundamental concept representations of base models. We demonstrate control distillation - where control mechanisms like Concept Sliders and LoRAs trained on base models can be seamlessly transferred to distilled models and vice-versa, effectively distilling control without any retraining. This preservation of representational structure prompted our investigation into the mechanisms of diversity collapse during distillation. To understand how distillation affects diversity, we introduce Diffusion Target (DT) Visualization, an analysis and debugging tool that reveals how models predict final outputs at intermediate steps. Through DT-Visualization, we identify generation artifacts, inconsistencies, and demonstrate that initial diffusion timesteps disproportionately determine output diversity, while later steps primarily refine details. Based on these insights, we introduce diversity distillation - a hybrid inference approach that strategically employs the base model for only the first critical timestep before transitioning to the efficient distilled model. Our experiments demonstrate that this simple modification not only restores the diversity capabilities from base to distilled models but surprisingly exceeds it, while maintaining nearly the computational efficiency of distilled inference, all without requiring additional training or model modifications. Our code and data are available at https://distillation.baulab.info

Black-Box Knowledge Distillation (B2KD) is a formulated problem for cloud-to-edge model compression with invisible data and models hosted on the server. B2KD faces challenges such as limited Internet exchange and edge-cloud disparity of data distributions. In this paper, we formalize a two-step workflow consisting of deprivatization and distillation, and theoretically provide a new optimization direction from logits to cell boundary different from direct logits alignment. With its guidance, we propose a new method Mapping-Emulation KD (MEKD) that distills a black-box cumbersome model into a lightweight one. Our method does not differentiate between treating soft or hard responses, and consists of: 1) deprivatization: emulating the inverse mapping of the teacher function with a generator, and 2) distillation: aligning low-dimensional logits of the teacher and student models by reducing the distance of high-dimensional image points. For different teacher-student pairs, our method yields inspiring distillation performance on various benchmarks, and outperforms the previous state-of-the-art approaches.

Large Reasoning Models(LRMs) such as OpenAI o1 and DeepSeek-R1 have shown remarkable reasoning capabilities by scaling test-time compute and generating long Chain-of-Thought(CoT). Distillation--post-training on LRMs-generated data--is a straightforward yet effective method to enhance the reasoning abilities of smaller models, but faces a critical bottleneck: we found that distilled long CoT data poses learning difficulty for small models and leads to the inheritance of biases (i.e. over-thinking) when using Supervised Fine-tuning(SFT) and Reinforcement Learning(RL) methods. To alleviate this bottleneck, we propose constructing tree-based CoT data from scratch via Monte Carlo Tree Search(MCTS). We then exploit a set of CoT-aware approaches, including Thoughts Length Balance, Fine-grained DPO, and Joint Post-training Objective, to enhance SFT and RL on the construted data.

Diffusion models, praised for their success in generative tasks, are increasingly being applied to robotics, demonstrating exceptional performance in behavior cloning. However, their slow generation process stemming from iterative denoising steps poses a challenge for real-time applications in resource-constrained robotics setups and dynamically changing environments. In this paper, we introduce the One-Step Diffusion Policy (OneDP), a novel approach that distills knowledge from pre-trained diffusion policies into a single-step action generator, significantly accelerating response times for robotic control tasks. We ensure the distilled generator closely aligns with the original policy distribution by minimizing the Kullback-Leibler (KL) divergence along the diffusion chain, requiring only 2%-10% additional pre-training cost for convergence. We evaluated OneDP on 6 challenging simulation tasks as well as 4 self-designed real-world tasks using the Franka robot. The results demonstrate that OneDP not only achieves state-of-the-art success rates but also delivers an order-of-magnitude improvement in inference speed, boosting action prediction frequency from 1.5 Hz to 62 Hz, establishing its potential for dynamic and computationally constrained robotic applications. We share the project page at https://research.nvidia.com/labs/dir/onedp/.

Several solutions for lightweight TTS have shown promising results. Still, they either rely on a hand-crafted design that reaches non-optimum size or use a neural architecture search but often suffer training costs. We present Nix-TTS, a lightweight TTS achieved via knowledge distillation to a high-quality yet large-sized, non-autoregressive, and end-to-end (vocoder-free) TTS teacher model. Specifically, we offer module-wise distillation, enabling flexible and independent distillation to the encoder and decoder module. The resulting Nix-TTS inherited the advantageous properties of being non-autoregressive and end-to-end from the teacher, yet significantly smaller in size, with only 5.23M parameters or up to 89.34% reduction of the teacher model; it also achieves over 3.04x and 8.36x inference speedup on Intel-i7 CPU and Raspberry Pi 3B respectively and still retains a fair voice naturalness and intelligibility compared to the teacher model. We provide pretrained models and audio samples of Nix-TTS.

Distilling the reasoning capabilities from a large language model (LLM) to a smaller student model often involves training on substantial amounts of reasoning data. However, distillation over lengthy sequences with prompt (P), chain-of-thought (CoT), and answer (A) segments makes the process computationally expensive. In this work, we investigate how the allocation of supervision across different segments (P, CoT, A) affects student performance. Our analysis shows that selective knowledge distillation over only the CoT tokens can be effective when the prompt and answer information is encompassed by it. Building on this insight, we establish a truncation protocol to quantify computation-quality tradeoffs as a function of sequence length. We observe that training on only the first 50% of tokens of every training sequence can retain, on average, approx94% of full-sequence performance on math benchmarks while reducing training time, memory usage, and FLOPs by about 50% each. These findings suggest that reasoning distillation benefits from prioritizing early reasoning tokens and provides a simple lever for computation-quality tradeoffs. Codes are available at https://github.com/weiruichen01/distilling-the-essence.

Large Language Models (LLMs) have showcased exceptional capabilities in various domains, attracting significant interest from both academia and industry. Despite their impressive performance, the substantial size and computational demands of LLMs pose considerable challenges for practical deployment, particularly in environments with limited resources. The endeavor to compress language models while maintaining their accuracy has become a focal point of research. Among the various methods, knowledge distillation has emerged as an effective technique to enhance inference speed without greatly compromising performance. This paper presents a thorough survey from three aspects: method, evaluation, and application, exploring knowledge distillation techniques tailored specifically for LLMs. Specifically, we divide the methods into white-box KD and black-box KD to better illustrate their differences. Furthermore, we also explored the evaluation tasks and distillation effects between different distillation methods, and proposed directions for future research. Through in-depth understanding of the latest advancements and practical applications, this survey provides valuable resources for researchers, paving the way for sustained progress in this field.

Recent advances in knowledge distillation (KD) predominantly emphasize feature-level knowledge transfer, frequently overlooking critical information embedded within the teacher's logit distributions. In this paper, we revisit logit-based distillation and reveal an underexplored yet critical element: Top-K knowledge. Motivated by this insight, we propose Top-scaled Knowledge Distillation (TopKD), a simple, efficient, and architecture-agnostic framework that significantly enhances logit-based distillation. TopKD consists of two main components: (1) a Top-K Scaling Module (TSM), which adaptively amplifies the most informative logits, and (2) a Top-K Decoupled Loss (TDL), which offers targeted and effective supervision. Notably, TopKD integrates seamlessly into existing KD methods without introducing extra modules or requiring architectural changes. Extensive experiments on CIFAR-100, ImageNet, STL-10, and Tiny-ImageNet demonstrate that TopKD consistently surpasses state-of-the-art distillation methods. Moreover, our method demonstrates substantial effectiveness when distilling Vision Transformers, underscoring its versatility across diverse network architectures. These findings highlight the significant potential of logits to advance knowledge distillation.

Dataset Distillation (DD) seeks to create a compact dataset from a large, real-world dataset. While recent methods often rely on heuristic approaches to balance efficiency and quality, the fundamental relationship between original and synthetic data remains underexplored. This paper revisits knowledge distillation-based dataset distillation within a solid theoretical framework. We introduce the concepts of Informativeness and Utility, capturing crucial information within a sample and essential samples in the training set, respectively. Building on these principles, we define optimal dataset distillation mathematically. We then present InfoUtil, a framework that balances informativeness and utility in synthesizing the distilled dataset. InfoUtil incorporates two key components: (1) game-theoretic informativeness maximization using Shapley Value attribution to extract key information from samples, and (2) principled utility maximization by selecting globally influential samples based on Gradient Norm. These components ensure that the distilled dataset is both informative and utility-optimized. Experiments demonstrate that our method achieves a 6.1\% performance improvement over the previous state-of-the-art approach on ImageNet-1K dataset using ResNet-18.

Knowledge distillation (KD) methods compress large models into smaller students with manually-designed student architectures given pre-specified computational cost. This requires several trials to find a viable student, and further repeating the process for each student or computational budget change. We use Neural Architecture Search (NAS) to automatically distill several compressed students with variable cost from a large model. Current works train a single SuperLM consisting of millions of subnetworks with weight-sharing, resulting in interference between subnetworks of different sizes. Our framework AutoDistil addresses above challenges with the following steps: (a) Incorporates inductive bias and heuristics to partition Transformer search space into K compact sub-spaces (K=3 for typical student sizes of base, small and tiny); (b) Trains one SuperLM for each sub-space using task-agnostic objective (e.g., self-attention distillation) with weight-sharing of students; (c) Lightweight search for the optimal student without re-training. Fully task-agnostic training and search allow students to be reused for fine-tuning on any downstream task. Experiments on GLUE benchmark against state-of-the-art KD and NAS methods demonstrate AutoDistil to outperform leading compression techniques with upto 2.7x reduction in computational cost and negligible loss in task performance.

This technical report presents quantization-aware distillation (QAD) and our best practices for recovering accuracy of NVFP4-quantized large language models (LLMs) and vision-language models (VLMs). QAD distills a full-precision teacher model into a quantized student model using a KL divergence loss. While applying distillation to quantized models is not a new idea, we observe key advantages of QAD for today's LLMs: 1. It shows remarkable effectiveness and stability for models trained through multi-stage post-training pipelines, including supervised fine-tuning (SFT), reinforcement learning (RL), and model merging, where traditional quantization-aware training (QAT) suffers from engineering complexity and training instability; 2. It is robust to data quality and coverage, enabling accuracy recovery without full training data. We evaluate QAD across multiple post-trained models including AceReason Nemotron, Nemotron 3 Nano, Nemotron Nano V2, Nemotron Nano V2 VL (VLM), and Llama Nemotron Super v1, showing consistent recovery to near-BF16 accuracy.

Masked discrete diffusion is a dominant paradigm for high-quality language modeling where tokens are iteratively corrupted to a mask state, yet its inference efficiency is bottlenecked by the lack of deterministic sampling tools. While diffusion duality enables deterministic distillation for uniform models, these approaches generally underperform masked models and rely on complex integral operators. Conversely, in the masked domain, prior methods typically assume the absence of deterministic trajectories, forcing a reliance on stochastic distillation. To bridge this gap, we establish explicit Masked Diffusion Duality, proving that the masked process arises as the projection of a continuous Gaussian process via a novel maximum-value index preservation mechanism. Furthermore, we introduce Masked Consistency Distillation (MCD), a principled framework that leverages this duality to analytically construct the deterministic coupled trajectories required for consistency distillation, bypassing numerical ODE solvers. This result strictly improves upon prior stochastic distillation methods, achieving a 16times inference speedup without compromising generation quality. Our findings not only provide a solid theoretical foundation connecting masked and continuous diffusion, but also unlock the full potential of consistency distillation for high-performance discrete generation. Our code is available at https://anonymous.4open.science/r/MCD-70FD.

While diffusion models can learn complex distributions, sampling requires a computationally expensive iterative process. Existing distillation methods enable efficient sampling, but have notable limitations, such as performance degradation with very few sampling steps, reliance on training data access, or mode-seeking optimization that may fail to capture the full distribution. We propose EM Distillation (EMD), a maximum likelihood-based approach that distills a diffusion model to a one-step generator model with minimal loss of perceptual quality. Our approach is derived through the lens of Expectation-Maximization (EM), where the generator parameters are updated using samples from the joint distribution of the diffusion teacher prior and inferred generator latents. We develop a reparametrized sampling scheme and a noise cancellation technique that together stabilizes the distillation process. We further reveal an interesting connection of our method with existing methods that minimize mode-seeking KL. EMD outperforms existing one-step generative methods in terms of FID scores on ImageNet-64 and ImageNet-128, and compares favorably with prior work on distilling text-to-image diffusion models.

Recent advances in distilling expensive diffusion models into efficient few-step generators show significant promise. However, these methods typically demand substantial computational resources and extended training periods, limiting accessibility for resource-constrained researchers, and existing supplementary loss functions have notable limitations. Regression loss requires pre-generating large datasets before training and limits the student model to the teacher's performance, while GAN-based losses suffer from training instability and require careful tuning. In this paper, we propose Embedding Loss (EL), a novel supplementary loss function that complements existing diffusion distillation methods to enhance generation quality and accelerate training with smaller batch sizes. Leveraging feature embeddings from a diverse set of randomly initialized networks, EL effectively aligns the feature distributions between the distilled few-step generator and the original data. By computing Maximum Mean Discrepancy (MMD) in the embedded feature space, EL ensures robust distribution matching, thereby preserving sample fidelity and diversity during distillation. Within distribution matching distillation frameworks, EL demonstrates strong empirical performance for one-step generators. On the CIFAR-10 dataset, our approach achieves state-of-the-art FID values of 1.475 for unconditional generation and 1.380 for conditional generation. Beyond CIFAR-10, we further validate EL across multiple benchmarks and distillation methods, including ImageNet, AFHQ-v2, and FFHQ datasets, using DMD, DI, and CM distillation frameworks, demonstrating consistent improvements over existing one-step distillation methods. Our method also reduces training iterations by up to 80%, offering a more practical and scalable solution for deploying diffusion-based generative models in resource-constrained environments.

Distribution Matching Distillation (DMD) distills score-based generative models into efficient one-step generators, without requiring a one-to-one correspondence with the sampling trajectories of their teachers. However, limited model capacity causes one-step distilled models underperform on complex generative tasks, e.g., synthesizing intricate object motions in text-to-video generation. Directly extending DMD to multi-step distillation increases memory usage and computational depth, leading to instability and reduced efficiency. While prior works propose stochastic gradient truncation as a potential solution, we observe that it substantially reduces the generation diversity of multi-step distilled models, bringing it down to the level of their one-step counterparts. To address these limitations, we propose Phased DMD, a multi-step distillation framework that bridges the idea of phase-wise distillation with Mixture-of-Experts (MoE), reducing learning difficulty while enhancing model capacity. Phased DMD is built upon two key ideas: progressive distribution matching and score matching within subintervals. First, our model divides the SNR range into subintervals, progressively refining the model to higher SNR levels, to better capture complex distributions. Next, to ensure the training objective within each subinterval is accurate, we have conducted rigorous mathematical derivations. We validate Phased DMD by distilling state-of-the-art image and video generation models, including Qwen-Image (20B parameters) and Wan2.2 (28B parameters). Experimental results demonstrate that Phased DMD preserves output diversity better than DMD while retaining key generative capabilities. We will release our code and models.

Transformer-based architectures have become the de-facto standard models for diverse vision tasks owing to their superior performance. As the size of the models continues to scale up, model distillation becomes extremely important in various real applications, particularly on devices limited by computational resources. However, prevailing knowledge distillation methods exhibit diminished efficacy when confronted with a large capacity gap between the teacher and the student, e.g, 10x compression rate. In this paper, we present a novel approach named Automatic Multi-step Distillation (AMD) for large-scale vision model compression. In particular, our distillation process unfolds across multiple steps. Initially, the teacher undergoes distillation to form an intermediate teacher-assistant model, which is subsequently distilled further to the student. An efficient and effective optimization framework is introduced to automatically identify the optimal teacher-assistant that leads to the maximal student performance. We conduct extensive experiments on multiple image classification datasets, including CIFAR-10, CIFAR-100, and ImageNet. The findings consistently reveal that our approach outperforms several established baselines, paving a path for future knowledge distillation methods on large-scale vision models.

Knowledge Distillation (KD) can transfer the reasoning abilities of large models to smaller ones, which can reduce the costs to generate Chain-of-Thoughts for reasoning tasks. KD methods typically ask the student to mimic the teacher's distribution over the entire output. However, a student with limited capacity can be overwhelmed by such extensive supervision causing a distribution mismatch, especially in complex reasoning tasks. We propose Token-Selective Dual Knowledge Distillation (TSD-KD), a framework for student-centric distillation. TSD-KD focuses on distilling important tokens for reasoning and encourages the student to explain reasoning in its own words. TSD-KD combines indirect and direct distillation. Indirect distillation uses a weak form of feedback based on preference ranking. The student proposes candidate responses generated on its own; the teacher re-ranks those candidates as indirect feedback without enforcing its entire distribution. Direct distillation uses distribution matching; however, it selectively distills tokens based on the relative confidence between teacher and student. Finally, we add entropy regularization to maintain the student's confidence during distillation. Overall, our method provides the student with targeted and indirect feedback to support its own reasoning process and to facilitate self-improvement. The experiments show the state-of-the-art performance of TSD-KD on 10 challenging reasoning benchmarks, outperforming the baseline and runner-up in accuracy by up to 54.4\% and 40.3\%, respectively. Notably, a student trained by TSD-KD even outperformed its own teacher model in four cases by up to 20.3\%. The source code is available at https://github.com/kmswin1/TSD-KD.

As deep vision models grow increasingly complex to achieve higher performance, deployment efficiency has become a critical concern. Knowledge distillation (KD) mitigates this issue by transferring knowledge from large teacher models to compact student models. While many feature-based KD methods rely on spatial filtering to guide distillation, they typically treat all object instances uniformly, ignoring instance-level variability. Moreover, existing attention filtering mechanisms are typically heuristic or teacher-driven, rather than learned with the student. To address these limitations, we propose Learnable Instance Attention Filtering for Adaptive Detector Distillation (LIAF-KD), a novel framework that introduces learnable instance selectors to dynamically evaluate and reweight instance importance during distillation. Notably, the student contributes to this process based on its evolving learning state. Experiments on the KITTI and COCO datasets demonstrate consistent improvements, with a 2% gain on a GFL ResNet-50 student without added complexity, outperforming state-of-the-art methods.

Consistency distillation methods have demonstrated significant success in accelerating generative tasks of diffusion models. However, since previous consistency distillation methods use simple and straightforward strategies in selecting target timesteps, they usually struggle with blurs and detail losses in generated images. To address these limitations, we introduce Target-Driven Distillation (TDD), which (1) adopts a delicate selection strategy of target timesteps, increasing the training efficiency; (2) utilizes decoupled guidances during training, making TDD open to post-tuning on guidance scale during inference periods; (3) can be optionally equipped with non-equidistant sampling and x0 clipping, enabling a more flexible and accurate way for image sampling. Experiments verify that TDD achieves state-of-the-art performance in few-step generation, offering a better choice among consistency distillation models.

Large Language Models (LLMs) have exhibited impressive capabilities in various tasks, yet their vast parameter sizes restrict their applicability in resource-constrained settings. Knowledge distillation (KD) offers a viable solution by transferring expertise from large teacher models to compact student models. However, traditional KD techniques face specific challenges when applied to LLMs, including restricted access to LLM outputs, significant teacher-student capacity gaps, and the inherited mis-calibration issue. In this work, we present PLaD, a novel preference-based LLM distillation framework. PLaD exploits the teacher-student capacity discrepancy to generate pseudo-preference pairs where teacher outputs are preferred over student outputs. Then, PLaD leverages a ranking loss to re-calibrate student's estimation of sequence likelihood, which steers the student's focus towards understanding the relative quality of outputs instead of simply imitating the teacher. PLaD bypasses the need for access to teacher LLM's internal states, tackles the student's expressivity limitations, and mitigates the student mis-calibration issue. Through extensive experiments on two sequence generation tasks and with various LLMs, we demonstrate the effectiveness of our proposed PLaD framework.

Knowledge distillation can be a cost-effective technique to distill knowledge in Large Language Models, if the teacher output logits can be pre-computed and cached. However, successfully applying this to pre-training remains largely unexplored. In this work, we prove that naive approaches for sparse knowledge distillation such as caching Top-K probabilities, while intuitive, provide biased estimates of teacher probability distribution to the student, resulting in suboptimal performance and calibration. We propose an importance-sampling-based method `Random Sampling Knowledge Distillation', which provides unbiased estimates, preserves the gradient in expectation, and requires storing significantly sparser logits. Our method enables faster training of student models with marginal overhead (<10%) compared to cross-entropy based training, while maintaining competitive performance compared to full distillation, across a range of model sizes from 300M to 3B.