Daily Papers

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/.

The standard post-training recipe for large reasoning models, supervised fine-tuning followed by reinforcement learning (SFT-then-RL), may limit the benefits of the RL stage: while SFT imitates expert demonstrations, it often causes overconfidence and reduces generation diversity, leaving RL with a narrowed solution space to explore. Adding entropy regularization during SFT is not a cure-all; it tends to flatten token distributions toward uniformity, increasing entropy without improving meaningful exploration capability. In this paper, we propose CurioSFT, an entropy-preserving SFT method designed to enhance exploration capabilities through intrinsic curiosity. It consists of (a) Self-Exploratory Distillation, which distills the model toward a self-generated, temperature-scaled teacher to encourage exploration within its capability; and (b) Entropy-Guided Temperature Selection, which adaptively adjusts distillation strength to mitigate knowledge forgetting by amplifying exploration at reasoning tokens while stabilizing factual tokens. Extensive experiments on mathematical reasoning tasks demonstrate that, in SFT stage, CurioSFT outperforms the vanilla SFT by 2.5 points on in-distribution tasks and 2.9 points on out-of-distribution tasks. We also verify that exploration capabilities preserved during SFT successfully translate into concrete gains in RL stage, yielding an average improvement of 5.0 points.

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.

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.

The pervasiveness of proprietary language models has raised critical privacy concerns, necessitating advancements in private inference (PI), where computations are performed directly on encrypted data without revealing users' sensitive information. While PI offers a promising solution, its practical deployment is hindered by substantial communication and latency overheads, primarily stemming from nonlinear operations. To address this, we introduce an information-theoretic framework to characterize the role of nonlinearities in decoder-only language models, laying a principled foundation for optimizing transformer-architectures tailored to the demands of PI. By leveraging Shannon's entropy as a quantitative measure, we uncover the previously unexplored dual significance of nonlinearities: beyond ensuring training stability, they are crucial for maintaining attention head diversity. Specifically, we find that their removal triggers two critical failure modes: {\em entropy collapse} in deeper layers that destabilizes training, and {\em entropic overload} in earlier layers that leads to under-utilization of Multi-Head Attention's (MHA) representational capacity. We propose an entropy-guided attention mechanism paired with a novel entropy regularization technique to mitigate entropic overload. Additionally, we explore PI-friendly alternatives to layer normalization for preventing entropy collapse and stabilizing the training of LLMs with reduced-nonlinearities. Our study bridges the gap between information theory and architectural design, establishing entropy dynamics as a principled guide for developing efficient PI architectures. The code and implementation are available at https://github.com/Nandan91/entropy-guided-attention-llm{entropy-guided-llm}.

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.

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.

Long-term training of large language models (LLMs) requires maintaining stable exploration to prevent the model from collapsing into sub-optimal behaviors. Entropy is crucial in this context, as it controls exploration and helps avoid premature convergence to sub-optimal solutions. However, existing reinforcement learning methods struggle to maintain an appropriate level of entropy, as the training process involves a mix of positive and negative samples, each affecting entropy in different ways across steps. To address this, we propose Entropy stablilization via Proportional-Integral Control (EntroPIC), a novel method that adaptively adjusts the influence of positive and negative samples by dynamically tuning their loss coefficients. This approach stabilizes entropy throughout training, ensuring efficient exploration and steady progress. We provide a comprehensive theoretical analysis for both on-policy and off-policy learning settings, demonstrating that EntroPIC is effective at controlling entropy in large-scale LLM training. Experimental results show that our method successfully maintains desired entropy levels, enabling stable and optimal RL training for LLMs.

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.

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.

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.

While Reinforcement Learning with Verifiable Rewards (RLVR) can enhance LLM reasoning, its training process poses a critical risk: entropy collapse. This phenomenon is a rapid loss of policy diversity, stemming from the exploration-exploitation imbalance and leading to a lack of generalization. Recent entropy-intervention methods aim to prevent entropy collapse, yet their underlying mechanisms remain unclear. In this paper, we conduct a quantitative analysis to reveal token-level entropy changes and how existing entropy intervention methods help avoid entropy collapse. Our findings point out a fundamental limitation of existing methods: they attempt to control entropy dynamics indirectly. By only affecting related factors, such as the advantage signal and generation probability, their effectiveness is inherently limited and could potentially fail. To address this limitation, we introduce an entropy-change-aware reweighting scheme, namely Stabilizing Token-level Entropy-changE via Reweighting (STEER), that adaptively stabilizes entropy dynamics through fine-grained token-level adjustments. Our approach mitigates over-exploitation while fostering robust exploration. Extensive experiments demonstrate that STEER significantly mitigates entropy collapse, stabilizes entropy dynamics, and achieves stronger downstream performance across various mathematical reasoning benchmarks \footnote{Our code is available at https://github.com/zz-haooo/STEER.

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.

Multimodal reward models are crucial for aligning multimodal large language models with human preferences. Recent works have incorporated reasoning capabilities into these models, achieving promising results. However, training these models suffers from two critical challenges: (1) the inherent noise in preference datasets, which degrades model performance, and (2) the inefficiency of conventional training methods, which ignore the differences in sample difficulty. In this paper, we identify a strong correlation between response entropy and accuracy, indicating that entropy can serve as a reliable and unsupervised proxy for annotation noise and sample difficulty. Based on this insight, we propose a novel Entropy-Guided Training (EGT) approach for multimodal reasoning reward models, which combines two strategies: (1) entropy-guided data curation to mitigate the impact of unreliable samples, and (2) an entropy-guided training strategy that progressively introduces more complex examples. Extensive experiments across three benchmarks show that the EGT-trained model consistently outperforms state-of-the-art multimodal reward models.

Algorithmic efficiency techniques such as distillation (hinton2015distillation) are useful in improving model quality without increasing serving costs, provided a larger teacher model is available for a smaller student model to learn from during training. Standard distillation methods are limited to only forcing the student to match the teacher's outputs. Given the costs associated with training a large model, we believe we should be extracting more useful information from a teacher model than by just making the student match the teacher's outputs. In this paper, we introduce \guide (Guided Initialization and Distillation of Embeddings). \guide can be considered a distillation technique that forces the student to match the teacher in the parameter space. Using \guide we show 25-26\% reduction in the teacher-student quality gap when using large student models (400M - 1B parameters) trained on approx 20B tokens. We also present a thorough analysis demonstrating that \guide can be combined with knowledge distillation with near additive improvements. Furthermore, we show that applying \guide alone leads to substantially better model quality than applying knowledge distillation by itself. Most importantly, \guide introduces no training or inference overhead and hence any model quality gains from our method are virtually free.

This paper analyzes Cross-Entropy (CE) loss in knowledge distillation (KD) for recommender systems. KD for recommender systems targets at distilling rankings, especially among items most likely to be preferred, and can only be computed on a small subset of items. Considering these features, we reveal the connection between CE loss and NDCG in the field of KD. We prove that when performing KD on an item subset, minimizing CE loss maximizes the lower bound of NDCG, only if an assumption of closure is satisfied. It requires that the item subset consists of the student's top items. However, this contradicts our goal of distilling rankings of the teacher's top items. We empirically demonstrate the vast gap between these two kinds of top items. To bridge the gap between our goal and theoretical support, we propose Rejuvenated Cross-Entropy for Knowledge Distillation (RCE-KD). It splits the top items given by the teacher into two subsets based on whether they are highly ranked by the student. For the subset that defies the condition, a sampling strategy is devised to use teacher-student collaboration to approximate our assumption of closure. We also combine the losses on the two subsets adaptively. Extensive experiments demonstrate the effectiveness of our method. Our code is available at https://github.com/BDML-lab/RCE-KD.

To bridge the gaps between topology-aware Graph Neural Networks (GNNs) and inference-efficient Multi-Layer Perceptron (MLPs), GLNN proposes to distill knowledge from a well-trained teacher GNN into a student MLP. Despite their great progress, comparatively little work has been done to explore the reliability of different knowledge points (nodes) in GNNs, especially their roles played during distillation. In this paper, we first quantify the knowledge reliability in GNN by measuring the invariance of their information entropy to noise perturbations, from which we observe that different knowledge points (1) show different distillation speeds (temporally); (2) are differentially distributed in the graph (spatially). To achieve reliable distillation, we propose an effective approach, namely Knowledge-inspired Reliable Distillation (KRD), that models the probability of each node being an informative and reliable knowledge point, based on which we sample a set of additional reliable knowledge points as supervision for training student MLPs. Extensive experiments show that KRD improves over the vanilla MLPs by 12.62% and outperforms its corresponding teacher GNNs by 2.16% averaged over 7 datasets and 3 GNN architectures.

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.

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 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.

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.

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.

The burgeoning complexity of contemporary deep learning models, while achieving unparalleled accuracy, has inadvertently introduced deployment challenges in resource-constrained environments. Knowledge distillation, a technique aiming to transfer knowledge from a high-capacity "teacher" model to a streamlined "student" model, emerges as a promising solution to this dilemma. This paper provides a comprehensive overview of the knowledge distillation paradigm, emphasizing its foundational principles such as the utility of soft labels and the significance of temperature scaling. Through meticulous examination, we elucidate the critical determinants of successful distillation, including the architecture of the student model, the caliber of the teacher, and the delicate balance of hyperparameters. While acknowledging its profound advantages, we also delve into the complexities and challenges inherent in the process. Our exploration underscores knowledge distillation's potential as a pivotal technique in optimizing the trade-off between model performance and deployment efficiency.

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.

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%.

Reinforcement learning with verifiable rewards (RLVR) has demonstrated superior performance in enhancing the reasoning capability of large language models (LLMs). However, this accuracy-oriented learning paradigm often suffers from entropy collapse, which reduces policy exploration and limits reasoning capabilities. To address this challenge, we propose an efficient reinforcement learning framework that leverages entropy signals at both the semantic and token levels to improve reasoning. From the data perspective, we introduce semantic entropy-guided curriculum learning, organizing training data from low to high semantic entropy to guide progressive optimization from easier to more challenging tasks. For the algorithmic design, we adopt non-uniform token treatment by imposing KL regularization on low-entropy tokens that critically impact policy exploration and applying stronger constraints on high-covariance portions within these tokens. By jointly optimizing data organization and algorithmic design, our method effectively mitigates entropy collapse and enhances LLM reasoning. Experimental results across 6 benchmarks with 3 different parameter-scale base models demonstrate that our method outperforms other entropy-based approaches in improving reasoning.

Knowledge Distillation (KD) trains a smaller student model using a large, pre-trained teacher model, with temperature as a key hyperparameter controlling the softness of output probabilities. Traditional methods use a fixed temperature throughout training, which is suboptimal. Moreover, architectural differences between teacher and student often result in mismatched logit magnitudes. We demonstrate that students benefit from softer probabilities early in training but require sharper probabilities in later stages. We introduce Dynamic Temperature Scheduler (DTS), which adjusts temperature dynamically based on the cross-entropy loss gap between teacher and student. To our knowledge, this is the first temperature scheduling method that adapts based on the divergence between teacher and student distributions. Our method integrates seamlessly with existing KD frameworks. We validate DTS across multiple KD strategies on vision (CIFAR-100, Tiny-ImageNet) and NLP tasks (GLUE, Dolly, SelfIns, UnNI, S-NI), consistently outperforming static-temperature baselines. Code is available at https://github.com/Sibgat-Ul/DTS.

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.

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.

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.

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.

Standard LLM distillation wastes compute on two fronts: problems the student has already mastered (near-zero gradients) and problems far beyond its reach (incoherent gradients that erode existing capabilities). We show that this waste is not merely intuitive but structurally inevitable: the gradient signal-to-noise ratio in distillation provably vanishes at both pass-rate extremes. This theoretical observation leads to Paced, a framework that concentrates distillation on the zone of proximal development -- the frontier of a student model's competence -- via a principled pass-rate weight w(p) = p^α(1 - p)^β derived from the boundary-vanishing structure of distillation gradients. Key results: (1) Theory: We prove that the Beta kernel w(p) = p^α(1-p)^β is a leading-order weight family arising from the SNR structure of distillation, and that it is minimax-robust -- under bounded multiplicative misspecification, worst-case efficiency loss is only O(δ^2). (2)Distillation: On distillation from a larger teacher to a smaller student model with forward KL, Paced achieves significant gain over the base model, while keeping benchmark forgetting at a low level. (3)Self-distillation: On instruction-tuned models with reverse KL, gains are exceeding baselines as well. (4)Two-stage synergy: A forward-KL-then-reverse-KL schedule yields the strongest results in our setting, reaching substantial improvements on standard reasoning benchmarks -- supporting a mode-coverage-then-consolidation interpretation of the distillation process. All configurations require only student rollouts to estimate pass rates, need no architectural changes, and are compatible with any KL direction.

Dataset distillation is the task of synthesizing a small dataset such that a model trained on the synthetic set will match the test accuracy of the model trained on the full dataset. In this paper, we propose a new formulation that optimizes our distilled data to guide networks to a similar state as those trained on real data across many training steps. Given a network, we train it for several iterations on our distilled data and optimize the distilled data with respect to the distance between the synthetically trained parameters and the parameters trained on real data. To efficiently obtain the initial and target network parameters for large-scale datasets, we pre-compute and store training trajectories of expert networks trained on the real dataset. Our method handily outperforms existing methods and also allows us to distill higher-resolution visual data.

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.

Knowledge distillation (KD) is an effective training strategy to improve the lightweight student models under the guidance of cumbersome teachers. However, the large architecture difference across the teacher-student pairs limits the distillation gains. In contrast to previous adaptive distillation methods to reduce the teacher-student gap, we explore a novel training-free framework to search for the best student architectures for a given teacher. Our work first empirically show that the optimal model under vanilla training cannot be the winner in distillation. Secondly, we find that the similarity of feature semantics and sample relations between random-initialized teacher-student networks have good correlations with final distillation performances. Thus, we efficiently measure similarity matrixs conditioned on the semantic activation maps to select the optimal student via an evolutionary algorithm without any training. In this way, our student architecture search for Distillation WithOut Training (DisWOT) significantly improves the performance of the model in the distillation stage with at least 180times training acceleration. Additionally, we extend similarity metrics in DisWOT as new distillers and KD-based zero-proxies. Our experiments on CIFAR, ImageNet and NAS-Bench-201 demonstrate that our technique achieves state-of-the-art results on different search spaces. Our project and code are available at https://lilujunai.github.io/DisWOT-CVPR2023/.

Knowledge distillation (KD) is a general neural network training approach that uses a teacher model to guide the student model. Existing works mainly study KD from the network output side (e.g., trying to design a better KD loss function), while few have attempted to understand it from the input side. Especially, its interplay with data augmentation (DA) has not been well understood. In this paper, we ask: Why do some DA schemes (e.g., CutMix) inherently perform much better than others in KD? What makes a "good" DA in KD? Our investigation from a statistical perspective suggests that a good DA scheme should reduce the covariance of the teacher-student cross-entropy. A practical metric, the stddev of teacher's mean probability (T. stddev), is further presented and well justified empirically. Besides the theoretical understanding, we also introduce a new entropy-based data-mixing DA scheme, CutMixPick, to further enhance CutMix. Extensive empirical studies support our claims and demonstrate how we can harvest considerable performance gains simply by using a better DA scheme in knowledge distillation.

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.

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

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.

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/

While diffusion distillation has enabled one-step generation through methods like Variational Score Distillation, adapting distilled models to emerging new controls -- such as novel structural constraints or latest user preferences -- remains challenging. Conventional approaches typically requires modifying the base diffusion model and redistilling it -- a process that is both computationally intensive and time-consuming. To address these challenges, we introduce Joint Distribution Matching (JDM), a novel approach that minimizes the reverse KL divergence between image-condition joint distributions. By deriving a tractable upper bound, JDM decouples fidelity learning from condition learning. This asymmetric distillation scheme enables our one-step student to handle controls unknown to the teacher model and facilitates improved classifier-free guidance (CFG) usage and seamless integration of human feedback learning (HFL). Experimental results demonstrate that JDM surpasses baseline methods such as multi-step ControlNet by mere one-step in most cases, while achieving state-of-the-art performance in one-step text-to-image synthesis through improved usage of CFG or HFL integration.

Knowledge distillation is classically a procedure where a neural network is trained on the output of another network along with the original targets in order to transfer knowledge between the architectures. The special case of self-distillation, where the network architectures are identical, has been observed to improve generalization accuracy. In this paper, we consider an iterative variant of self-distillation in a kernel regression setting, in which successive steps incorporate both model outputs and the ground-truth targets. This allows us to provide the first theoretical results on the importance of using the weighted ground-truth targets in self-distillation. Our focus is on fitting nonlinear functions to training data with a weighted mean square error objective function suitable for distillation, subject to ell_2 regularization of the model parameters. We show that any such function obtained with self-distillation can be calculated directly as a function of the initial fit, and that infinite distillation steps yields the same optimization problem as the original with amplified regularization. Furthermore, we provide a closed form solution for the optimal choice of weighting parameter at each step, and show how to efficiently estimate this weighting parameter for deep learning and significantly reduce the computational requirements compared to a grid search.

The mechanisms behind the success of multi-view self-supervised learning (MVSSL) are not yet fully understood. Contrastive MVSSL methods have been studied through the lens of InfoNCE, a lower bound of the Mutual Information (MI). However, the relation between other MVSSL methods and MI remains unclear. We consider a different lower bound on the MI consisting of an entropy and a reconstruction term (ER), and analyze the main MVSSL families through its lens. Through this ER bound, we show that clustering-based methods such as DeepCluster and SwAV maximize the MI. We also re-interpret the mechanisms of distillation-based approaches such as BYOL and DINO, showing that they explicitly maximize the reconstruction term and implicitly encourage a stable entropy, and we confirm this empirically. We show that replacing the objectives of common MVSSL methods with this ER bound achieves competitive performance, while making them stable when training with smaller batch sizes or smaller exponential moving average (EMA) coefficients. Github repo: https://github.com/apple/ml-entropy-reconstruction.

We aim to identify how different components in the KD pipeline affect the resulting performance and how much the optimal KD pipeline varies across different datasets/tasks, such as the data augmentation policy, the loss function, and the intermediate representation for transferring the knowledge between teacher and student. To tease apart their effects, we propose Distiller, a meta KD framework that systematically combines a broad range of techniques across different stages of the KD pipeline, which enables us to quantify each component's contribution. Within Distiller, we unify commonly used objectives for distillation of intermediate representations under a universal mutual information (MI) objective and propose a class of MI-alpha objective functions with better bias/variance trade-off for estimating the MI between the teacher and the student. On a diverse set of NLP datasets, the best Distiller configurations are identified via large-scale hyperparameter optimization. Our experiments reveal the following: 1) the approach used to distill the intermediate representations is the most important factor in KD performance, 2) among different objectives for intermediate distillation, MI-alpha performs the best, and 3) data augmentation provides a large boost for small training datasets or small student networks. Moreover, we find that different datasets/tasks prefer different KD algorithms, and thus propose a simple AutoDistiller algorithm that can recommend a good KD pipeline for a new dataset.

While diffusion models have achieved great success in the field of video generation, this progress is accompanied by a rapidly escalating computational burden. Among the existing acceleration methods, Feature Caching is popular due to its training-free property and considerable speedup performance, but it inevitably faces semantic and detail drop with further compression. Another widely adopted method, training-aware step-distillation, though successful in image generation, also faces drastic degradation in video generation with a few steps. Furthermore, the quality loss becomes more severe when simply applying training-free feature caching to the step-distilled models, due to the sparser sampling steps. This paper novelly introduces a distillation-compatible learnable feature caching mechanism for the first time. We employ a lightweight learnable neural predictor instead of traditional training-free heuristics for diffusion models, enabling a more accurate capture of the high-dimensional feature evolution process. Furthermore, we explore the challenges of highly compressed distillation on large-scale video models and propose a conservative Restricted MeanFlow approach to achieve more stable and lossless distillation. By undertaking these initiatives, we further push the acceleration boundaries to 11.8times while preserving generation quality. Extensive experiments demonstrate the effectiveness of our method. The code will be made publicly available soon.

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.

Knowledge distillation from LLMs is essential for the efficient deployment of language models. Prior works have proposed data generation using LLMs for preparing distilled models. We argue that generating data with LLMs is prone to sampling mainly from the center of original content distribution. This limitation hinders the distilled model from learning the true underlying data distribution and to forget the tails of the distributions (samples with lower probability). To this end, we propose GOLD, a task-agnostic data generation and knowledge distillation framework, which employs an iterative out-of-distribution-guided feedback mechanism for the LLM. As a result, the generated data improves the generalizability of distilled models. An energy-based OOD evaluation approach is also introduced to deal with noisy generated data. Our extensive experiments on 10 different classification and sequence-to-sequence tasks in NLP show that GOLD respectively outperforms prior arts and the LLM with an average improvement of 5% and 14%. We will also show that the proposed method is applicable to less explored and novel tasks. The code is available.

While achieving exceptional generative quality, modern diffusion, flow, and other matching models suffer from slow inference, as they require many steps of iterative generation. Recent distillation methods address this by training efficient one-step generators under the guidance of a pre-trained teacher model. However, these methods are often constrained to only one specific framework, e.g., only to diffusion or only to flow models. Furthermore, these methods are naturally data-free, and to benefit from the usage of real data, it is required to use an additional complex adversarial training with an extra discriminator model. In this paper, we present RealUID, a universal distillation framework for all matching models that seamlessly incorporates real data into the distillation procedure without GANs. Our RealUID approach offers a simple theoretical foundation that covers previous distillation methods for Flow Matching and Diffusion models, and is also extended to their modifications, such as Bridge Matching and Stochastic Interpolants. The code can be found in https://github.com/David-cripto/RealUID.

Diffusion models have shown tremendous results in image generation. However, due to the iterative nature of the diffusion process and its reliance on classifier-free guidance, inference times are slow. In this paper, we propose a new distillation approach for guided diffusion models in which an external lightweight guide model is trained while the original text-to-image model remains frozen. We show that our method reduces the inference computation of classifier-free guided latent-space diffusion models by almost half, and only requires 1\% trainable parameters of the base model. Furthermore, once trained, our guide model can be applied to various fine-tuned, domain-specific versions of the base diffusion model without the need for additional training: this "plug-and-play" functionality drastically improves inference computation while maintaining the visual fidelity of generated images. Empirically, we show that our approach is able to produce visually appealing results and achieve a comparable FID score to the teacher with as few as 8 to 16 steps.

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.

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.

Flow-based generative models achieve state-of-the-art sample quality, but require the expensive solution of a differential equation at inference time. Flow map models, commonly known as consistency models, encompass many recent efforts to improve inference-time efficiency by learning the solution operator of this differential equation. Yet despite their promise, these models lack a unified description that clearly explains how to learn them efficiently in practice. Here, building on the methodology proposed in Boffi et. al. (2024), we present a systematic algorithmic framework for directly learning the flow map associated with a flow or diffusion model. By exploiting a relationship between the velocity field underlying a continuous-time flow and the instantaneous rate of change of the flow map, we show how to convert any distillation scheme into a direct training algorithm via self-distillation, eliminating the need for pre-trained teachers. We introduce three algorithmic families based on different mathematical characterizations of the flow map: Eulerian, Lagrangian, and Progressive methods, which we show encompass and extend all known distillation and direct training schemes for consistency models. We find that the novel class of Lagrangian methods, which avoid both spatial derivatives and bootstrapping from small steps by design, achieve significantly more stable training and higher performance than more standard Eulerian and Progressive schemes. Our methodology unifies existing training schemes under a single common framework and reveals new design principles for accelerated generative modeling. Associated code is available at https://github.com/nmboffi/flow-maps.

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.

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.

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.

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.

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.

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.

Diffusion models excel at producing high-quality samples but naively require hundreds of iterations, prompting multiple attempts to distill the generation process into a faster network. However, many existing approaches suffer from a variety of challenges: the process for distillation training can be complex, often requiring multiple training stages, and the resulting models perform poorly when utilized in single-step generative applications. In this paper, we introduce a simple yet effective means of distilling diffusion models directly from initial noise to the resulting image. Of particular importance to our approach is to leverage a new Deep Equilibrium (DEQ) model as the distilled architecture: the Generative Equilibrium Transformer (GET). Our method enables fully offline training with just noise/image pairs from the diffusion model while achieving superior performance compared to existing one-step methods on comparable training budgets. We demonstrate that the DEQ architecture is crucial to this capability, as GET matches a 5times larger ViT in terms of FID scores while striking a critical balance of computational cost and image quality. Code, checkpoints, and datasets are available.

Diffusion model distillation has emerged as a powerful technique for creating efficient few-step and single-step generators. Among these, Distribution Matching Distillation (DMD) and its variants stand out for their impressive performance, which is widely attributed to their core mechanism of matching the student's output distribution to that of a pre-trained teacher model. In this work, we challenge this conventional understanding. Through a rigorous decomposition of the DMD training objective, we reveal that in complex tasks like text-to-image generation, where CFG is typically required for desirable few-step performance, the primary driver of few-step distillation is not distribution matching, but a previously overlooked component we identify as CFG Augmentation (CA). We demonstrate that this term acts as the core ``engine'' of distillation, while the Distribution Matching (DM) term functions as a ``regularizer'' that ensures training stability and mitigates artifacts. We further validate this decoupling by demonstrating that while the DM term is a highly effective regularizer, it is not unique; simpler non-parametric constraints or GAN-based objectives can serve the same stabilizing function, albeit with different trade-offs. This decoupling of labor motivates a more principled analysis of the properties of both terms, leading to a more systematic and in-depth understanding. This new understanding further enables us to propose principled modifications to the distillation process, such as decoupling the noise schedules for the engine and the regularizer, leading to further performance gains. Notably, our method has been adopted by the Z-Image ( https://github.com/Tongyi-MAI/Z-Image ) project to develop a top-tier 8-step image generation model, empirically validating the generalization and robustness of our findings.

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.

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.

Post-training endows pretrained LLMs with a variety of desirable skills, including instruction-following, reasoning, and others. However, these post-trained LLMs only encode knowledge up to a cut-off date, necessitating continual adaptation. Unfortunately, existing solutions cannot simultaneously learn new knowledge from an adaptation document corpora and mitigate the forgetting of earlier learned capabilities. To address this, we introduce Distillation via Split Contexts (DiSC), a simple context-distillation based approach for continual knowledge adaptation. \methodname~derives student and teacher distributions by conditioning on distinct segments of the training example and minimizes the KL divergence between the shared tokens. This allows us to efficiently apply context-distillation without requiring explicit generation steps during training. We run experiments on four post-trained models and two adaptation domains. Compared to prior finetuning and distillation methods for continual adaptation, DiSC consistently reports the best trade-off between learning new knowledge and mitigating forgetting of previously learned skills like instruction-following, reasoning, and factual knowledge.

Majorities of distillation methods on pre-trained diffusion models or on pre-trained rectified flow, focus on either the distillation outputs or the trajectories between random noises and clean images to speed up sample generations from pre-trained models. In those trajectory-based distillation methods, consistency distillation requires the self-consistent trajectory projection to regulate the trajectory, which might avoid the common ODE approximation error {while still be concerning about sampling efficiencies}. At the same time, rectified flow distillations enforce straight trajectory for fast sampling, although an ODE solver is still required. In this work, we propose a trajectory distillation method, \modelname, that enjoys the benefits of both and enables few-step generations. TraFlow adopts the settings of consistency trajectory models, and further enforces the properties of self-consistency and straightness throughout the entire trajectory. These two properties are pursued by reaching a balance with following three targets: (1) reconstruct the output from pre-trained models; (2) learn the amount of changes by pre-trained models; (3) satisfy the self-consistency over its trajectory. Extensive experimental results have shown the effectiveness of our proposed method.

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.

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.

Despite the impressive performance of diffusion models such as Stable Diffusion (SD) in image generation, their slow inference limits practical deployment. Recent works accelerate inference by distilling multi-step diffusion into one-step generators. To better understand the distillation mechanism, we analyze U-Net/DiT weight changes between one-step students and their multi-step teacher counterparts. Our analysis reveals that changes in weight direction significantly exceed those in weight norm, highlighting it as the key factor during distillation. Motivated by this insight, we propose the Low-rank Rotation of weight Direction (LoRaD), a parameter-efficient adapter tailored to one-step diffusion distillation. LoRaD is designed to model these structured directional changes using learnable low-rank rotation matrices. We further integrate LoRaD into Variational Score Distillation (VSD), resulting in Weight Direction-aware Distillation (WaDi)-a novel one-step distillation framework. WaDi achieves state-of-the-art FID scores on COCO 2014 and COCO 2017 while using only approximately 10% of the trainable parameters of the U-Net/DiT. Furthermore, the distilled one-step model demonstrates strong versatility and scalability, generalizing well to various downstream tasks such as controllable generation, relation inversion, and high-resolution synthesis.

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.

Accelerating the sampling speed of diffusion models remains a significant challenge. Recent score distillation methods distill a heavy teacher model into an one-step student generator, which is optimized by calculating the difference between the two score functions on the samples generated by the student model. However, there is a score mismatch issue in the early stage of the distillation process, because existing methods mainly focus on using the endpoint of pre-trained diffusion models as teacher models, overlooking the importance of the convergence trajectory between the student generator and the teacher model. To address this issue, we extend the score distillation process by introducing the entire convergence trajectory of teacher models and propose Distribution Backtracking Distillation (DisBack) for distilling student generators. DisBask is composed of two stages: Degradation Recording and Distribution Backtracking. Degradation Recording is designed to obtain the convergence trajectory of teacher models, which records the degradation path from the trained teacher model to the untrained initial student generator. The degradation path implicitly represents the intermediate distributions of teacher models. Then Distribution Backtracking trains a student generator to backtrack the intermediate distributions for approximating the convergence trajectory of teacher models. Extensive experiments show that DisBack achieves faster and better convergence than the existing distillation method and accomplishes comparable generation performance. Notably, DisBack is easy to implement and can be generalized to existing distillation methods to boost performance. Our code is publicly available on https://github.com/SYZhang0805/DisBack.

Diffusion distillation represents a highly promising direction for achieving faithful text-to-image generation in a few sampling steps. However, despite recent successes, existing distilled models still do not provide the full spectrum of diffusion abilities, such as real image inversion, which enables many precise image manipulation methods. This work aims to enrich distilled text-to-image diffusion models with the ability to effectively encode real images into their latent space. To this end, we introduce invertible Consistency Distillation (iCD), a generalized consistency distillation framework that facilitates both high-quality image synthesis and accurate image encoding in only 3-4 inference steps. Though the inversion problem for text-to-image diffusion models gets exacerbated by high classifier-free guidance scales, we notice that dynamic guidance significantly reduces reconstruction errors without noticeable degradation in generation performance. As a result, we demonstrate that iCD equipped with dynamic guidance may serve as a highly effective tool for zero-shot text-guided image editing, competing with more expensive state-of-the-art alternatives.

We propose two approaches to extend the notion of knowledge distillation to Gaussian Process Regression (GPR) and Gaussian Process Classification (GPC); data-centric and distribution-centric. The data-centric approach resembles most current distillation techniques for machine learning, and refits a model on deterministic predictions from the teacher, while the distribution-centric approach, re-uses the full probabilistic posterior for the next iteration. By analyzing the properties of these approaches, we show that the data-centric approach for GPR closely relates to known results for self-distillation of kernel ridge regression and that the distribution-centric approach for GPR corresponds to ordinary GPR with a very particular choice of hyperparameters. Furthermore, we demonstrate that the distribution-centric approach for GPC approximately corresponds to data duplication and a particular scaling of the covariance and that the data-centric approach for GPC requires redefining the model from a Binomial likelihood to a continuous Bernoulli likelihood to be well-specified. To the best of our knowledge, our proposed approaches are the first to formulate knowledge distillation specifically for Gaussian Process models.

Although large models have shown a strong capacity to solve large-scale problems in many areas including natural language and computer vision, their voluminous parameters are hard to deploy in a real-time system due to computational and energy constraints. Addressing this, knowledge distillation through Teacher-Student architecture offers a sustainable pathway to compress the knowledge of large models into more manageable sizes without significantly compromising performance. To enhance the robustness and interpretability of this framework, it is critical to understand how individual training data impact model performance, which is an area that remains underexplored. We propose the Knowledge Distillation with Adaptive Influence Weight (KD-AIF) framework which leverages influence functions from robust statistics to assign weights to training data, grounded in the four key SAFE principles: Sustainability, Accuracy, Fairness, and Explainability. This novel approach not only optimizes distillation but also increases transparency by revealing the significance of different data. The exploration of various update mechanisms within the KD-AIF framework further elucidates its potential to significantly improve learning efficiency and generalization in student models, marking a step toward more explainable and deployable Large Models. KD-AIF is effective in knowledge distillation while also showing exceptional performance in semi-supervised learning with outperforms existing baselines and methods in multiple benchmarks (CIFAR-100, CIFAR-10-4k, SVHN-1k, and GLUE).

Knowledge distillation (KD) has been recognized as an effective tool to compress and accelerate models. However, current KD approaches generally suffer from an accuracy drop and/or an excruciatingly long distillation process. In this paper, we tackle the issue by first providing a new insight into a phenomenon that we call the Inter-Block Optimization Entanglement (IBOE), which makes the conventional end-to-end KD approaches unstable with noisy gradients. We then propose StableKD, a novel KD framework that breaks the IBOE and achieves more stable optimization. StableKD distinguishes itself through two operations: Decomposition and Recomposition, where the former divides a pair of teacher and student networks into several blocks for separate distillation, and the latter progressively merges them back, evolving towards end-to-end distillation. We conduct extensive experiments on CIFAR100, Imagewoof, and ImageNet datasets with various teacher-student pairs. Compared to other KD approaches, our simple yet effective StableKD greatly boosts the model accuracy by 1% ~ 18%, speeds up the convergence up to 10 times, and outperforms them with only 40% of the training data.

Knowledge Distillation (KD) consists of transferring “knowledge” from one machine learning model (the teacher) to another (the student). Commonly, the teacher is a high-capacity model with formidable performance, while the student is more compact. By transferring knowledge, one hopes to benefit from the student’s compactness, without sacrificing too much performance. We study KD from a new perspective: rather than compressing models, we train students parameterized identically to their teachers. Surprisingly, these Born-Again Networks (BANs), outperform their teachers significantly, both on computer vision and language modeling tasks. Our experiments with BANs based on DenseNets demonstrate state-of-the-art performance on the CIFAR-10 (3.5%) and CIFAR-100 (15.5%) datasets, by validation error. Additional experiments explore two distillation objectives: (i) Confidence-Weighted by Teacher Max (CWTM) and (ii) Dark Knowledge with Permuted Predictions (DKPP). Both methods elucidate the essential components of KD, demonstrating the effect of the teacher outputs on both predicted and non-predicted classes.

In long-horizon tasks, recent agents based on Large Language Models (LLMs) face a significant challenge that sparse, outcome-based rewards make it difficult to assign credit to intermediate steps. Previous methods mainly focus on creating dense reward signals to guide learning, either through traditional reinforcement learning techniques like inverse reinforcement learning or by using Process Reward Models for step-by-step feedback. In this paper, we identify a fundamental problem in the learning dynamics of LLMs: the magnitude of policy gradients is inherently coupled with the entropy, which leads to inefficient small updates for confident correct actions and potentially destabilizes large updates for uncertain ones. To resolve this, we propose Entropy-Modulated Policy Gradients (EMPG), a framework that re-calibrates the learning signal based on step-wise uncertainty and the final task outcome. EMPG amplifies updates for confident correct actions, penalizes confident errors, and attenuates updates from uncertain steps to stabilize exploration. We further introduce a bonus term for future clarity that encourages agents to find more predictable solution paths. Through comprehensive experiments on three challenging agent tasks, WebShop, ALFWorld, and Deep Search, we demonstrate that EMPG achieves substantial performance gains and significantly outperforms strong policy gradient baselines. Project page is at https://empgseed-seed.github.io/

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.

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.

LLMs have boosted progress in many AI applications. Recently, there were attempts to distill the vast knowledge of LLMs into information retrieval systems. Those distillation methods mostly use output probabilities of LLMs which are unavailable in the latest black-box LLMs. We propose Syntriever, a training framework for retrievers using synthetic data from black-box LLMs. Syntriever consists of two stages. Firstly in the distillation stage, we synthesize relevant and plausibly irrelevant passages and augmented queries using chain-of-thoughts for the given queries. LLM is asked to self-verify the synthetic data for possible hallucinations, after which retrievers are trained with a loss designed to cluster the embeddings of relevant passages. Secondly in the alignment stage, we align the retriever with the preferences of LLMs. We propose a preference modeling called partial Plackett-Luce ranking to learn LLM preferences with regularization which prevents the model from deviating excessively from that trained in the distillation stage. Experiments show that Syntriever achieves state-of-the-art performances on benchmark datasets from various domains in nDCG@K. The code is available at https://github.com/kmswin1/Syntriever{https://github.com/kmswin1/Syntriever}.

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.

Fast and high-quality language generation is the holy grail that people pursue in the age of AI. In this work, we introduce Discrete Diffusion Divergence Instruct (DiDi-Instruct), a training-based method that initializes from a pre-trained (masked) discrete diffusion language model (dLLM) and distills a few-step student for fast generation. The resulting DiDi-Instruct model achieves comparable or superior performance to its dLLM teacher and the GPT-2 baseline while enabling up to 64times acceleration. The theoretical foundation of DiDi-Instruct is a novel framework based on integral KL-divergence minimization, which yields a practical training algorithm. We further introduce grouped reward normalization, intermediate-state matching, and the reward-guided ancestral sampler that significantly improve training stability, model coverage, and inference quality. On OpenWebText, DiDi-Instruct achieves perplexity from 62.2 (8 NFEs) to 18.4 (128 NFEs), which outperforms prior accelerated dLLMs and GPT-2 baseline. These gains come with a negligible entropy loss (around 1%) and reduce additional training wall-clock time by more than 20times compared to competing dLLM distillation methods. We further validate the robustness and effectiveness of DiDi-Instruct through extensive ablation studies, model scaling, and the generation of discrete protein sequences. In conclusion, DiDi-Instruct is an efficient yet effective distillation method, enabling language generation in the blink of an eye. We will release both code and models at github.com/haoyangzheng-ai/didi-instruct.

Current video diffusion models achieve impressive generation quality but struggle in interactive applications due to bidirectional attention dependencies. The generation of a single frame requires the model to process the entire sequence, including the future. We address this limitation by adapting a pretrained bidirectional diffusion transformer to a causal transformer that generates frames on-the-fly. To further reduce latency, we extend distribution matching distillation (DMD) to videos, distilling 50-step diffusion model into a 4-step generator. To enable stable and high-quality distillation, we introduce a student initialization scheme based on teacher's ODE trajectories, as well as an asymmetric distillation strategy that supervises a causal student model with a bidirectional teacher. This approach effectively mitigates error accumulation in autoregressive generation, allowing long-duration video synthesis despite training on short clips. Our model supports fast streaming generation of high quality videos at 9.4 FPS on a single GPU thanks to KV caching. Our approach also enables streaming video-to-video translation, image-to-video, and dynamic prompting in a zero-shot manner. We will release the code based on an open-source model in the future.

Diffusion models have achieved remarkable generation quality, but they suffer from significant inference cost due to their reliance on multiple sequential denoising steps, motivating recent efforts to distill this inference process into a few-step regime. However, existing distillation methods typically approximate the teacher trajectory by using linear shortcuts, which makes it difficult to match its constantly changing tangent directions as velocities evolve across timesteps, thereby leading to quality degradation. To address this limitation, we propose ArcFlow, a few-step distillation framework that explicitly employs non-linear flow trajectories to approximate pre-trained teacher trajectories. Concretely, ArcFlow parameterizes the velocity field underlying the inference trajectory as a mixture of continuous momentum processes. This enables ArcFlow to capture velocity evolution and extrapolate coherent velocities to form a continuous non-linear trajectory within each denoising step. Importantly, this parameterization admits an analytical integration of this non-linear trajectory, which circumvents numerical discretization errors and results in high-precision approximation of the teacher trajectory. To train this parameterization into a few-step generator, we implement ArcFlow via trajectory distillation on pre-trained teacher models using lightweight adapters. This strategy ensures fast, stable convergence while preserving generative diversity and quality. Built on large-scale models (Qwen-Image-20B and FLUX.1-dev), ArcFlow only fine-tunes on less than 5% of original parameters and achieves a 40x speedup with 2 NFEs over the original multi-step teachers without significant quality degradation. Experiments on benchmarks show the effectiveness of ArcFlow both qualitatively and quantitatively.

For RL algorithms, appropriate entropy control is crucial to their effectiveness. To control the policy entropy, a commonly used method is entropy regularization, which is adopted in various popular RL algorithms including PPO, SAC and A3C. Although entropy regularization proves effective in robotic and games RL conventionally, studies found that it gives weak to no gains in LLM-RL training. In this work, we study the issues of entropy bonus in LLM-RL setting. Specifically, we first argue that the conventional entropy regularization suffers from the LLM's extremely large response space and the sparsity of the optimal outputs. As a remedy, we propose AEnt, an entropy control method that utilizes a new clamped entropy bonus with an automatically adjusted coefficient. The clamped entropy is evaluated with the re-normalized policy defined on certain smaller token space, which encourages exploration within a more compact response set. In addition, the algorithm automatically adjusts entropy coefficient according to the clamped entropy value, effectively controlling the entropy-induced bias while leveraging the entropy's benefits. AEnt is tested in math-reasoning tasks under different base models and datasets, and it is observed that AEnt outperforms the baselines consistently across multiple benchmarks.

Probabilistic Circuits (PCs) are a general and unified computational framework for tractable probabilistic models that support efficient computation of various inference tasks (e.g., computing marginal probabilities). Towards enabling such reasoning capabilities in complex real-world tasks, Liu et al. (2022) propose to distill knowledge (through latent variable assignments) from less tractable but more expressive deep generative models. However, it is still unclear what factors make this distillation work well. In this paper, we theoretically and empirically discover that the performance of a PC can exceed that of its teacher model. Therefore, instead of performing distillation from the most expressive deep generative model, we study what properties the teacher model and the PC should have in order to achieve good distillation performance. This leads to a generic algorithmic improvement as well as other data-type-specific ones over the existing latent variable distillation pipeline. Empirically, we outperform SoTA TPMs by a large margin on challenging image modeling benchmarks. In particular, on ImageNet32, PCs achieve 4.06 bits-per-dimension, which is only 0.34 behind variational diffusion models (Kingma et al., 2021).

Knowledge distillation has emerged as a pivotal technique for transferring knowledge from stronger large language models (LLMs) to smaller, more efficient models. However, traditional distillation approaches face challenges related to knowledge conflicts and high resource demands, particularly when leveraging multiple teacher models. In this paper, we introduce the concept of Knowledge Purification, which consolidates the rationales from multiple teacher LLMs into a single rationale, thereby mitigating conflicts and enhancing efficiency. To investigate the effectiveness of knowledge purification, we further propose five purification methods from various perspectives. Our experiments demonstrate that these methods not only improve the performance of the distilled model but also effectively alleviate knowledge conflicts. Moreover, router-based methods exhibit robust generalization capabilities, underscoring the potential of innovative purification techniques in optimizing multi-teacher distillation and facilitating the practical deployment of powerful yet lightweight models.

The application of diffusion models in 3D LiDAR scene completion is limited due to diffusion's slow sampling speed. Score distillation accelerates diffusion sampling but with performance degradation, while post-training with direct policy optimization (DPO) boosts performance using preference data. This paper proposes Distillation-DPO, a novel diffusion distillation framework for LiDAR scene completion with preference aligment. First, the student model generates paired completion scenes with different initial noises. Second, using LiDAR scene evaluation metrics as preference, we construct winning and losing sample pairs. Such construction is reasonable, since most LiDAR scene metrics are informative but non-differentiable to be optimized directly. Third, Distillation-DPO optimizes the student model by exploiting the difference in score functions between the teacher and student models on the paired completion scenes. Such procedure is repeated until convergence. Extensive experiments demonstrate that, compared to state-of-the-art LiDAR scene completion diffusion models, Distillation-DPO achieves higher-quality scene completion while accelerating the completion speed by more than 5-fold. Our method is the first to explore adopting preference learning in distillation to the best of our knowledge and provide insights into preference-aligned distillation. Our code is public available on https://github.com/happyw1nd/DistillationDPO.

Recent advances in diffusion transformers (DiTs) have set new standards in image generation, yet remain impractical for on-device deployment due to their high computational and memory costs. In this work, we present an efficient DiT framework tailored for mobile and edge devices that achieves transformer-level generation quality under strict resource constraints. Our design combines three key components. First, we propose a compact DiT architecture with an adaptive global-local sparse attention mechanism that balances global context modeling and local detail preservation. Second, we propose an elastic training framework that jointly optimizes sub-DiTs of varying capacities within a unified supernetwork, allowing a single model to dynamically adjust for efficient inference across different hardware. Finally, we develop Knowledge-Guided Distribution Matching Distillation, a step-distillation pipeline that integrates the DMD objective with knowledge transfer from few-step teacher models, producing high-fidelity and low-latency generation (e.g., 4-step) suitable for real-time on-device use. Together, these contributions enable scalable, efficient, and high-quality diffusion models for deployment on diverse hardware.

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.

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.

Knowledge distillation compresses large teachers into smaller students, but performance saturates at a loss floor that persists across training methods and objectives. We argue this floor is geometric: neural networks represent far more features than dimensions through superposition, and a student of width d_S can encode at most d_S cdot g(α) features, where g(α) = 1/((1-α)ln1{1-α}) is a sparsity-dependent capacity function. Features beyond this budget are permanently lost, yielding an importance-weighted loss floor. We validate on a toy model (48 configurations, median accuracy >93%) and on Pythia-410M, where sparse autoencoders measure F approx 28{,}700 features at αapprox 0.992 (critical width d_S^* approx 1{,}065). Distillation into five student widths confirms the predicted monotonic floor ordering. The observed floor decomposes into a geometric component and a width-independent architectural baseline (R^2 = 0.993). Linear probing shows coarse concepts survive even 88% feature loss, revealing the floor arises from aggregate loss of fine-grained features in the importance distribution's long tail. Our results connect representation geometry to distillation limits and provide a practical tool for predicting distillation performance from SAE measurements alone.

Diffusion distillation has dramatically accelerated class-conditional image synthesis, but its applicability to open-ended text-to-image (T2I) generation is still unclear. We present the first systematic study that adapts and compares state-of-the-art distillation techniques on a strong T2I teacher model, FLUX.1-lite. By casting existing methods into a unified framework, we identify the key obstacles that arise when moving from discrete class labels to free-form language prompts. Beyond a thorough methodological analysis, we offer practical guidelines on input scaling, network architecture, and hyperparameters, accompanied by an open-source implementation and pretrained student models. Our findings establish a solid foundation for deploying fast, high-fidelity, and resource-efficient diffusion generators in real-world T2I applications. Code is available on github.com/alibaba-damo-academy/T2I-Distill.

Recent hybrid video generation models combine autoregressive temporal dynamics with diffusion-based spatial denoising, but their sequential, iterative nature leads to error accumulation and long inference times. In this work, we propose a distillation-based framework for efficient causal video generation that enables high-quality synthesis with extremely limited denoising steps. Our approach builds upon the Distribution Matching Distillation (DMD) framework and proposes a novel Adversarial Self-Distillation (ASD) strategy, which aligns the outputs of the student model's n-step denoising process with its (n+1)-step version at the distribution level. This design provides smoother supervision by bridging small intra-student gaps and more informative guidance by combining teacher knowledge with locally consistent student behavior, substantially improving training stability and generation quality in extremely few-step scenarios (e.g., 1-2 steps). In addition, we present a First-Frame Enhancement (FFE) strategy, which allocates more denoising steps to the initial frames to mitigate error propagation while applying larger skipping steps to later frames. Extensive experiments on VBench demonstrate that our method surpasses state-of-the-art approaches in both one-step and two-step video generation. Notably, our framework produces a single distilled model that flexibly supports multiple inference-step settings, eliminating the need for repeated re-distillation and enabling efficient, high-quality video synthesis.

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), 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.

Diffusion models have demonstrated excellent potential for generating diverse images. However, their performance often suffers from slow generation due to iterative denoising. Knowledge distillation has been recently proposed as a remedy that can reduce the number of inference steps to one or a few without significant quality degradation. However, existing distillation methods either require significant amounts of offline computation for generating synthetic training data from the teacher model or need to perform expensive online learning with the help of real data. In this work, we present a novel technique called BOOT, that overcomes these limitations with an efficient data-free distillation algorithm. The core idea is to learn a time-conditioned model that predicts the output of a pre-trained diffusion model teacher given any time step. Such a model can be efficiently trained based on bootstrapping from two consecutive sampled steps. Furthermore, our method can be easily adapted to large-scale text-to-image diffusion models, which are challenging for conventional methods given the fact that the training sets are often large and difficult to access. We demonstrate the effectiveness of our approach on several benchmark datasets in the DDIM setting, achieving comparable generation quality while being orders of magnitude faster than the diffusion teacher. The text-to-image results show that the proposed approach is able to handle highly complex distributions, shedding light on more efficient generative modeling.

Knowledge distillation aims to learn a lightweight student network from a pre-trained teacher network. In practice, existing knowledge distillation methods are usually infeasible when the original training data is unavailable due to some privacy issues and data management considerations. Therefore, data-free knowledge distillation approaches proposed to collect training instances from the Internet. However, most of them have ignored the common distribution shift between the instances from original training data and webly collected data, affecting the reliability of the trained student network. To solve this problem, we propose a novel method dubbed ``Knowledge Distillation between Different Distributions" (KD^{3}), which consists of three components. Specifically, we first dynamically select useful training instances from the webly collected data according to the combined predictions of teacher network and student network. Subsequently, we align both the weighted features and classifier parameters of the two networks for knowledge memorization. Meanwhile, we also build a new contrastive learning block called MixDistribution to generate perturbed data with a new distribution for instance alignment, so that the student network can further learn a distribution-invariant representation. Intensive experiments on various benchmark datasets demonstrate that our proposed KD^{3} can outperform the state-of-the-art data-free knowledge distillation approaches.

We introduce LLaVA-MoD, a novel framework designed to enable the efficient training of small-scale Multimodal Language Models (s-MLLM) by distilling knowledge from large-scale MLLM (l-MLLM). Our approach tackles two fundamental challenges in MLLM distillation. First, we optimize the network structure of s-MLLM by integrating a sparse Mixture of Experts (MoE) architecture into the language model, striking a balance between computational efficiency and model expressiveness. Second, we propose a progressive knowledge transfer strategy to ensure comprehensive knowledge migration. This strategy begins with mimic distillation, where we minimize the Kullback-Leibler (KL) divergence between output distributions to enable the student model to emulate the teacher network's understanding. Following this, we introduce preference distillation via Direct Preference Optimization (DPO), where the key lies in treating l-MLLM as the reference model. During this phase, the s-MLLM's ability to discriminate between superior and inferior examples is significantly enhanced beyond l-MLLM, leading to a better student that surpasses its teacher, particularly in hallucination benchmarks. Extensive experiments demonstrate that LLaVA-MoD outperforms existing models across various multimodal benchmarks while maintaining a minimal number of activated parameters and low computational costs. Remarkably, LLaVA-MoD, with only 2B activated parameters, surpasses Qwen-VL-Chat-7B by an average of 8.8% across benchmarks, using merely 0.3% of the training data and 23% trainable parameters. These results underscore LLaVA-MoD's ability to effectively distill comprehensive knowledge from its teacher model, paving the way for the development of more efficient MLLMs. The code will be available on: https://github.com/shufangxun/LLaVA-MoD.

Flow-based 3D generation models typically require dozens of sampling steps during inference. Though few-step distillation methods, particularly Consistency Models (CMs), have achieved substantial advancements in accelerating 2D diffusion models, they remain under-explored for more complex 3D generation tasks. In this study, we propose a novel framework, MDT-dist, for few-step 3D flow distillation. Our approach is built upon a primary objective: distilling the pretrained model to learn the Marginal-Data Transport. Directly learning this objective needs to integrate the velocity fields, while this integral is intractable to be implemented. Therefore, we propose two optimizable objectives, Velocity Matching (VM) and Velocity Distillation (VD), to equivalently convert the optimization target from the transport level to the velocity and the distribution level respectively. Velocity Matching (VM) learns to stably match the velocity fields between the student and the teacher, but inevitably provides biased gradient estimates. Velocity Distillation (VD) further enhances the optimization process by leveraging the learned velocity fields to perform probability density distillation. When evaluated on the pioneer 3D generation framework TRELLIS, our method reduces sampling steps of each flow transformer from 25 to 1 or 2, achieving 0.68s (1 step x 2) and 0.94s (2 steps x 2) latency with 9.0x and 6.5x speedup on A800, while preserving high visual and geometric fidelity. Extensive experiments demonstrate that our method significantly outperforms existing CM distillation methods, and enables TRELLIS to achieve superior performance in few-step 3D generation.

While advancements in the reasoning abilities of LLMs have significantly enhanced their performance in solving mathematical problems, coding tasks, and general puzzles, their effectiveness in accurately adhering to instructions remains inconsistent, particularly with more complex directives. Our investigation identifies lazy reasoning during the thinking stage as the primary factor contributing to poor instruction adherence. To mitigate this issue, we propose a comprehensive framework designed to enable rigorous reasoning processes involving preview and self-checking, essential for satisfying strict instruction constraints. Specifically, we first generate instructions with complex constraints and apply a filtering process to obtain valid prompts, resulting in three distinct prompt datasets categorized as hard, easy, and pass. Then, we employ rejection sampling on the pass prompts to curate a small yet high-quality dataset, enabling a cold-start initialization of the model and facilitating its adaptation to effective reasoning patterns. Subsequently, we employ an entropy-preserving supervised fine-tuning (Entropy-SFT) strategy coupled with token-wise entropy-adaptive (TEA-RL) reinforcement learning guided by rule-based dense rewards. This approach encourages the model to transform its reasoning mechanism, ultimately fostering generalizable reasoning abilities that encompass preview and self-checking. Extensive experiments conducted on instruction-following benchmarks demonstrate remarkable performance improvements across various model scales. Notably, our Light-IF-32B model surpasses both larger open-source models such as DeepSeek-R1 and closed-source models like Doubao-1.6.

Diffusion models excel in high-quality generation but suffer from slow inference due to iterative sampling. While recent methods have successfully transformed diffusion models into one-step generators, they neglect model size reduction, limiting their applicability in compute-constrained scenarios. This paper aims to develop small, efficient one-step diffusion models based on the powerful rectified flow framework, by exploring joint compression of inference steps and model size. The rectified flow framework trains one-step generative models using two operations, reflow and distillation. Compared with the original framework, squeezing the model size brings two new challenges: (1) the initialization mismatch between large teachers and small students during reflow; (2) the underperformance of naive distillation on small student models. To overcome these issues, we propose Annealing Reflow and Flow-Guided Distillation, which together comprise our SlimFlow framework. With our novel framework, we train a one-step diffusion model with an FID of 5.02 and 15.7M parameters, outperforming the previous state-of-the-art one-step diffusion model (FID=6.47, 19.4M parameters) on CIFAR10. On ImageNet 64times64 and FFHQ 64times64, our method yields small one-step diffusion models that are comparable to larger models, showcasing the effectiveness of our method in creating compact, efficient one-step diffusion models.

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.

Timestep distillation is an effective approach for improving the generation efficiency of diffusion models. The Consistency Model (CM), as a trajectory-based framework, demonstrates significant potential due to its strong theoretical foundation and high-quality few-step generation. Nevertheless, current continuous-time consistency distillation methods still rely heavily on training data and computational resources, hindering their deployment in resource-constrained scenarios and limiting their scalability to diverse domains. To address this issue, we propose Trajectory-Backward Consistency Model (TBCM), which eliminates the dependence on external training data by extracting latent representations directly from the teacher model's generation trajectory. Unlike conventional methods that require VAE encoding and large-scale datasets, our self-contained distillation paradigm significantly improves both efficiency and simplicity. Moreover, the trajectory-extracted samples naturally bridge the distribution gap between training and inference, thereby enabling more effective knowledge transfer. Empirically, TBCM achieves 6.52 FID and 28.08 CLIP scores on MJHQ-30k under one-step generation, while reducing training time by approximately 40% compared to Sana-Sprint and saving a substantial amount of GPU memory, demonstrating superior efficiency without sacrificing quality. We further reveal the diffusion-generation space discrepancy in continuous-time consistency distillation and analyze how sampling strategies affect distillation performance, offering insights for future distillation research. GitHub Link: https://github.com/hustvl/TBCM.

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.

Knowledge distillation (KD) has been widely used for model compression and knowledge transfer. Typically, a big teacher model trained on sufficient data transfers knowledge to a small student model. However, despite the success of KD, little effort has been made to study whether KD leaks the training data of the teacher model. In this paper, we experimentally reveal that KD suffers from the risk of privacy leakage. To alleviate this issue, we propose a novel knowledge distillation method, swing distillation, which can effectively protect the private information of the teacher model from flowing to the student model. In our framework, the temperature coefficient is dynamically and adaptively adjusted according to the degree of private information contained in the data, rather than a predefined constant hyperparameter. It assigns different temperatures to tokens according to the likelihood that a token in a position contains private information. In addition, we inject noise into soft targets provided to the student model, in order to avoid unshielded knowledge transfer. Experiments on multiple datasets and tasks demonstrate that the proposed swing distillation can significantly reduce (by over 80% in terms of canary exposure) the risk of privacy leakage in comparison to KD with competitive or better performance. Furthermore, swing distillation is robust against the increasing privacy budget.

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.

In this work, we investigate the implicit regularization induced by teacher-student learning dynamics in self-distillation. To isolate its effect, we describe a simple experiment where we consider teachers at random initialization instead of trained teachers. Surprisingly, when distilling a student into such a random teacher, we observe that the resulting model and its representations already possess very interesting characteristics; (1) we observe a strong improvement of the distilled student over its teacher in terms of probing accuracy. (2) The learned representations are data-dependent and transferable between different tasks but deteriorate strongly if trained on random inputs. (3) The student checkpoint contains sparse subnetworks, so-called lottery tickets, and lies on the border of linear basins in the supervised loss landscape. These observations have interesting consequences for several important areas in machine learning: (1) Self-distillation can work solely based on the implicit regularization present in the gradient dynamics without relying on any dark knowledge, (2) self-supervised learning can learn features even in the absence of data augmentation and (3) training dynamics during the early phase of supervised training do not necessarily require label information. Finally, we shed light on an intriguing local property of the loss landscape: the process of feature learning is strongly amplified if the student is initialized closely to the teacher. These results raise interesting questions about the nature of the landscape that have remained unexplored so far. Code is available at https://github.com/safelix/dinopl.

We propose Score-of-Mixture Training (SMT), a novel framework for training one-step generative models by minimizing a class of divergences called the alpha-skew Jensen-Shannon divergence. At its core, SMT estimates the score of mixture distributions between real and fake samples across multiple noise levels. Similar to consistency models, our approach supports both training from scratch (SMT) and distillation using a pretrained diffusion model, which we call Score-of-Mixture Distillation (SMD). It is simple to implement, requires minimal hyperparameter tuning, and ensures stable training. Experiments on CIFAR-10 and ImageNet 64x64 show that SMT/SMD are competitive with and can even outperform existing methods.

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.

Knowledge distillation involves transferring soft labels from a teacher to a student using a shared temperature-based softmax function. However, the assumption of a shared temperature between teacher and student implies a mandatory exact match between their logits in terms of logit range and variance. This side-effect limits the performance of student, considering the capacity discrepancy between them and the finding that the innate logit relations of teacher are sufficient for student to learn. To address this issue, we propose setting the temperature as the weighted standard deviation of logit and performing a plug-and-play Z-score pre-process of logit standardization before applying softmax and Kullback-Leibler divergence. Our pre-process enables student to focus on essential logit relations from teacher rather than requiring a magnitude match, and can improve the performance of existing logit-based distillation methods. We also show a typical case where the conventional setting of sharing temperature between teacher and student cannot reliably yield the authentic distillation evaluation; nonetheless, this challenge is successfully alleviated by our Z-score. We extensively evaluate our method for various student and teacher models on CIFAR-100 and ImageNet, showing its significant superiority. The vanilla knowledge distillation powered by our pre-process can achieve favorable performance against state-of-the-art methods, and other distillation variants can obtain considerable gain with the assistance of our pre-process.

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) has shown great promise in transferring knowledge from larger teacher models to smaller student models. However, existing KD strategies for large language models often minimize output distributions between student and teacher models indiscriminately for each token. This overlooks the imbalanced nature of tokens and their varying transfer difficulties. In response, we propose a distillation strategy called Self-Evolution KD. The core of this approach involves dynamically integrating teacher distribution and one-hot distribution of ground truth into the student distribution as prior knowledge, which promotes the distillation process. It adjusts the ratio of prior knowledge based on token learning difficulty, fully leveraging the teacher model's potential. Experimental results show our method brings an average improvement of approximately 1.4 SacreBLEU points across four translation directions in the WMT22 test sets. Further analysis indicates that the improvement comes from better knowledge transfer from teachers, confirming our hypothesis.

Reinforcement fine-tuning (RFT) is essential for enhancing the reasoning capabilities of large language models (LLM), yet the widely adopted Group Relative Policy Optimization (GRPO) suffers from entropy collapse, where entropy monotonically decreases, exploration vanishes, and policies converge prematurely. Existing entropy-regularized methods only partially alleviate this issue while introducing bias and instability, leaving entropy control unresolved and the connection between entropy, exploration, and performance unclear. We propose Arbitrary Entropy Policy Optimization (AEPO), which eliminates entropy collapse by replacing entropy bonuses with REINFORCE policy gradient on temperature-adjusted distributions and stabilizing entropy through temperature regulation. AEPO integrates three key designs: policy gradient as regularization, distribution as regularization, and REINFORCE as regularization, enabling precise entropy control without distorting optimization. Experiments demonstrate three major contributions: AEPO (1) stabilizes entropy at arbitrary target levels, effectively removing collapse in GRPO; (2) reveals a non-monotonic relation where performance first improves then declines with increasing entropy, clarifying the link between entropy, exploration, and reasoning; and (3) generalizes beyond entropy, providing a broader RFT paradigm where superior target distributions can serve as REINFORCE regularizers.

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.

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.

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.

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.

Dataset Distillation (DD) emerges as a powerful strategy to encapsulate the expansive information of large datasets into significantly smaller, synthetic equivalents, thereby preserving model performance with reduced computational overhead. Pursuing this objective, we introduce the Wasserstein distance, a metric grounded in optimal transport theory, to enhance distribution matching in DD. Our approach employs the Wasserstein barycenter to provide a geometrically meaningful method for quantifying distribution differences and capturing the centroid of distribution sets efficiently. By embedding synthetic data in the feature spaces of pretrained classification models, we facilitate effective distribution matching that leverages prior knowledge inherent in these models. Our method not only maintains the computational advantages of distribution matching-based techniques but also achieves new state-of-the-art performance across a range of high-resolution datasets. Extensive testing demonstrates the effectiveness and adaptability of our method, underscoring the untapped potential of Wasserstein metrics in dataset distillation.

The pursuit of efficient and controllable high-quality content generation remains a central challenge in artificial intelligence-generated content (AIGC). While one-step generators, enabled by diffusion distillation techniques, offer excellent generation quality and computational efficiency, adapting them to new control conditions--such as structural constraints, semantic guidelines, or external inputs--poses a significant challenge. Conventional approaches often necessitate computationally expensive modifications to the base model and subsequent diffusion distillation. This paper introduces Noise Consistency Training (NCT), a novel and lightweight approach to directly integrate new control signals into pre-trained one-step generators without requiring access to original training images or retraining the base diffusion model. NCT operates by introducing an adapter module and employs a noise consistency loss in the noise space of the generator. This loss aligns the adapted model's generation behavior across noises that are conditionally dependent to varying degrees, implicitly guiding it to adhere to the new control. Theoretically, this training objective can be understood as minimizing the distributional distance between the adapted generator and the conditional distribution induced by the new conditions. NCT is modular, data-efficient, and easily deployable, relying only on the pre-trained one-step generator and a control signal model. Extensive experiments demonstrate that NCT achieves state-of-the-art controllable generation in a single forward pass, surpassing existing multi-step and distillation-based methods in both generation quality and computational efficiency. Code is available at https://github.com/Luo-Yihong/NCT

Knowledge distillation methods have recently shown to be a promising direction to speedup the synthesis of large-scale diffusion models by requiring only a few inference steps. While several powerful distillation methods were recently proposed, the overall quality of student samples is typically lower compared to the teacher ones, which hinders their practical usage. In this work, we investigate the relative quality of samples produced by the teacher text-to-image diffusion model and its distilled student version. As our main empirical finding, we discover that a noticeable portion of student samples exhibit superior fidelity compared to the teacher ones, despite the ``approximate'' nature of the student. Based on this finding, we propose an adaptive collaboration between student and teacher diffusion models for effective text-to-image synthesis. Specifically, the distilled model produces the initial sample, and then an oracle decides whether it needs further improvements with a slow teacher model. Extensive experiments demonstrate that the designed pipeline surpasses state-of-the-art text-to-image alternatives for various inference budgets in terms of human preference. Furthermore, the proposed approach can be naturally used in popular applications such as text-guided image editing and controllable generation.

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.