Daily Papers

Comprehensive and constructive evaluation protocols play an important role in the development of sophisticated text-to-video (T2V) generation models. Existing evaluation protocols primarily focus on temporal consistency and content continuity, yet largely ignore the dynamics of video content. Dynamics are an essential dimension for measuring the visual vividness and the honesty of video content to text prompts. In this study, we propose an effective evaluation protocol, termed DEVIL, which centers on the dynamics dimension to evaluate T2V models. For this purpose, we establish a new benchmark comprising text prompts that fully reflect multiple dynamics grades, and define a set of dynamics scores corresponding to various temporal granularities to comprehensively evaluate the dynamics of each generated video. Based on the new benchmark and the dynamics scores, we assess T2V models with the design of three metrics: dynamics range, dynamics controllability, and dynamics-based quality. Experiments show that DEVIL achieves a Pearson correlation exceeding 90% with human ratings, demonstrating its potential to advance T2V generation models. Code is available at https://github.com/MingXiangL/DEVIL.

Audio-driven 3D talking avatar generation is increasingly important in virtual communication, digital humans, and interactive media, where avatars must preserve identity, synchronize lip motion with speech, express emotion, and exhibit lifelike spatial dynamics, collectively defining a broader objective of expressivity. However, achieving this remains challenging due to insufficient training data with limited subject identities, narrow audio representations, and restricted explicit controllability. In this paper, we propose 3DXTalker, an expressive 3D talking avatar through data-curated identity modeling, audio-rich representations, and spatial dynamics controllability. 3DXTalker enables scalable identity modeling via 2D-to-3D data curation pipeline and disentangled representations, alleviating data scarcity and improving identity generalization. Then, we introduce frame-wise amplitude and emotional cues beyond standard speech embeddings, ensuring superior lip synchronization and nuanced expression modulation. These cues are unified by a flow-matching-based transformer for coherent facial dynamics. Moreover, 3DXTalker also enables natural head-pose motion generation while supporting stylized control via prompt-based conditioning. Extensive experiments show that 3DXTalker integrates lip synchronization, emotional expression, and head-pose dynamics within a unified framework, achieves superior performance in 3D talking avatar generation.

Image-to-Video (I2V) generation aims to synthesize a video clip according to a given image and condition (e.g., text). The key challenge of this task lies in simultaneously generating natural motions while preserving the original appearance of the images. However, current I2V diffusion models (I2V-DMs) often produce videos with limited motion degrees or exhibit uncontrollable motion that conflicts with the textual condition. To address these limitations, we propose a novel Extrapolating and Decoupling framework, which introduces model merging techniques to the I2V domain for the first time. Specifically, our framework consists of three separate stages: (1) Starting with a base I2V-DM, we explicitly inject the textual condition into the temporal module using a lightweight, learnable adapter and fine-tune the integrated model to improve motion controllability. (2) We introduce a training-free extrapolation strategy to amplify the dynamic range of the motion, effectively reversing the fine-tuning process to enhance the motion degree significantly. (3) With the above two-stage models excelling in motion controllability and degree, we decouple the relevant parameters associated with each type of motion ability and inject them into the base I2V-DM. Since the I2V-DM handles different levels of motion controllability and dynamics at various denoising time steps, we adjust the motion-aware parameters accordingly over time. Extensive qualitative and quantitative experiments have been conducted to demonstrate the superiority of our framework over existing methods.

Recent text-to-video (T2V) models have demonstrated strong capabilities in producing high-quality, dynamic videos. To improve the visual controllability, recent works have considered fine-tuning pre-trained T2V models to support image-to-video (I2V) generation. However, such adaptation frequently suppresses motion dynamics of generated outputs, resulting in more static videos compared to their T2V counterparts. In this work, we analyze this phenomenon and identify that it stems from the premature exposure to high-frequency details in the input image, which biases the sampling process toward a shortcut trajectory that overfits to the static appearance of the reference image. To address this, we propose adaptive low-pass guidance (ALG), a simple fix to the I2V model sampling procedure to generate more dynamic videos without compromising per-frame image quality. Specifically, ALG adaptively modulates the frequency content of the conditioning image by applying low-pass filtering at the early stage of denoising. Extensive experiments demonstrate that ALG significantly improves the temporal dynamics of generated videos, while preserving image fidelity and text alignment. Especially, under VBench-I2V test suite, ALG achieves an average improvement of 36% in dynamic degree without a significant drop in video quality or image fidelity.

We propose Heterogeneous Masked Autoregression (HMA) for modeling action-video dynamics to generate high-quality data and evaluation in scaling robot learning. Building interactive video world models and policies for robotics is difficult due to the challenge of handling diverse settings while maintaining computational efficiency to run in real time. HMA uses heterogeneous pre-training from observations and action sequences across different robotic embodiments, domains, and tasks. HMA uses masked autoregression to generate quantized or soft tokens for video predictions. \ourshort achieves better visual fidelity and controllability than the previous robotic video generation models with 15 times faster speed in the real world. After post-training, this model can be used as a video simulator from low-level action inputs for evaluating policies and generating synthetic data. See this link https://liruiw.github.io/hma for more information.

World models can foresee the outcomes of different actions, which is of paramount importance for autonomous driving. Nevertheless, existing driving world models still have limitations in generalization to unseen environments, prediction fidelity of critical details, and action controllability for flexible application. In this paper, we present Vista, a generalizable driving world model with high fidelity and versatile controllability. Based on a systematic diagnosis of existing methods, we introduce several key ingredients to address these limitations. To accurately predict real-world dynamics at high resolution, we propose two novel losses to promote the learning of moving instances and structural information. We also devise an effective latent replacement approach to inject historical frames as priors for coherent long-horizon rollouts. For action controllability, we incorporate a versatile set of controls from high-level intentions (command, goal point) to low-level maneuvers (trajectory, angle, and speed) through an efficient learning strategy. After large-scale training, the capabilities of Vista can seamlessly generalize to different scenarios. Extensive experiments on multiple datasets show that Vista outperforms the most advanced general-purpose video generator in over 70% of comparisons and surpasses the best-performing driving world model by 55% in FID and 27% in FVD. Moreover, for the first time, we utilize the capacity of Vista itself to establish a generalizable reward for real-world action evaluation without accessing the ground truth actions.

Jailbreaks on large language models (LLMs) have recently received increasing attention. For a comprehensive assessment of LLM safety, it is essential to consider jailbreaks with diverse attributes, such as contextual coherence and sentiment/stylistic variations, and hence it is beneficial to study controllable jailbreaking, i.e. how to enforce control on LLM attacks. In this paper, we formally formulate the controllable attack generation problem, and build a novel connection between this problem and controllable text generation, a well-explored topic of natural language processing. Based on this connection, we adapt the Energy-based Constrained Decoding with Langevin Dynamics (COLD), a state-of-the-art, highly efficient algorithm in controllable text generation, and introduce the COLD-Attack framework which unifies and automates the search of adversarial LLM attacks under a variety of control requirements such as fluency, stealthiness, sentiment, and left-right-coherence. The controllability enabled by COLD-Attack leads to diverse new jailbreak scenarios which not only cover the standard setting of generating fluent (suffix) attack with continuation constraint, but also allow us to address new controllable attack settings such as revising a user query adversarially with paraphrasing constraint, and inserting stealthy attacks in context with position constraint. Our extensive experiments on various LLMs (Llama-2, Mistral, Vicuna, Guanaco, GPT-3.5, and GPT-4) show COLD-Attack's broad applicability, strong controllability, high success rate, and attack transferability. Our code is available at https://github.com/Yu-Fangxu/COLD-Attack.

The pursuit of controllability as a higher standard of visual content creation has yielded remarkable progress in customizable image synthesis. However, achieving controllable video synthesis remains challenging due to the large variation of temporal dynamics and the requirement of cross-frame temporal consistency. Based on the paradigm of compositional generation, this work presents VideoComposer that allows users to flexibly compose a video with textual conditions, spatial conditions, and more importantly temporal conditions. Specifically, considering the characteristic of video data, we introduce the motion vector from compressed videos as an explicit control signal to provide guidance regarding temporal dynamics. In addition, we develop a Spatio-Temporal Condition encoder (STC-encoder) that serves as a unified interface to effectively incorporate the spatial and temporal relations of sequential inputs, with which the model could make better use of temporal conditions and hence achieve higher inter-frame consistency. Extensive experimental results suggest that VideoComposer is able to control the spatial and temporal patterns simultaneously within a synthesized video in various forms, such as text description, sketch sequence, reference video, or even simply hand-crafted motions. The code and models will be publicly available at https://videocomposer.github.io.

Controlling both camera motion and object dynamics is essential for coherent and expressive video generation, yet current methods typically handle only one motion type or rely on ambiguous 2D cues that entangle camera-induced parallax with true object movement. We present SymphoMotion, a unified motion-control framework that jointly governs camera trajectories and object dynamics within a single model. SymphoMotion features a Camera Trajectory Control mechanism that integrates explicit camera paths with geometry-aware cues to ensure stable, structurally consistent viewpoint transitions, and an Object Dynamics Control mechanism that combines 2D visual guidance with 3D trajectory embeddings to enable depth-aware, spatially coherent object manipulation. To support large-scale training and evaluation, we further construct RealCOD-25K, a comprehensive real-world dataset containing paired camera poses and object-level 3D trajectories across diverse indoor and outdoor scenes, addressing a key data gap in unified motion control. Extensive experiments and user studies show that SymphoMotion significantly outperforms existing methods in visual fidelity, camera controllability, and object-motion accuracy, establishing a new benchmark for unified motion control in video generation.Codes and data are publicly available at https://grenoble-zhang.github.io/SymphoMotion/.

Ultrafast electron microscopy (UEM) has found widespread applications in physics, chemistry, and materials science, enabling real-space imaging of dynamics on ultrafast timescales. Recent advances have pushed the temporal resolution of UEM into the attosecond regime, enabling the attomicroscopy technique to directly visualize electron motion. In this work, we extend the capabilities of this powerful imaging tool to investigate ultrafast electron dynamics in a biological system by imaging and controlling light induced electronic and chemical changes in the conductive network of multicellular cable bacteria. Using electron energy loss spectroscopy (EELS), we first observed a laser induced increase in {\pi}-electron density, accompanied by spectral peak broadening and a blueshift features indicative of enhanced conductivity and structural modification. We also traced the effect of ultrafast laser pumping on bulk plasmon electron oscillations by monitoring changes in the plasmon like resonance peak. Additionally, we visualized laser induced chemical structural changes in cable bacteria in real space. The imaging results revealed carbon enrichment alongside a depletion of nitrogen and oxygen, highlighting the controllability of chemical dynamics. Moreover, time resolved EELS measurements further revealed a picosecond scale decay and recovery of both {\pi}-electron and plasmonic features, attributed to electron phonon coupling. In addition to shedding light on the mechanism of electron motion in cable bacteria, these findings demonstrate ultrafast modulation and switching of conductivity, underscoring their potential as bio-optoelectronic components operating on ultrafast timescales.

A primary bottleneck in large-scale text-to-video generation today is physical consistency and controllability. Despite recent advances, state-of-the-art models often produce unrealistic motions, such as objects falling upward, or abrupt changes in velocity and direction. Moreover, these models lack precise parameter control, struggling to generate physically consistent dynamics under different initial conditions. We argue that this fundamental limitation stems from current models learning motion distributions solely from appearance, while lacking an understanding of the underlying dynamics. In this work, we propose NewtonGen, a framework that integrates data-driven synthesis with learnable physical principles. At its core lies trainable Neural Newtonian Dynamics (NND), which can model and predict a variety of Newtonian motions, thereby injecting latent dynamical constraints into the video generation process. By jointly leveraging data priors and dynamical guidance, NewtonGen enables physically consistent video synthesis with precise parameter control.

The ultimate goal of video generation is to satisfy a fundamental trilemma: achieving high visual quality, maintaining rigorous physical consistency, and enabling precise controllability. While recent models can maintain this balance in simple, isolated scenarios, we observe that this equilibrium is fragile and often breaks down as scene complexity increases (e.g., involving collisions or dense traffic). To address this, we introduce Motion Forcing, a framework designed to stabilize this trilemma even in complex generative tasks. Our key insight is to explicitly decouple physical reasoning from visual synthesis via a hierarchical ``Point-Shape-Appearance'' paradigm. This approach decomposes generation into verifiable stages: modeling complex dynamics as sparse geometric anchors (Point), expanding them into dynamic depth maps that explicitly resolve 3D geometry (Shape), and finally rendering high-fidelity textures (Appearance). Furthermore, to foster robust physical understanding, we employ a Masked Point Recovery strategy. By randomly masking input anchors during training and enforcing the reconstruction of complete dynamic depth, the model is compelled to move beyond passive pattern matching and learn latent physical laws (e.g., inertia) to infer missing trajectories. Extensive experiments on autonomous driving benchmarks show that Motion Forcing significantly outperforms state-of-the-art baselines, maintaining trilemma stability across complex scenes. Evaluations on physics and robotics further confirm our framework's generality.

Recent advancements have integrated camera pose as a user-friendly and physics-informed condition in video diffusion models, enabling precise camera control. In this paper, we identify one of the key challenges as effectively modeling noisy cross-frame interactions to enhance geometry consistency and camera controllability. We innovatively associate the quality of a condition with its ability to reduce uncertainty and interpret noisy cross-frame features as a form of noisy condition. Recognizing that noisy conditions provide deterministic information while also introducing randomness and potential misguidance due to added noise, we propose applying epipolar attention to only aggregate features along corresponding epipolar lines, thereby accessing an optimal amount of noisy conditions. Additionally, we address scenarios where epipolar lines disappear, commonly caused by rapid camera movements, dynamic objects, or occlusions, ensuring robust performance in diverse environments. Furthermore, we develop a more robust and reproducible evaluation pipeline to address the inaccuracies and instabilities of existing camera control metrics. Our method achieves a 25.64% improvement in camera controllability on the RealEstate10K dataset without compromising dynamics or generation quality and demonstrates strong generalization to out-of-domain images. Training and inference require only 24GB and 12GB of memory, respectively, for 16-frame sequences at 256x256 resolution. We will release all checkpoints, along with training and evaluation code. Dynamic videos are best viewed at https://zgctroy.github.io/CamI2V.

There is growing interest in leveraging mechanistic interpretability and controllability to better understand and influence the internal dynamics of large language models (LLMs). However, current methods face fundamental challenges in reliably localizing and manipulating feature representations. Sparse Autoencoders (SAEs) have recently emerged as a promising direction for feature extraction at scale, yet they, too, are limited by incomplete feature isolation and unreliable monosemanticity. To systematically quantify these limitations, we introduce Feature Monosemanticity Score (FMS), a novel metric to quantify feature monosemanticity in latent representation. Building on these insights, we propose Guided Sparse Autoencoders (G-SAE), a method that conditions latent representations on labeled concepts during training. We demonstrate that reliable localization and disentanglement of target concepts within the latent space improve interpretability, detection of behavior, and control. Specifically, our evaluations on toxicity detection, writing style identification, and privacy attribute recognition show that G-SAE not only enhances monosemanticity but also enables more effective and fine-grained steering with less quality degradation. Our findings provide actionable guidelines for measuring and advancing mechanistic interpretability and control of LLMs.

Vision-Language-Action (VLA) models and world models have recently emerged as promising paradigms for general-purpose robotic intelligence, yet their progress is hindered by the lack of reliable evaluation protocols that reflect real-world deployment. Existing benchmarks are largely simulator-centric, which provide controllability but fail to capture the reality gap caused by perception noise, complex contact dynamics, hardware constraints, and system latency. Moreover, fragmented real-world evaluations across different robot platforms prevent fair and reproducible comparison. To address these challenges, we introduce ManipArena, a standardized evaluation framework designed to bridge simulation and real-world execution. ManipArena comprises 20 diverse tasks across 10,812 expert trajectories emphasizing reasoning-oriented manipulation tasks requiring semantic and spatial reasoning, supports multi-level generalization through controlled out-of-distribution settings, and incorporates long-horizon mobile manipulation beyond tabletop scenarios. The framework further provides rich sensory diagnostics, including low-level motor signals, and synchronized real-to-sim environments constructed via high-quality 3D scanning. Together, these features enable fair, realistic, and reproducible evaluation for both VLA and world model approaches, providing a scalable foundation for diagnosing and advancing embodied intelligence systems.

Evaluating the performance of autonomous vehicle planning algorithms necessitates simulating long-tail safety-critical traffic scenarios. However, traditional methods for generating such scenarios often fall short in terms of controllability and realism; they also neglect the dynamics of agent interactions. To address these limitations, we introduce SAFE-SIM, a novel diffusion-based controllable closed-loop safety-critical simulation framework. Our approach yields two distinct advantages: 1) generating realistic long-tail safety-critical scenarios that closely reflect real-world conditions, and 2) providing controllable adversarial behavior for more comprehensive and interactive evaluations. We develop a novel approach to simulate safety-critical scenarios through an adversarial term in the denoising process of diffusion models, which allows an adversarial agent to challenge a planner with plausible maneuvers while all agents in the scene exhibit reactive and realistic behaviors. Furthermore, we propose novel guidance objectives and a partial diffusion process that enables users to control key aspects of the scenarios, such as the collision type and aggressiveness of the adversarial agent, while maintaining the realism of the behavior. We validate our framework empirically using the nuScenes and nuPlan datasets across multiple planners, demonstrating improvements in both realism and controllability. These findings affirm that diffusion models provide a robust and versatile foundation for safety-critical, interactive traffic simulation, extending their utility across the broader autonomous driving landscape. Project website: https://safe-sim.github.io/.

A world model enables an intelligent agent to imagine, predict, and reason about how the world evolves in response to its actions, and accordingly to plan and strategize. While recent video generation models produce realistic visual sequences, they typically operate in the prompt-to-full-video manner without causal control, interactivity, or long-horizon consistency required for purposeful reasoning. Existing world modeling efforts, on the other hand, often focus on restricted domains (e.g., physical, game, or 3D-scene dynamics) with limited depth and controllability, and struggle to generalize across diverse environments and interaction formats. In this work, we introduce PAN, a general, interactable, and long-horizon world model that predicts future world states through high-quality video simulation conditioned on history and natural language actions. PAN employs the Generative Latent Prediction (GLP) architecture that combines an autoregressive latent dynamics backbone based on a large language model (LLM), which grounds simulation in extensive text-based knowledge and enables conditioning on language-specified actions, with a video diffusion decoder that reconstructs perceptually detailed and temporally coherent visual observations, to achieve a unification between latent space reasoning (imagination) and realizable world dynamics (reality). Trained on large-scale video-action pairs spanning diverse domains, PAN supports open-domain, action-conditioned simulation with coherent, long-term dynamics. Extensive experiments show that PAN achieves strong performance in action-conditioned world simulation, long-horizon forecasting, and simulative reasoning compared to other video generators and world models, taking a step towards general world models that enable predictive simulation of future world states for reasoning and acting.

We introduce the WorldScore benchmark, the first unified benchmark for world generation. We decompose world generation into a sequence of next-scene generation tasks with explicit camera trajectory-based layout specifications, enabling unified evaluation of diverse approaches from 3D and 4D scene generation to video generation models. The WorldScore benchmark encompasses a curated dataset of 3,000 test examples that span diverse worlds: static and dynamic, indoor and outdoor, photorealistic and stylized. The WorldScore metrics evaluate generated worlds through three key aspects: controllability, quality, and dynamics. Through extensive evaluation of 19 representative models, including both open-source and closed-source ones, we reveal key insights and challenges for each category of models. Our dataset, evaluation code, and leaderboard can be found at https://haoyi-duan.github.io/WorldScore/

We introduce controlgym, a library of thirty-six safety-critical industrial control settings, and ten infinite-dimensional partial differential equation (PDE)-based control problems. Integrated within the OpenAI Gym/Gymnasium (Gym) framework, controlgym allows direct applications of standard reinforcement learning (RL) algorithms like stable-baselines3. Our control environments complement those in Gym with continuous, unbounded action and observation spaces, motivated by real-world control applications. Moreover, the PDE control environments uniquely allow the users to extend the state dimensionality of the system to infinity while preserving the intrinsic dynamics. This feature is crucial for evaluating the scalability of RL algorithms for control. This project serves the learning for dynamics & control (L4DC) community, aiming to explore key questions: the convergence of RL algorithms in learning control policies; the stability and robustness issues of learning-based controllers; and the scalability of RL algorithms to high- and potentially infinite-dimensional systems. We open-source the controlgym project at https://github.com/xiangyuan-zhang/controlgym.

Ensuring safety is of paramount importance in physical human-robot interaction applications. This requires both adherence to safety constraints defined on the system state, as well as guaranteeing compliant behavior of the robot. If the underlying dynamical system is known exactly, the former can be addressed with the help of control barrier functions. The incorporation of elastic actuators in the robot's mechanical design can address the latter requirement. However, this elasticity can increase the complexity of the resulting system, leading to unmodeled dynamics, such that control barrier functions cannot directly ensure safety. In this paper, we mitigate this issue by learning the unknown dynamics using Gaussian process regression. By employing the model in a feedback linearizing control law, the safety conditions resulting from control barrier functions can be robustified to take into account model errors, while remaining feasible. In order to enforce them on-line, we formulate the derived safety conditions in the form of a second-order cone program. We demonstrate our proposed approach with simulations on a two-degree-of-freedom planar robot with elastic joints.

Even for known nonlinear dynamical systems, feedback controller synthesis is a difficult problem that often requires leveraging the particular structure of the dynamics to induce a stable closed-loop system. For general nonlinear models, including those fit to data, there may not be enough known structure to reliably synthesize a stabilizing feedback controller. In this paper, we discuss a state-dependent nonlinear tracking controller formulation based on a state-dependent Riccati equation for general nonlinear control-affine systems. This formulation depends on a nonlinear factorization of the system of vector fields defining the control-affine dynamics, which always exists under mild smoothness assumptions. We propose a method for learning this factorization from a finite set of data. On a variety of simulated nonlinear dynamical systems, we empirically demonstrate the efficacy of learned versions of this controller in stable trajectory tracking. Alongside our learning method, we evaluate recent ideas in jointly learning a controller and stabilizability certificate for known dynamical systems; we show experimentally that such methods can be frail in comparison.

We consider funnel control for linear infinite-dimensional systems that are impedance passive, meaning that they satisfy an energy balance in which the stored energy equals the squared norm of the state and the supplied power is the inner product of input and output. For the analysis we employ the system node approach, which offers a unified framework for infinite-dimensional systems with boundary and distributed control and observation. The resulting closed-loop dynamics are governed by a nonlinear evolution equation; we establish its solvability and hence the applicability of funnel control to this class. The applicability is illustrated by an Euler-Bernoulli beam, which is studied in two distinct scenarios: once with boundary control and once with distributed control.

It is well-known that inverse dynamics models can improve tracking performance in robot control. These models need to precisely capture the robot dynamics, which consist of well-understood components, e.g., rigid body dynamics, and effects that remain challenging to capture, e.g., stick-slip friction and mechanical flexibilities. Such effects exhibit hysteresis and partial observability, rendering them, particularly challenging to model. Hence, hybrid models, which combine a physical prior with data-driven approaches are especially well-suited in this setting. We present a novel hybrid model formulation that enables us to identify fully physically consistent inertial parameters of a rigid body dynamics model which is paired with a recurrent neural network architecture, allowing us to capture unmodeled partially observable effects using the network memory. We compare our approach against state-of-the-art inverse dynamics models on a 7 degree of freedom manipulator. Using data sets obtained through an optimal experiment design approach, we study the accuracy of offline torque prediction and generalization capabilities of joint learning methods. In control experiments on the real system, we evaluate the model as a feed-forward term for impedance control and show the feedback gains can be drastically reduced to achieve a given tracking accuracy.

This work introduces MotionLCM, extending controllable motion generation to a real-time level. Existing methods for spatial control in text-conditioned motion generation suffer from significant runtime inefficiency. To address this issue, we first propose the motion latent consistency model (MotionLCM) for motion generation, building upon the latent diffusion model (MLD). By employing one-step (or few-step) inference, we further improve the runtime efficiency of the motion latent diffusion model for motion generation. To ensure effective controllability, we incorporate a motion ControlNet within the latent space of MotionLCM and enable explicit control signals (e.g., pelvis trajectory) in the vanilla motion space to control the generation process directly, similar to controlling other latent-free diffusion models for motion generation. By employing these techniques, our approach can generate human motions with text and control signals in real-time. Experimental results demonstrate the remarkable generation and controlling capabilities of MotionLCM while maintaining real-time runtime efficiency.

To enhance the controllability of text-to-image diffusion models, current ControlNet-like models have explored various control signals to dictate image attributes. However, existing methods either handle conditions inefficiently or use a fixed number of conditions, which does not fully address the complexity of multiple conditions and their potential conflicts. This underscores the need for innovative approaches to manage multiple conditions effectively for more reliable and detailed image synthesis. To address this issue, we propose a novel framework, DynamicControl, which supports dynamic combinations of diverse control signals, allowing adaptive selection of different numbers and types of conditions. Our approach begins with a double-cycle controller that generates an initial real score sorting for all input conditions by leveraging pre-trained conditional generation models and discriminative models. This controller evaluates the similarity between extracted conditions and input conditions, as well as the pixel-level similarity with the source image. Then, we integrate a Multimodal Large Language Model (MLLM) to build an efficient condition evaluator. This evaluator optimizes the ordering of conditions based on the double-cycle controller's score ranking. Our method jointly optimizes MLLMs and diffusion models, utilizing MLLMs' reasoning capabilities to facilitate multi-condition text-to-image (T2I) tasks. The final sorted conditions are fed into a parallel multi-control adapter, which learns feature maps from dynamic visual conditions and integrates them to modulate ControlNet, thereby enhancing control over generated images. Through both quantitative and qualitative comparisons, DynamicControl demonstrates its superiority over existing methods in terms of controllability, generation quality and composability under various conditional controls.

Sampling-based algorithms are viewed as practical solutions for high-dimensional motion planning. Recent progress has taken advantage of random geometric graph theory to show how asymptotic optimality can also be achieved with these methods. Achieving this desirable property for systems with dynamics requires solving a two-point boundary value problem (BVP) in the state space of the underlying dynamical system. It is difficult, however, if not impractical, to generate a BVP solver for a variety of important dynamical models of robots or physically simulated ones. Thus, an open challenge was whether it was even possible to achieve optimality guarantees when planning for systems without access to a BVP solver. This work resolves the above question and describes how to achieve asymptotic optimality for kinodynamic planning using incremental sampling-based planners by introducing a new rigorous framework. Two new methods, Stable Sparse-RRT (SST) and SST*, result from this analysis, which are asymptotically near-optimal and optimal, respectively. The techniques are shown to converge fast to high-quality paths, while they maintain only a sparse set of samples, which makes them computationally efficient. The good performance of the planners is confirmed by experimental results using dynamical systems benchmarks, as well as physically simulated robots.

The current dominant paradigm in sensorimotor control, whether imitation or reinforcement learning, is to train policies directly in raw action spaces such as torque, joint angle, or end-effector position. This forces the agent to make decisions individually at each timestep in training, and hence, limits the scalability to continuous, high-dimensional, and long-horizon tasks. In contrast, research in classical robotics has, for a long time, exploited dynamical systems as a policy representation to learn robot behaviors via demonstrations. These techniques, however, lack the flexibility and generalizability provided by deep learning or reinforcement learning and have remained under-explored in such settings. In this work, we begin to close this gap and embed the structure of a dynamical system into deep neural network-based policies by reparameterizing action spaces via second-order differential equations. We propose Neural Dynamic Policies (NDPs) that make predictions in trajectory distribution space as opposed to prior policy learning methods where actions represent the raw control space. The embedded structure allows end-to-end policy learning for both reinforcement and imitation learning setups. We show that NDPs outperform the prior state-of-the-art in terms of either efficiency or performance across several robotic control tasks for both imitation and reinforcement learning setups. Project video and code are available at https://shikharbahl.github.io/neural-dynamic-policies/

Ever since the original algorithm by Nesterov (1983), the true nature of the acceleration phenomenon has remained elusive, with various interpretations of why the method is actually faster. The diagnosis of the algorithm through the lens of Ordinary Differential Equations (ODEs) and the corresponding dynamical system formulation to explain the underlying dynamics has a rich history. In the literature, the ODEs that explain algorithms are typically derived by considering the limiting case of the algorithm maps themselves, that is, an ODE formulation follows the development of an algorithm. This obfuscates the underlying higher order principles and thus provides little evidence of the working of the algorithm. Such has been the case with Nesterov algorithm and the various analogies used to describe the acceleration phenomena, viz, momentum associated with the rolling of a Heavy-Ball down a slope, Hessian damping etc. The main focus of our work is to ideate the genesis of the Nesterov algorithm from the viewpoint of dynamical systems leading to demystifying the mathematical rigour behind the algorithm. Instead of reverse engineering ODEs from discrete algorithms, this work explores tools from the recently developed control paradigm titled Passivity and Immersion approach and the Geometric Singular Perturbation theory which are applied to arrive at the formulation of a dynamical system that explains and models the acceleration phenomena. This perspective helps to gain insights into the various terms present and the sequence of steps used in Nesterovs accelerated algorithm for the smooth strongly convex and the convex case. The framework can also be extended to derive the acceleration achieved using the triple momentum method and provides justifications for the non-convergence to the optimal solution in the Heavy-Ball method.

Diffusion models have emerged as powerful tools for generative tasks, producing high-quality outputs across diverse domains. However, how the generated data responds to the initial noise perturbation in diffusion models remains under-explored, which hinders understanding the controllability of the sampling process. In this work, we first observe an interesting phenomenon: the relationship between the change of generation outputs and the scale of initial noise perturbation is highly linear through the diffusion ODE sampling. Then we provide both theoretical and empirical study to justify this linearity property of this input-output (noise-generation data) relationship. Inspired by these new insights, we propose a novel Controllable and Constrained Sampling method (CCS) together with a new controller algorithm for diffusion models to sample with desired statistical properties while preserving good sample quality. We perform extensive experiments to compare our proposed sampling approach with other methods on both sampling controllability and sampled data quality. Results show that our CCS method achieves more precisely controlled sampling while maintaining superior sample quality and diversity.

As generative models become ubiquitous, there is a critical need for fine-grained control over the generation process. Yet, while controlled generation methods from prompting to fine-tuning proliferate, a fundamental question remains unanswered: are these models truly controllable in the first place? In this work, we provide a theoretical framework to formally answer this question. Framing human-model interaction as a control process, we propose a novel algorithm to estimate the controllable sets of models in a dialogue setting. Notably, we provide formal guarantees on the estimation error as a function of sample complexity: we derive probably-approximately correct bounds for controllable set estimates that are distribution-free, employ no assumptions except for output boundedness, and work for any black-box nonlinear control system (i.e., any generative model). We empirically demonstrate the theoretical framework on different tasks in controlling dialogue processes, for both language models and text-to-image generation. Our results show that model controllability is surprisingly fragile and highly dependent on the experimental setting. This highlights the need for rigorous controllability analysis, shifting the focus from simply attempting control to first understanding its fundamental limits.

Prompt engineering is crucial for deploying LLMs but is poorly understood mathematically. We formalize LLM systems as a class of discrete stochastic dynamical systems to explore prompt engineering through the lens of control theory. We investigate the reachable set of output token sequences R_y(mathbf x_0) for which there exists a control input sequence mathbf u for each mathbf y in R_y(mathbf x_0) that steers the LLM to output mathbf y from initial state sequence mathbf x_0. We offer analytic analysis on the limitations on the controllability of self-attention in terms of reachable set, where we prove an upper bound on the reachable set of outputs R_y(mathbf x_0) as a function of the singular values of the parameter matrices. We present complementary empirical analysis on the controllability of a panel of LLMs, including Falcon-7b, Llama-7b, and Falcon-40b. Our results demonstrate a lower bound on the reachable set of outputs R_y(mathbf x_0) w.r.t. initial state sequences mathbf x_0 sampled from the Wikitext dataset. We find that the correct next Wikitext token following sequence mathbf x_0 is reachable over 97% of the time with prompts of kleq 10 tokens. We also establish that the top 75 most likely next tokens, as estimated by the LLM itself, are reachable at least 85% of the time with prompts of kleq 10 tokens. Intriguingly, short prompt sequences can dramatically alter the likelihood of specific outputs, even making the least likely tokens become the most likely ones. This control-centric analysis of LLMs demonstrates the significant and poorly understood role of input sequences in steering output probabilities, offering a foundational perspective for enhancing language model system capabilities.

Dynamical systems provide a comprehensive way to study complex and changing behaviors across various sciences. Many modern systems are too complicated to analyze directly or we do not have access to models, driving significant interest in learning methods. Koopman operators have emerged as a dominant approach because they allow the study of nonlinear dynamics using linear techniques by solving an infinite-dimensional spectral problem. However, current algorithms face challenges such as lack of convergence, hindering practical progress. This paper addresses a fundamental open question: When can we robustly learn the spectral properties of Koopman operators from trajectory data of dynamical systems, and when can we not? Understanding these boundaries is crucial for analysis, applications, and designing algorithms. We establish a foundational approach that combines computational analysis and ergodic theory, revealing the first fundamental barriers -- universal for any algorithm -- associated with system geometry and complexity, regardless of data quality and quantity. For instance, we demonstrate well-behaved smooth dynamical systems on tori where non-trivial eigenfunctions of the Koopman operator cannot be determined by any sequence of (even randomized) algorithms, even with unlimited training data. Additionally, we identify when learning is possible and introduce optimal algorithms with verification that overcome issues in standard methods. These results pave the way for a sharp classification theory of data-driven dynamical systems based on how many limits are needed to solve a problem. These limits characterize all previous methods, presenting a unified view. Our framework systematically determines when and how Koopman spectral properties can be learned.

In this paper, we propose feedback designs for manipulating a quantum state to a target state by performing sequential measurements. In light of Belavkin's quantum feedback control theory, for a given set of (projective or non-projective) measurements and a given time horizon, we show that finding the measurement selection policy that maximizes the probability of successful state manipulation is an optimal control problem for a controlled Markovian process. The optimal policy is Markovian and can be solved by dynamical programming. Numerical examples indicate that making use of feedback information significantly improves the success probability compared to classical scheme without taking feedback. We also consider other objective functionals including maximizing the expected fidelity to the target state as well as minimizing the expected arrival time. The connections and differences among these objectives are also discussed.

In latent diffusion models, the autoencoder (AE) is typically expected to balance two capabilities: faithful reconstruction and a generation-friendly latent space (e.g., low gFID). In recent ImageNet-scale AE studies, we observe a systematic bias toward generative metrics in handling this trade-off: reconstruction metrics are increasingly under-reported, and ablation-based AE selection often favors the best-gFID configuration even when reconstruction fidelity degrades. We theoretically analyze why this gFID-dominant preference can appear unproblematic for ImageNet generation, yet becomes risky when scaling to controllable diffusion: AEs can induce condition drift, which limits achievable condition alignment. Meanwhile, we find that reconstruction fidelity, especially instance-level measures, better indicates controllability. We empirically validate the impact of tilted autoencoder evaluation on controllability by studying several recent ImageNet AEs. Using a multi-dimensional condition-drift evaluation protocol reflecting controllable generation tasks, we find that gFID is only weakly predictive of condition preservation, whereas reconstruction-oriented metrics are substantially more aligned. ControlNet experiments further confirm that controllability tracks condition preservation rather than gFID. Overall, our results expose a gap between ImageNet-centric AE evaluation and the requirements of scalable controllable diffusion, offering practical guidance for more reliable benchmarking and model selection.

Motion planning under dynamics constraints, i.e., kinodynamic planning, enables safe robot operation by generating dynamically feasible trajectories that the robot can accurately track. For high-\dof robots such as manipulators, sampling-based motion planners are commonly used, especially for complex tasks in cluttered environments. However, enforcing constraints on robot dynamics in such planners requires solving either challenging two-point boundary value problems (BVPs) or propagating robot dynamics over time, both of which are computational bottlenecks that drastically increase planning times. Meanwhile, recent efforts have shown that sampling-based motion planners can generate plans in microseconds using parallelization, but are limited to geometric paths. This paper develops AkinoPDF, a fast parallelized sampling-based kinodynamic motion planning technique for a broad class of differentially flat robot systems, including manipulators, ground and aerial vehicles, and more. Differential flatness allows us to transform the motion planning problem from the original state space to a flat output space, where an analytical time-parameterized solution of the BVP and dynamics integration can be obtained. A trajectory in the flat output space is then converted back to a closed-form dynamically feasible trajectory in the original state space, enabling fast validation via ``single instruction, multiple data" parallelism. Our method is fast, exact, and compatible with any sampling-based motion planner. We extensively verify the effectiveness of our approach in both simulated benchmarks and real experiments with cluttered and dynamic environments, requiring mere microseconds to milliseconds of planning time.

Probabilistic completeness is an important property in motion planning. Although it has been established with clear assumptions for geometric planners, the panorama of completeness results for kinodynamic planners is still incomplete, as most existing proofs rely on strong assumptions that are difficult, if not impossible, to verify on practical systems. In this paper, we focus on an important class of kinodynamic planners, namely those that interpolate trajectories in the state space. We provide a proof of probabilistic completeness for these planners under assumptions that can be readily verified from the system's equations of motion and the user-defined interpolation function. Our proof relies crucially on a property of interpolated trajectories, termed second-order continuity (SOC), which we show is tightly related to the ability of a planner to benefit from denser sampling. We analyze the impact of this property in simulations on a low-torque pendulum. Our results show that a simple RRT using a second-order continuous interpolation swiftly finds solution, while it is impossible for the same planner using standard Bezier curves (which are not SOC) to find any solution.

Mobile manipulation in dynamic environments is challenging due to movable obstacles blocking the robot's path. Traditional methods, which treat navigation and manipulation as separate tasks, often fail in such 'manipulate-to-navigate' scenarios, as obstacles must be removed before navigation. In these cases, active interaction with the environment is required to clear obstacles while ensuring sufficient space for movement. To address the manipulate-to-navigate problem, we propose a reinforcement learning-based approach for learning manipulation actions that facilitate subsequent navigation. Our method combines manipulability priors to focus the robot on high manipulability body positions with affordance maps for selecting high-quality manipulation actions. By focusing on feasible and meaningful actions, our approach reduces unnecessary exploration and allows the robot to learn manipulation strategies more effectively. We present two new manipulate-to-navigate simulation tasks called Reach and Door with the Boston Dynamics Spot robot. The first task tests whether the robot can select a good hand position in the target area such that the robot base can move effectively forward while keeping the end effector position fixed. The second task requires the robot to move a door aside in order to clear the navigation path. Both of these tasks need first manipulation and then navigating the base forward. Results show that our method allows a robot to effectively interact with and traverse dynamic environments. Finally, we transfer the learned policy to a real Boston Dynamics Spot robot, which successfully performs the Reach task.

Controllability plays a crucial role in video generation since it allows users to create desired content. However, existing models largely overlooked the precise control of camera pose that serves as a cinematic language to express deeper narrative nuances. To alleviate this issue, we introduce CameraCtrl, enabling accurate camera pose control for text-to-video(T2V) models. After precisely parameterizing the camera trajectory, a plug-and-play camera module is then trained on a T2V model, leaving others untouched. Additionally, a comprehensive study on the effect of various datasets is also conducted, suggesting that videos with diverse camera distribution and similar appearances indeed enhance controllability and generalization. Experimental results demonstrate the effectiveness of CameraCtrl in achieving precise and domain-adaptive camera control, marking a step forward in the pursuit of dynamic and customized video storytelling from textual and camera pose inputs. Our project website is at: https://hehao13.github.io/projects-CameraCtrl/.

A common pipeline in learning-based control is to iteratively estimate a model of system dynamics, and apply a trajectory optimization algorithm - e.g.~iLQR - on the learned model to minimize a target cost. This paper conducts a rigorous analysis of a simplified variant of this strategy for general nonlinear systems. We analyze an algorithm which iterates between estimating local linear models of nonlinear system dynamics and performing iLQR-like policy updates. We demonstrate that this algorithm attains sample complexity polynomial in relevant problem parameters, and, by synthesizing locally stabilizing gains, overcomes exponential dependence in problem horizon. Experimental results validate the performance of our algorithm, and compare to natural deep-learning baselines.

We introduce Riemannian Lyapunov Optimizers (RLOs), a family of optimization algorithms that unifies classic optimizers within one geometric framework. Unlike heuristic improvements to existing optimizers, RLOs are systematically derived from a novel control-theoretic framework that reinterprets optimization as an extended state discrete-time controlled dynamical system on a Riemannian parameter manifold. Central to this framework is the identification of a Normally Attracting Invariant Manifold (NAIM), which organizes training dynamics into two distinct stages: rapid alignment of the speed state to a target graph, followed by controlled evolution within it. We formalize this by constructing a strict Lyapunov function that certifies convergence to a target manifold. This perspective yields a constructive ``optimizer generator" that not only recovers classic algorithms but enables the principled design of RLOs. We validate our theory via geometric diagnostics and demonstrate that grounding optimizer design in control theory yields state-of-the-art performance in large-scale benchmarks. Overall, RLOs bridge control theory and modern machine learning optimization, providing a unified language and a systematic toolkit for designing stable, effective optimizers.

One of the key capabilities of intelligent agents is the ability to discover useful skills without external supervision. However, the current unsupervised skill discovery methods are often limited to acquiring simple, easy-to-learn skills due to the lack of incentives to discover more complex, challenging behaviors. We introduce a novel unsupervised skill discovery method, Controllability-aware Skill Discovery (CSD), which actively seeks complex, hard-to-control skills without supervision. The key component of CSD is a controllability-aware distance function, which assigns larger values to state transitions that are harder to achieve with the current skills. Combined with distance-maximizing skill discovery, CSD progressively learns more challenging skills over the course of training as our jointly trained distance function reduces rewards for easy-to-achieve skills. Our experimental results in six robotic manipulation and locomotion environments demonstrate that CSD can discover diverse complex skills including object manipulation and locomotion skills with no supervision, significantly outperforming prior unsupervised skill discovery methods. Videos and code are available at https://seohong.me/projects/csd/

We present Kinodynamic RRT*, an incremental sampling-based approach for asymptotically optimal motion planning for robots with linear differential constraints. Our approach extends RRT*, which was introduced for holonomic robots (Karaman et al. 2011), by using a fixed-final-state-free-final-time controller that exactly and optimally connects any pair of states, where the cost function is expressed as a trade-off between the duration of a trajectory and the expended control effort. Our approach generalizes earlier work on extending RRT* to kinodynamic systems, as it guarantees asymptotic optimality for any system with controllable linear dynamics, in state spaces of any dimension. Our approach can be applied to non-linear dynamics as well by using their first-order Taylor approximations. In addition, we show that for the rich subclass of systems with a nilpotent dynamics matrix, closed-form solutions for optimal trajectories can be derived, which keeps the computational overhead of our algorithm compared to traditional RRT* at a minimum. We demonstrate the potential of our approach by computing asymptotically optimal trajectories in three challenging motion planning scenarios: (i) a planar robot with a 4-D state space and double integrator dynamics, (ii) an aerial vehicle with a 10-D state space and linearized quadrotor dynamics, and (iii) a car-like robot with a 5-D state space and non-linear dynamics.

We examine two properties of AI systems: capability (what a system can do) and steerability (how reliably one can shift behavior toward intended outcomes). A central question is whether capability growth reduces steerability and risks control collapse. We also distinguish between authorized steerability (builders reliably reaching intended behaviors) and unauthorized steerability (attackers eliciting disallowed behaviors). This distinction highlights a fundamental safety--security dilemma of AI models: safety requires high steerability to enforce control (e.g., stop/refuse), while security requires low steerability for malicious actors to elicit harmful behaviors. This tension presents a significant challenge for open-weight models, which currently exhibit high steerability via common techniques like fine-tuning or adversarial attacks. Using Qwen3 and InstrumentalEval, we find that a short anti-instrumental prompt suffix sharply reduces the measured convergence rate (e.g., shutdown avoidance, self-replication). For Qwen3-30B Instruct, the convergence rate drops from 81.69% under a pro-instrumental suffix to 2.82% under an anti-instrumental suffix. Under anti-instrumental prompting, larger aligned models show lower convergence rates than smaller ones (Instruct: 2.82% vs. 4.23%; Thinking: 4.23% vs. 9.86%). Code is available at github.com/j-hoscilowicz/instrumental_steering.

Operating robots precisely and at high speeds has been a long-standing goal of robotics research. Balancing these competing demands is key to enabling the seamless collaboration of robots and humans and increasing task performance. However, traditional motor-driven systems often fall short in this balancing act. Due to their rigid and often heavy design exacerbated by positioning the motors into the joints, faster motions of such robots transfer high forces at impact. To enable precise and safe dynamic motions, we introduce a four degree-of-freedom~(DoF) tendon-driven robot arm. Tendons allow placing the actuation at the base to reduce the robot's inertia, which we show significantly reduces peak collision forces compared to conventional robots with motors placed near the joints. Pairing our robot with pneumatic muscles allows generating high forces and highly accelerated motions, while benefiting from impact resilience through passive compliance. Since tendons are subject to additional friction and hence prone to wear and tear, we validate the reliability of our robotic arm on various experiments, including long-term dynamic motions. We also demonstrate its ease of control by quantifying the nonlinearities of the system and the performance on a challenging dynamic table tennis task learned from scratch using reinforcement learning. We open-source the entire hardware design, which can be largely 3D printed, the control software, and a proprioceptive dataset of 25 days of diverse robot motions at webdav.tuebingen.mpg.de/pamy2.

Generative Behavior Cloning (GBC) is a simple yet effective framework for robot learning, particularly in multi-task settings. Recent GBC methods often employ diffusion policies with open-loop (OL) control, where actions are generated via a diffusion process and executed in multi-step chunks without replanning. While this approach has demonstrated strong success rates and generalization, its inherent stochasticity can result in erroneous action sampling, occasionally leading to unexpected task failures. Moreover, OL control suffers from delayed responses, which can degrade performance in noisy or dynamic environments. To address these limitations, we propose two novel techniques to enhance the consistency and reactivity of diffusion policies: (1) self-guidance, which improves action fidelity by leveraging past observations and implicitly promoting future-aware behavior; and (2) adaptive chunking, which selectively updates action sequences when the benefits of reactivity outweigh the need for temporal consistency. Extensive experiments show that our approach substantially improves GBC performance across a wide range of simulated and real-world robotic manipulation tasks. Our code is available at https://github.com/junhyukso/SGAC

Controllable human image animation aims to generate videos from reference images using driving videos. Due to the limited control signals provided by sparse guidance (e.g., skeleton pose), recent works have attempted to introduce additional dense conditions (e.g., depth map) to ensure motion alignment. However, such strict dense guidance impairs the quality of the generated video when the body shape of the reference character differs significantly from that of the driving video. In this paper, we present DisPose to mine more generalizable and effective control signals without additional dense input, which disentangles the sparse skeleton pose in human image animation into motion field guidance and keypoint correspondence. Specifically, we generate a dense motion field from a sparse motion field and the reference image, which provides region-level dense guidance while maintaining the generalization of the sparse pose control. We also extract diffusion features corresponding to pose keypoints from the reference image, and then these point features are transferred to the target pose to provide distinct identity information. To seamlessly integrate into existing models, we propose a plug-and-play hybrid ControlNet that improves the quality and consistency of generated videos while freezing the existing model parameters. Extensive qualitative and quantitative experiments demonstrate the superiority of DisPose compared to current methods. Code: https://github.com/lihxxx/DisPose{https://github.com/lihxxx/DisPose}.

In recent years, significant progress has been made in the development of text-to-image generation models. However, these models still face limitations when it comes to achieving full controllability during the generation process. Often, specific training or the use of limited models is required, and even then, they have certain restrictions. To address these challenges, A two-stage method that effectively combines controllability and high quality in the generation of images is proposed. This approach leverages the expertise of pre-trained models to achieve precise control over the generated images, while also harnessing the power of diffusion models to achieve state-of-the-art quality. By separating controllability from high quality, This method achieves outstanding results. It is compatible with both latent and image space diffusion models, ensuring versatility and flexibility. Moreover, This approach consistently produces comparable outcomes to the current state-of-the-art methods in the field. Overall, This proposed method represents a significant advancement in text-to-image generation, enabling improved controllability without compromising on the quality of the generated images.

Deep reinforcement learning (DRL) has shown significant promise for uncovering sophisticated control policies that interact in environments with complicated dynamics, such as stabilizing the magnetohydrodynamics of a tokamak fusion reactor or minimizing the drag force exerted on an object in a fluid flow. However, these algorithms require an abundance of training examples and may become prohibitively expensive for many applications. In addition, the reliance on deep neural networks often results in an uninterpretable, black-box policy that may be too computationally expensive to use with certain embedded systems. Recent advances in sparse dictionary learning, such as the sparse identification of nonlinear dynamics (SINDy), have shown promise for creating efficient and interpretable data-driven models in the low-data regime. In this work we introduce SINDy-RL, a unifying framework for combining SINDy and DRL to create efficient, interpretable, and trustworthy representations of the dynamics model, reward function, and control policy. We demonstrate the effectiveness of our approaches on benchmark control environments and challenging fluids problems. SINDy-RL achieves comparable performance to state-of-the-art DRL algorithms using significantly fewer interactions in the environment and results in an interpretable control policy orders of magnitude smaller than a deep neural network policy.

The accurate modeling of dynamics in interactive environments is critical for successful long-range prediction. Such a capability could advance Reinforcement Learning (RL) and Planning algorithms, but achieving it is challenging. Inaccuracies in model estimates can compound, resulting in increased errors over long horizons. We approach this problem from the lens of Koopman theory, where the nonlinear dynamics of the environment can be linearized in a high-dimensional latent space. This allows us to efficiently parallelize the sequential problem of long-range prediction using convolution while accounting for the agent's action at every time step. Our approach also enables stability analysis and better control over gradients through time. Taken together, these advantages result in significant improvement over the existing approaches, both in the efficiency and the accuracy of modeling dynamics over extended horizons. We also show that this model can be easily incorporated into dynamics modeling for model-based planning and model-free RL and report promising experimental results.

Synthesizing optimal controllers for dynamical systems often involves solving optimization problems with hard real-time constraints. These constraints determine the class of numerical methods that can be applied: computationally expensive but accurate numerical routines are replaced by fast and inaccurate methods, trading inference time for solution accuracy. This paper provides techniques to improve the quality of optimized control policies given a fixed computational budget. We achieve the above via a hypersolvers approach, which hybridizes a differential equation solver and a neural network. The performance is evaluated in direct and receding-horizon optimal control tasks in both low and high dimensions, where the proposed approach shows consistent Pareto improvements in solution accuracy and control performance.

To enhance controllability in text-to-image generation, ControlNet introduces image-based control signals, while ControlNet++ improves pixel-level cycle consistency between generated images and the input control signal. To avoid the prohibitive cost of back-propagating through the sampling process, ControlNet++ optimizes only low-noise timesteps (e.g., t < 200) using a single-step approximation, which not only ignores the contribution of high-noise timesteps but also introduces additional approximation errors. A straightforward alternative for optimizing controllability across all timesteps is Direct Preference Optimization (DPO), a fine-tuning method that increases model preference for more controllable images (I^{w}) over less controllable ones (I^{l}). However, due to uncertainty in generative models, it is difficult to ensure that win--lose image pairs differ only in controllability while keeping other factors, such as image quality, fixed. To address this, we propose performing preference learning over control conditions rather than generated images. Specifically, we construct winning and losing control signals, c^{w} and c^{l}, and train the model to prefer c^{w}. This method, which we term Condition Preference Optimization (CPO), eliminates confounding factors and yields a low-variance training objective. Our approach theoretically exhibits lower contrastive loss variance than DPO and empirically achieves superior results. Moreover, CPO requires less computation and storage for dataset curation. Extensive experiments show that CPO significantly improves controllability over the state-of-the-art ControlNet++ across multiple control types: over 10% error rate reduction in segmentation, 70--80% in human pose, and consistent 2--5% reductions in edge and depth maps.

While large-scale diffusion models have revolutionized video synthesis, achieving precise control over both multi-subject identity and multi-granularity motion remains a significant challenge. Recent attempts to bridge this gap often suffer from limited motion granularity, control ambiguity, and identity degradation, leading to suboptimal performance on identity preservation and motion control. In this work, we present DreamVideo-Omni, a unified framework enabling harmonious multi-subject customization with omni-motion control via a progressive two-stage training paradigm. In the first stage, we integrate comprehensive control signals for joint training, encompassing subject appearances, global motion, local dynamics, and camera movements. To ensure robust and precise controllability, we introduce a condition-aware 3D rotary positional embedding to coordinate heterogeneous inputs and a hierarchical motion injection strategy to enhance global motion guidance. Furthermore, to resolve multi-subject ambiguity, we introduce group and role embeddings to explicitly anchor motion signals to specific identities, effectively disentangling complex scenes into independent controllable instances. In the second stage, to mitigate identity degradation, we design a latent identity reward feedback learning paradigm by training a latent identity reward model upon a pretrained video diffusion backbone. This provides motion-aware identity rewards in the latent space, prioritizing identity preservation aligned with human preferences. Supported by our curated large-scale dataset and the comprehensive DreamOmni Bench for multi-subject and omni-motion control evaluation, DreamVideo-Omni demonstrates superior performance in generating high-quality videos with precise controllability.

Video generation technologies are developing rapidly and have broad potential applications. Among these technologies, camera control is crucial for generating professional-quality videos that accurately meet user expectations. However, existing camera control methods still suffer from several limitations, including control precision and the neglect of the control for subject motion dynamics. In this work, we propose I2VControl-Camera, a novel camera control method that significantly enhances controllability while providing adjustability over the strength of subject motion. To improve control precision, we employ point trajectory in the camera coordinate system instead of only extrinsic matrix information as our control signal. To accurately control and adjust the strength of subject motion, we explicitly model the higher-order components of the video trajectory expansion, not merely the linear terms, and design an operator that effectively represents the motion strength. We use an adapter architecture that is independent of the base model structure. Experiments on static and dynamic scenes show that our framework outperformances previous methods both quantitatively and qualitatively. The project page is: https://wanquanf.github.io/I2VControlCamera .

We address the problem of learning the dynamics of an unknown non-parametric system linking a target and a feature time series. The feature time series is measured on a sparse and irregular grid, while we have access to only a few points of the target time series. Once learned, we can use these dynamics to predict values of the target from the previous values of the feature time series. We frame this task as learning the solution map of a controlled differential equation (CDE). By leveraging the rich theory of signatures, we are able to cast this non-linear problem as a high-dimensional linear regression. We provide an oracle bound on the prediction error which exhibits explicit dependencies on the individual-specific sampling schemes. Our theoretical results are illustrated by simulations which show that our method outperforms existing algorithms for recovering the full time series while being computationally cheap. We conclude by demonstrating its potential on real-world epidemiological data.

We introduce a new class of time-continuous recurrent neural network models. Instead of declaring a learning system's dynamics by implicit nonlinearities, we construct networks of linear first-order dynamical systems modulated via nonlinear interlinked gates. The resulting models represent dynamical systems with varying (i.e., liquid) time-constants coupled to their hidden state, with outputs being computed by numerical differential equation solvers. These neural networks exhibit stable and bounded behavior, yield superior expressivity within the family of neural ordinary differential equations, and give rise to improved performance on time-series prediction tasks. To demonstrate these properties, we first take a theoretical approach to find bounds over their dynamics and compute their expressive power by the trajectory length measure in latent trajectory space. We then conduct a series of time-series prediction experiments to manifest the approximation capability of Liquid Time-Constant Networks (LTCs) compared to classical and modern RNNs. Code and data are available at https://github.com/raminmh/liquid_time_constant_networks

Dynamical systems with complex behaviours, e.g. immune system cells interacting with a pathogen, are commonly modelled by splitting the behaviour into different regimes, or modes, each with simpler dynamics, and then learning the switching behaviour from one mode to another. Switching Dynamical Systems (SDS) are a powerful tool that automatically discovers these modes and mode-switching behaviour from time series data. While effective, these methods focus on independent objects, where the modes of one object are independent of the modes of the other objects. In this paper, we focus on the more general interacting object setting for switching dynamical systems, where the per-object dynamics also depends on an unknown and dynamically changing subset of other objects and their modes. To this end, we propose a novel graph-based approach for switching dynamical systems, GRAph Switching dynamical Systems (GRASS), in which we use a dynamic graph to characterize interactions between objects and learn both intra-object and inter-object mode-switching behaviour. We introduce two new datasets for this setting, a synthesized ODE-driven particles dataset and a real-world Salsa Couple Dancing dataset. Experiments show that GRASS can consistently outperforms previous state-of-the-art methods.

Controllable image synthesis, which enables fine-grained control over generated outputs, has emerged as a key focus in visual generative modeling. However, controllable generation remains challenging for Visual Autoregressive (VAR) models due to their hierarchical, next-scale prediction style. Existing VAR-based methods often suffer from inefficient control encoding and disruptive injection mechanisms that compromise both fidelity and efficiency. In this work, we present SCALAR, a controllable generation method based on VAR, incorporating a novel Scale-wise Conditional Decoding mechanism. SCALAR leverages a pretrained image encoder to extract semantic control signal encodings, which are projected into scale-specific representations and injected into the corresponding layers of the VAR backbone. This design provides persistent and structurally aligned guidance throughout the generation process. Building on SCALAR, we develop SCALAR-Uni, a unified extension that aligns multiple control modalities into a shared latent space, supporting flexible multi-conditional guidance in a single model. Extensive experiments show that SCALAR achieves superior generation quality and control precision across various tasks.

Controllable character animation is an emerging task that generates character videos controlled by pose sequences from given character images. Although character consistency has made significant progress via reference UNet, another crucial factor, pose control, has not been well studied by existing methods yet, resulting in several issues: 1) The generation may fail when the input pose sequence is corrupted. 2) The hands generated using the DWPose sequence are blurry and unrealistic. 3) The generated video will be shaky if the pose sequence is not smooth enough. In this paper, we present RealisDance to handle all the above issues. RealisDance adaptively leverages three types of poses, avoiding failed generation caused by corrupted pose sequences. Among these pose types, HaMeR provides accurate 3D and depth information of hands, enabling RealisDance to generate realistic hands even for complex gestures. Besides using temporal attention in the main UNet, RealisDance also inserts temporal attention into the pose guidance network, smoothing the video from the pose condition aspect. Moreover, we introduce pose shuffle augmentation during training to further improve generation robustness and video smoothness. Qualitative experiments demonstrate the superiority of RealisDance over other existing methods, especially in hand quality.

Deploying large, complex policies in the real world requires the ability to steer them to fit the needs of a situation. Most common steering approaches, like goal-conditioning, require training the robot policy with a distribution of test-time objectives in mind. To overcome this limitation, we present DynaGuide, a steering method for diffusion policies using guidance from an external dynamics model during the diffusion denoising process. DynaGuide separates the dynamics model from the base policy, which gives it multiple advantages, including the ability to steer towards multiple objectives, enhance underrepresented base policy behaviors, and maintain robustness on low-quality objectives. The separate guidance signal also allows DynaGuide to work with off-the-shelf pretrained diffusion policies. We demonstrate the performance and features of DynaGuide against other steering approaches in a series of simulated and real experiments, showing an average steering success of 70% on a set of articulated CALVIN tasks and outperforming goal-conditioning by 5.4x when steered with low-quality objectives. We also successfully steer an off-the-shelf real robot policy to express preference for particular objects and even create novel behavior. Videos and more can be found on the project website: https://dynaguide.github.io

Achieving both realism and controllability in interactive closed-loop traffic simulation remains a key challenge in autonomous driving. Data-driven simulation methods reproduce realistic trajectories but suffer from covariate shift in closed-loop deployment, compounded by simplified dynamics models that further reduce reliability. Conversely, physics-based simulation methods enhance reliable and controllable closed-loop interactions but often lack expert demonstrations, compromising realism. To address these challenges, we introduce a dual-stage AV-centered simulation framework that conducts open-loop imitation learning pre-training in a data-driven simulator to capture trajectory-level realism and multimodality, followed by closed-loop reinforcement learning fine-tuning in a physics-based simulator to enhance controllability and mitigate covariate shift. In the fine-tuning stage, we propose RIFT, a simple yet effective closed-loop RL fine-tuning strategy that preserves the trajectory-level multimodality through a GRPO-style group-relative advantage formulation, while enhancing controllability and training stability by replacing KL regularization with the dual-clip mechanism. Extensive experiments demonstrate that RIFT significantly improves the realism and controllability of generated traffic scenarios, providing a robust platform for evaluating autonomous vehicle performance in diverse and interactive scenarios.

We introduce a method for generating realistic pedestrian trajectories and full-body animations that can be controlled to meet user-defined goals. We draw on recent advances in guided diffusion modeling to achieve test-time controllability of trajectories, which is normally only associated with rule-based systems. Our guided diffusion model allows users to constrain trajectories through target waypoints, speed, and specified social groups while accounting for the surrounding environment context. This trajectory diffusion model is integrated with a novel physics-based humanoid controller to form a closed-loop, full-body pedestrian animation system capable of placing large crowds in a simulated environment with varying terrains. We further propose utilizing the value function learned during RL training of the animation controller to guide diffusion to produce trajectories better suited for particular scenarios such as collision avoidance and traversing uneven terrain. Video results are available on the project page at https://nv-tlabs.github.io/trace-pace .

State density distribution, in contrast to worst-case reachability, can be leveraged for safety-related problems to better quantify the likelihood of the risk for potentially hazardous situations. In this work, we propose a data-driven method to compute the density distribution of reachable states for nonlinear and even black-box systems. Our semi-supervised approach learns system dynamics and the state density jointly from trajectory data, guided by the fact that the state density evolution follows the Liouville partial differential equation. With the help of neural network reachability tools, our approach can estimate the set of all possible future states as well as their density. Moreover, we could perform online safety verification with probability ranges for unsafe behaviors to occur. We use an extensive set of experiments to show that our learned solution can produce a much more accurate estimate on density distribution, and can quantify risks less conservatively and flexibly comparing with worst-case analysis.

Simulated humanoids are an appealing research domain due to their physical capabilities. Nonetheless, they are also challenging to control, as a policy must drive an unstable, discontinuous, and high-dimensional physical system. One widely studied approach is to utilize motion capture (MoCap) data to teach the humanoid agent low-level skills (e.g., standing, walking, and running) that can then be re-used to synthesize high-level behaviors. However, even with MoCap data, controlling simulated humanoids remains very hard, as MoCap data offers only kinematic information. Finding physical control inputs to realize the demonstrated motions requires computationally intensive methods like reinforcement learning. Thus, despite the publicly available MoCap data, its utility has been limited to institutions with large-scale compute. In this work, we dramatically lower the barrier for productive research on this topic by training and releasing high-quality agents that can track over three hours of MoCap data for a simulated humanoid in the dm_control physics-based environment. We release MoCapAct (Motion Capture with Actions), a dataset of these expert agents and their rollouts, which contain proprioceptive observations and actions. We demonstrate the utility of MoCapAct by using it to train a single hierarchical policy capable of tracking the entire MoCap dataset within dm_control and show the learned low-level component can be re-used to efficiently learn downstream high-level tasks. Finally, we use MoCapAct to train an autoregressive GPT model and show that it can control a simulated humanoid to perform natural motion completion given a motion prompt. Videos of the results and links to the code and dataset are available at https://microsoft.github.io/MoCapAct.

Video generative models pre-trained on large-scale internet datasets have achieved remarkable success, excelling at producing realistic synthetic videos. However, they often generate clips based on static prompts (e.g., text or images), limiting their ability to model interactive and dynamic scenarios. In this paper, we propose Dynamic World Simulation (DWS), a novel approach to transform pre-trained video generative models into controllable world simulators capable of executing specified action trajectories. To achieve precise alignment between conditioned actions and generated visual changes, we introduce a lightweight, universal action-conditioned module that seamlessly integrates into any existing model. Instead of focusing on complex visual details, we demonstrate that consistent dynamic transition modeling is the key to building powerful world simulators. Building upon this insight, we further introduce a motion-reinforced loss that enhances action controllability by compelling the model to capture dynamic changes more effectively. Experiments demonstrate that DWS can be versatilely applied to both diffusion and autoregressive transformer models, achieving significant improvements in generating action-controllable, dynamically consistent videos across games and robotics domains. Moreover, to facilitate the applications of the learned world simulator in downstream tasks such as model-based reinforcement learning, we propose prioritized imagination to improve sample efficiency, demonstrating competitive performance compared with state-of-the-art methods.

Model-based reinforcement learning is a powerful tool, but collecting data to fit an accurate model of the system can be costly. Exploring an unknown environment in a sample-efficient manner is hence of great importance. However, the complexity of dynamics and the computational limitations of real systems make this task challenging. In this work, we introduce FLEX, an exploration algorithm for nonlinear dynamics based on optimal experimental design. Our policy maximizes the information of the next step and results in an adaptive exploration algorithm, compatible with generic parametric learning models and requiring minimal resources. We test our method on a number of nonlinear environments covering different settings, including time-varying dynamics. Keeping in mind that exploration is intended to serve an exploitation objective, we also test our algorithm on downstream model-based classical control tasks and compare it to other state-of-the-art model-based and model-free approaches. The performance achieved by FLEX is competitive and its computational cost is low.

Recently, learning-based controllers have been shown to push mobile robotic systems to their limits and provide the robustness needed for many real-world applications. However, only classical optimization-based control frameworks offer the inherent flexibility to be dynamically adjusted during execution by, for example, setting target speeds or actuator limits. We present a framework to overcome this shortcoming of neural controllers by conditioning them on an auxiliary input. This advance is enabled by including a feature-wise linear modulation layer (FiLM). We use model-free reinforcement-learning to train quadrotor control policies for the task of navigating through a sequence of waypoints in minimum time. By conditioning the policy on the maximum available thrust or the viewing direction relative to the next waypoint, a user can regulate the aggressiveness of the quadrotor's flight during deployment. We demonstrate in simulation and in real-world experiments that a single control policy can achieve close to time-optimal flight performance across the entire performance envelope of the robot, reaching up to 60 km/h and 4.5g in acceleration. The ability to guide a learned controller during task execution has implications beyond agile quadrotor flight, as conditioning the control policy on human intent helps safely bringing learning based systems out of the well-defined laboratory environment into the wild.

While generative video models have achieved remarkable fidelity and consistency, applying these capabilities to video editing remains a complex challenge. Recent research has explored motion controllability as a means to enhance text-to-video generation or image animation; however, we identify precise motion control as a promising yet under-explored paradigm for editing existing videos. In this work, we propose modifying video motion by directly editing sparse trajectories extracted from the input. We term the deviation between input and output trajectories a "motion edit" and demonstrate that this representation, when coupled with a generative backbone, enables powerful video editing capabilities. To achieve this, we introduce a pipeline for generating "motion counterfactuals", video pairs that share identical content but distinct motion, and we fine-tune a motion-conditioned video diffusion architecture on this dataset. Our approach allows for edits that start at any timestamp and propagate naturally. In a four-way head-to-head user study, our model achieves over 65 percent preference against prior work. Please see our project page: https://ryanndagreat.github.io/MotionV2V

Stability guarantees are crucial when ensuring a fully autonomous robot does not take undesirable or potentially harmful actions. Unfortunately, global stability guarantees are hard to provide in dynamical systems learned from data, especially when the learned dynamics are governed by neural networks. We propose a novel methodology to learn neural contractive dynamical systems, where our neural architecture ensures contraction, and hence, global stability. To efficiently scale the method to high-dimensional dynamical systems, we develop a variant of the variational autoencoder that learns dynamics in a low-dimensional latent representation space while retaining contractive stability after decoding. We further extend our approach to learning contractive systems on the Lie group of rotations to account for full-pose end-effector dynamic motions. The result is the first highly flexible learning architecture that provides contractive stability guarantees with capability to perform obstacle avoidance. Empirically, we demonstrate that our approach encodes the desired dynamics more accurately than the current state-of-the-art, which provides less strong stability guarantees.

We investigate optimal control problems governed by the elliptic partial differential equation -Delta u=f subject to Dirichlet boundary conditions on a given domain Omega. The control variable in this setting is the right-hand side f, and the objective is to minimize a cost functional that depends simultaneously on the control f and on the associated state function u. We establish the existence of optimal controls and analyze their qualitative properties by deriving necessary conditions for optimality. In particular, when pointwise constraints of the form alphale flebeta are imposed a priori on the control, we examine situations where a {\it bang-bang} phenomenon arises, that is where the optimal control f assumes only the extremal values alpha and beta. More precisely, the control takes the form f=alpha1_E+beta1_{Omegasetminus E}, thereby placing the problem within the framework of shape optimization. Under suitable assumptions, we further establish certain regularity properties for the optimal sets E. Finally, in the last part of the paper, we present numerical simulations that illustrate our theoretical findings through a selection of representative examples.

In this paper, we present efficient quantum algorithms that are exponentially faster than classical algorithms for solving the quantum optimal control problem. This problem involves finding the control variable that maximizes a physical quantity at time T, where the system is governed by a time-dependent Schr\"odinger equation. This type of control problem also has an intricate relation with machine learning. Our algorithms are based on a time-dependent Hamiltonian simulation method and a fast gradient-estimation algorithm. We also provide a comprehensive error analysis to quantify the total error from various steps, such as the finite-dimensional representation of the control function, the discretization of the Schr\"odinger equation, the numerical quadrature, and optimization. Our quantum algorithms require fault-tolerant quantum computers.

The controllable generation of diffusion models aims to steer the model to generate samples that optimize some given objective functions. It is desirable for a variety of applications including image generation, molecule generation, and DNA/sequence generation. Reinforcement Learning (RL) based fine-tuning of the base model is a popular approach but it can overfit the reward function while requiring significant resources. We frame controllable generation as a problem of finding a distribution that optimizes a KL-regularized objective function. We present SLCD -- Supervised Learning based Controllable Diffusion, which iteratively generates online data and trains a small classifier to guide the generation of the diffusion model. Similar to the standard classifier-guided diffusion, SLCD's key computation primitive is classification and does not involve any complex concepts from RL or control. Via a reduction to no-regret online learning analysis, we show that under KL divergence, the output from SLCD provably converges to the optimal solution of the KL-regularized objective. Further, we empirically demonstrate that SLCD can generate high quality samples with nearly the same inference time as the base model in both image generation with continuous diffusion and biological sequence generation with discrete diffusion. Our code is available at https://github.com/Owen-Oertell/slcd

Density of the reachable states can help understand the risk of safety-critical systems, especially in situations when worst-case reachability is too conservative. Recent work provides a data-driven approach to compute the density distribution of autonomous systems' forward reachable states online. In this paper, we study the use of such approach in combination with model predictive control for verifiable safe path planning under uncertainties. We first use the learned density distribution to compute the risk of collision online. If such risk exceeds the acceptable threshold, our method will plan for a new path around the previous trajectory, with the risk of collision below the threshold. Our method is well-suited to handle systems with uncertainties and complicated dynamics as our data-driven approach does not need an analytical form of the systems' dynamics and can estimate forward state density with an arbitrary initial distribution of uncertainties. We design two challenging scenarios (autonomous driving and hovercraft control) for safe motion planning in environments with obstacles under system uncertainties. We first show that our density estimation approach can reach a similar accuracy as the Monte-Carlo-based method while using only 0.01X training samples. By leveraging the estimated risk, our algorithm achieves the highest success rate in goal reaching when enforcing the safety rate above 0.99.

Intelligent agents progress by continually refining their capabilities through actively exploring environments. Yet robot policies often lack sufficient exploration capability due to action mode collapse. Existing methods that encourage exploration typically rely on random perturbations, which are unsafe and induce unstable, erratic behaviors, thereby limiting their effectiveness. We propose Self-Improvement via On-Manifold Exploration (SOE), a framework that enhances policy exploration and improvement in robotic manipulation. SOE learns a compact latent representation of task-relevant factors and constrains exploration to the manifold of valid actions, ensuring safety, diversity, and effectiveness. It can be seamlessly integrated with arbitrary policy models as a plug-in module, augmenting exploration without degrading the base policy performance. Moreover, the structured latent space enables human-guided exploration, further improving efficiency and controllability. Extensive experiments in both simulation and real-world tasks demonstrate that SOE consistently outperforms prior methods, achieving higher task success rates, smoother and safer exploration, and superior sample efficiency. These results establish on-manifold exploration as a principled approach to sample-efficient policy self-improvement. Project website: https://ericjin2002.github.io/SOE

The objective of personalized medicine is to tailor interventions to an individual patient's unique characteristics. A key technology for this purpose involves medical digital twins, computational models of human biology that can be personalized and dynamically updated to incorporate patient-specific data collected over time. Certain aspects of human biology, such as the immune system, are not easily captured with physics-based models, such as differential equations. Instead, they are often multi-scale, stochastic, and hybrid. This poses a challenge to existing model-based control and optimization approaches that cannot be readily applied to such models. Recent advances in automatic differentiation and neural-network control methods hold promise in addressing complex control problems. However, the application of these approaches to biomedical systems is still in its early stages. This work introduces dynamics-informed neural-network controllers as an alternative approach to control of medical digital twins. As a first use case for this method, the focus is on agent-based models, a versatile and increasingly common modeling platform in biomedicine. The effectiveness of the proposed neural-network control method is illustrated and benchmarked against other methods with two widely-used agent-based model types. The relevance of the method introduced here extends beyond medical digital twins to other complex dynamical systems.

Deep Reinforcement Learning is emerging as a promising approach for the continuous control task of robotic arm movement. However, the challenges of learning robust and versatile control capabilities are still far from being resolved for real-world applications, mainly because of two common issues of this learning paradigm: the exploration strategy and the slow learning speed, sometimes known as "the curse of dimensionality". This work aims at exploring and assessing the advantages of the application of Quantum Computing to one of the state-of-art Reinforcement Learning techniques for continuous control - namely Soft Actor-Critic. Specifically, the performance of a Variational Quantum Soft Actor-Critic on the movement of a virtual robotic arm has been investigated by means of digital simulations of quantum circuits. A quantum advantage over the classical algorithm has been found in terms of a significant decrease in the amount of required parameters for satisfactory model training, paving the way for further promising developments.

Dynamical systems (DS) theory is fundamental for many areas of science and engineering. It can provide deep insights into the behavior of systems evolving in time, as typically described by differential or recursive equations. A common approach to facilitate mathematical tractability and interpretability of DS models involves decomposing nonlinear DS into multiple linear DS separated by switching manifolds, i.e. piecewise linear (PWL) systems. PWL models are popular in engineering and a frequent choice in mathematics for analyzing the topological properties of DS. However, hand-crafting such models is tedious and only possible for very low-dimensional scenarios, while inferring them from data usually gives rise to unnecessarily complex representations with very many linear subregions. Here we introduce Almost-Linear Recurrent Neural Networks (AL-RNNs) which automatically and robustly produce most parsimonious PWL representations of DS from time series data, using as few PWL nonlinearities as possible. AL-RNNs can be efficiently trained with any SOTA algorithm for dynamical systems reconstruction (DSR), and naturally give rise to a symbolic encoding of the underlying DS that provably preserves important topological properties. We show that for the Lorenz and R\"ossler systems, AL-RNNs discover, in a purely data-driven way, the known topologically minimal PWL representations of the corresponding chaotic attractors. We further illustrate on two challenging empirical datasets that interpretable symbolic encodings of the dynamics can be achieved, tremendously facilitating mathematical and computational analysis of the underlying systems.

This paper introduces Discrete-time Hybrid Automata Learning (DHAL), a framework using on-policy Reinforcement Learning to identify and execute mode-switching without trajectory segmentation or event function learning. Hybrid dynamical systems, which include continuous flow and discrete mode switching, can model robotics tasks like legged robot locomotion. Model-based methods usually depend on predefined gaits, while model-free approaches lack explicit mode-switching knowledge. Current methods identify discrete modes via segmentation before regressing continuous flow, but learning high-dimensional complex rigid body dynamics without trajectory labels or segmentation is a challenging open problem. Our approach incorporates a beta policy distribution and a multi-critic architecture to model contact-guided motions, exemplified by a challenging quadrupedal robot skateboard task. We validate our method through simulations and real-world tests, demonstrating robust performance in hybrid dynamical systems.

We consider an improper reinforcement learning setting where a learner is given M base controllers for an unknown Markov decision process, and wishes to combine them optimally to produce a potentially new controller that can outperform each of the base ones. This can be useful in tuning across controllers, learnt possibly in mismatched or simulated environments, to obtain a good controller for a given target environment with relatively few trials. Towards this, we propose two algorithms: (1) a Policy Gradient-based approach; and (2) an algorithm that can switch between a simple Actor-Critic (AC) based scheme and a Natural Actor-Critic (NAC) scheme depending on the available information. Both algorithms operate over a class of improper mixtures of the given controllers. For the first case, we derive convergence rate guarantees assuming access to a gradient oracle. For the AC-based approach we provide convergence rate guarantees to a stationary point in the basic AC case and to a global optimum in the NAC case. Numerical results on (i) the standard control theoretic benchmark of stabilizing an cartpole; and (ii) a constrained queueing task show that our improper policy optimization algorithm can stabilize the system even when the base policies at its disposal are unstable.

Late-lumping feedback design for infinite-dimensional linear systems with unbounded input operators is considered. The proposed scheme is suitable for the approximation of backstepping and flatness-based designs and relies on a decomposition of the feedback into a bounded and an unbounded part. Approximation applies to the bounded part only, while the unbounded part is assumed to allow for an exact realization. Based on spectral results, the convergence of the closed-loop dynamics to the desired dynamics is established. By duality, similar results apply to the approximation of the observer output-injection gains for systems with boundary observation. The proposed design and approximation steps are demonstrated and illustrated based on a hyperbolic infinite-dimensional system.

Inverse dynamics (ID), which aims at reproducing the driven torques from human kinematic observations, has been a critical tool for gait analysis. However, it is hindered from wider application to general motion due to its limited scalability. Conventional optimization-based ID requires expensive laboratory setups, restricting its availability. To alleviate this problem, we propose to exploit the recently progressive human motion imitation algorithms to learn human inverse dynamics in a data-driven manner. The key insight is that the human ID knowledge is implicitly possessed by motion imitators, though not directly applicable. In light of this, we devise an efficient data collection pipeline with state-of-the-art motion imitation algorithms and physics simulators, resulting in a large-scale human inverse dynamics benchmark as Imitated Dynamics (ImDy). ImDy contains over 150 hours of motion with joint torque and full-body ground reaction force data. With ImDy, we train a data-driven human inverse dynamics solver ImDyS(olver) in a fully supervised manner, which conducts ID and ground reaction force estimation simultaneously. Experiments on ImDy and real-world data demonstrate the impressive competency of ImDyS in human inverse dynamics and ground reaction force estimation. Moreover, the potential of ImDy(-S) as a fundamental motion analysis tool is exhibited with downstream applications. The project page is https://foruck.github.io/ImDy/.

The vulnerability of artificial intelligence (AI) and machine learning (ML) against adversarial disturbances and attacks significantly restricts their applicability in safety-critical systems including cyber-physical systems (CPS) equipped with neural network components at various stages of sensing and control. This paper addresses the reachable set estimation and safety verification problems for dynamical systems embedded with neural network components serving as feedback controllers. The closed-loop system can be abstracted in the form of a continuous-time sampled-data system under the control of a neural network controller. First, a novel reachable set computation method in adaptation to simulations generated out of neural networks is developed. The reachability analysis of a class of feedforward neural networks called multilayer perceptrons (MLP) with general activation functions is performed in the framework of interval arithmetic. Then, in combination with reachability methods developed for various dynamical system classes modeled by ordinary differential equations, a recursive algorithm is developed for over-approximating the reachable set of the closed-loop system. The safety verification for neural network control systems can be performed by examining the emptiness of the intersection between the over-approximation of reachable sets and unsafe sets. The effectiveness of the proposed approach has been validated with evaluations on a robotic arm model and an adaptive cruise control system.

Despite recent progress, video diffusion models still struggle to synthesize realistic videos involving highly dynamic motions or requiring fine-grained motion controllability. A central limitation lies in the scarcity of such examples in commonly used training datasets. To address this, we introduce DynaVid, a video synthesis framework that leverages synthetic motion data in training, which is represented as optical flow and rendered using computer graphics pipelines. This approach offers two key advantages. First, synthetic motion offers diverse motion patterns and precise control signals that are difficult to obtain from real data. Second, unlike rendered videos with artificial appearances, rendered optical flow encodes only motion and is decoupled from appearance, thereby preventing models from reproducing the unnatural look of synthetic videos. Building on this idea, DynaVid adopts a two-stage generation framework: a motion generator first synthesizes motion, and then a motion-guided video generator produces video frames conditioned on that motion. This decoupled formulation enables the model to learn dynamic motion patterns from synthetic data while preserving visual realism from real-world videos. We validate our framework on two challenging scenarios, vigorous human motion generation and extreme camera motion control, where existing datasets are particularly limited. Extensive experiments demonstrate that DynaVid improves the realism and controllability in dynamic motion generation and camera motion control.

Designing control policies whose performance level is guaranteed to remain above a given threshold in a span of environments is a critical feature for the adoption of reinforcement learning (RL) in real-world applications. The search for such robust policies is a notoriously difficult problem, related to the so-called dynamic model of transition function uncertainty, where the environment dynamics are allowed to change at each time step. But in practical cases, one is rather interested in robustness to a span of static transition models throughout interaction episodes. The static model is known to be harder to solve than the dynamic one, and seminal algorithms, such as robust value iteration, as well as most recent works on deep robust RL, build upon the dynamic model. In this work, we propose to revisit the static model. We suggest an analysis of why solving the static model under some mild hypotheses is a reasonable endeavor, based on an equivalence with the dynamic model, and formalize the general intuition that robust MDPs can be solved by tackling a series of static problems. We introduce a generic meta-algorithm called IWOCS, which incrementally identifies worst-case transition models so as to guide the search for a robust policy. Discussion on IWOCS sheds light on new ways to decouple policy optimization and adversarial transition functions and opens new perspectives for analysis. We derive a deep RL version of IWOCS and demonstrate it is competitive with state-of-the-art algorithms on classical benchmarks.

Generalizing policies across different domains with dynamics mismatch poses a significant challenge in reinforcement learning. For example, a robot learns the policy in a simulator, but when it is deployed in the real world, the dynamics of the environment may be different. Given the source and target domain with dynamics mismatch, we consider the online dynamics adaptation problem, in which case the agent can access sufficient source domain data while online interactions with the target domain are limited. Existing research has attempted to solve the problem from the dynamics discrepancy perspective. In this work, we reveal the limitations of these methods and explore the problem from the value difference perspective via a novel insight on the value consistency across domains. Specifically, we present the Value-Guided Data Filtering (VGDF) algorithm, which selectively shares transitions from the source domain based on the proximity of paired value targets across the two domains. Empirical results on various environments with kinematic and morphology shifts demonstrate that our method achieves superior performance compared to prior approaches.

Causal discovery for dynamical systems poses a major challenge in fields where active interventions are infeasible. Most methods used to investigate these systems and their associated benchmarks are tailored to deterministic, low-dimensional and weakly nonlinear time-series data. To address these limitations, we present CausalDynamics, a large-scale benchmark and extensible data generation framework to advance the structural discovery of dynamical causal models. Our benchmark consists of true causal graphs derived from thousands of coupled ordinary and stochastic differential equations as well as two idealized climate models. We perform a comprehensive evaluation of state-of-the-art causal discovery algorithms for graph reconstruction on systems with noisy, confounded, and lagged dynamics. CausalDynamics consists of a plug-and-play, build-your-own coupling workflow that enables the construction of a hierarchy of physical systems. We anticipate that our framework will facilitate the development of robust causal discovery algorithms that are broadly applicable across domains while addressing their unique challenges. We provide a user-friendly implementation and documentation on https://kausable.github.io/CausalDynamics.

We propose DOME, a diffusion-based world model that predicts future occupancy frames based on past occupancy observations. The ability of this world model to capture the evolution of the environment is crucial for planning in autonomous driving. Compared to 2D video-based world models, the occupancy world model utilizes a native 3D representation, which features easily obtainable annotations and is modality-agnostic. This flexibility has the potential to facilitate the development of more advanced world models. Existing occupancy world models either suffer from detail loss due to discrete tokenization or rely on simplistic diffusion architectures, leading to inefficiencies and difficulties in predicting future occupancy with controllability. Our DOME exhibits two key features:(1) High-Fidelity and Long-Duration Generation. We adopt a spatial-temporal diffusion transformer to predict future occupancy frames based on historical context. This architecture efficiently captures spatial-temporal information, enabling high-fidelity details and the ability to generate predictions over long durations. (2)Fine-grained Controllability. We address the challenge of controllability in predictions by introducing a trajectory resampling method, which significantly enhances the model's ability to generate controlled predictions. Extensive experiments on the widely used nuScenes dataset demonstrate that our method surpasses existing baselines in both qualitative and quantitative evaluations, establishing a new state-of-the-art performance on nuScenes. Specifically, our approach surpasses the baseline by 10.5% in mIoU and 21.2% in IoU for occupancy reconstruction and by 36.0% in mIoU and 24.6% in IoU for 4D occupancy forecasting.

Data-driven learning is rapidly evolving and places a new perspective on realizing state-space dynamical systems. However, dynamical systems derived from nonlinear ordinary differential equations (ODEs) suffer from limitations in computational efficiency. Thus, this paper stems from data-driven learning to advance states of dynamical systems utilizing a structured neural network (StNN). The proposed learning technique also seeks to identify an optimal, low-complexity operator to solve dynamical systems, the so-called Hankel operator, derived from time-delay measurements. Thus, we utilize the StNN based on the Hankel operator to solve dynamical systems as an alternative to existing data-driven techniques. We show that the proposed StNN reduces the number of parameters and computational complexity compared with the conventional neural networks and also with the classical data-driven techniques, such as Sparse Identification of Nonlinear Dynamics (SINDy) and Hankel Alternative view of Koopman (HAVOK), which is commonly known as delay-Dynamic Mode Decomposition(DMD) or Hankel-DMD. More specifically, we present numerical simulations to solve dynamical systems utilizing the StNN based on the Hankel operator beginning from the fundamental Lotka-Volterra model, where we compare the StNN with the LEarning Across Dynamical Systems (LEADS), and extend our analysis to highly nonlinear and chaotic Lorenz systems, comparing the StNN with conventional neural networks, SINDy, and HAVOK. Hence, we show that the proposed StNN paves the way for realizing state-space dynamical systems with a low-complexity learning algorithm, enabling prediction and understanding of future states.

Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it. In this work, we introduce a novel generative modeling framework grounded in phase space dynamics, where a phase space is defined as {an augmented space encompassing both position and velocity.} Leveraging insights from Stochastic Optimal Control, we construct a path measure in the phase space that enables efficient sampling. {In contrast to DMs, our framework demonstrates the capability to generate realistic data points at an early stage of dynamics propagation.} This early prediction sets the stage for efficient data generation by leveraging additional velocity information along the trajectory. On standard image generation benchmarks, our model yields favorable performance over baselines in the regime of small Number of Function Evaluations (NFEs). Furthermore, our approach rivals the performance of diffusion models equipped with efficient sampling techniques, underscoring its potential as a new tool generative modeling.

Existing imitation learning (IL) methods such as inverse reinforcement learning (IRL) usually have a double-loop training process, alternating between learning a reward function and a policy and tend to suffer long training time and high variance. In this work, we identify the benefits of differentiable physics simulators and propose a new IL method, i.e., Imitation Learning via Differentiable Physics (ILD), which gets rid of the double-loop design and achieves significant improvements in final performance, convergence speed, and stability. The proposed ILD incorporates the differentiable physics simulator as a physics prior into its computational graph for policy learning. It unrolls the dynamics by sampling actions from a parameterized policy, simply minimizing the distance between the expert trajectory and the agent trajectory, and back-propagating the gradient into the policy via temporal physics operators. With the physics prior, ILD policies can not only be transferable to unseen environment specifications but also yield higher final performance on a variety of tasks. In addition, ILD naturally forms a single-loop structure, which significantly improves the stability and training speed. To simplify the complex optimization landscape induced by temporal physics operations, ILD dynamically selects the learning objectives for each state during optimization. In our experiments, we show that ILD outperforms state-of-the-art methods in a variety of continuous control tasks with Brax, requiring only one expert demonstration. In addition, ILD can be applied to challenging deformable object manipulation tasks and can be generalized to unseen configurations.

Reinforcement learning (RL) for continuous control typically employs distributions whose support covers the entire action space. In this work, we investigate the colloquially known phenomenon that trained agents often prefer actions at the boundaries of that space. We draw theoretical connections to the emergence of bang-bang behavior in optimal control, and provide extensive empirical evaluation across a variety of recent RL algorithms. We replace the normal Gaussian by a Bernoulli distribution that solely considers the extremes along each action dimension - a bang-bang controller. Surprisingly, this achieves state-of-the-art performance on several continuous control benchmarks - in contrast to robotic hardware, where energy and maintenance cost affect controller choices. Since exploration, learning,and the final solution are entangled in RL, we provide additional imitation learning experiments to reduce the impact of exploration on our analysis. Finally, we show that our observations generalize to environments that aim to model real-world challenges and evaluate factors to mitigate the emergence of bang-bang solutions. Our findings emphasize challenges for benchmarking continuous control algorithms, particularly in light of potential real-world applications.

Diffusion models have become popular for policy learning in robotics due to their ability to capture high-dimensional and multimodal distributions. However, diffusion policies are stochastic and typically trained offline, limiting their ability to handle unseen and dynamic conditions where novel constraints not represented in the training data must be satisfied. To overcome this limitation, we propose diffusion predictive control with constraints (DPCC), an algorithm for diffusion-based control with explicit state and action constraints that can deviate from those in the training data. DPCC incorporates model-based projections into the denoising process of a trained trajectory diffusion model and uses constraint tightening to account for model mismatch. This allows us to generate constraint-satisfying, dynamically feasible, and goal-reaching trajectories for predictive control. We show through simulations of a robot manipulator that DPCC outperforms existing methods in satisfying novel test-time constraints while maintaining performance on the learned control task.

Humanoid whole-body control requires adapting to diverse tasks such as navigation, loco-manipulation, and tabletop manipulation, each demanding a different mode of control. For example, navigation relies on root velocity tracking, while tabletop manipulation prioritizes upper-body joint angle tracking. Existing approaches typically train individual policies tailored to a specific command space, limiting their transferability across modes. We present the key insight that full-body kinematic motion imitation can serve as a common abstraction for all these tasks and provide general-purpose motor skills for learning multiple modes of whole-body control. Building on this, we propose HOVER (Humanoid Versatile Controller), a multi-mode policy distillation framework that consolidates diverse control modes into a unified policy. HOVER enables seamless transitions between control modes while preserving the distinct advantages of each, offering a robust and scalable solution for humanoid control across a wide range of modes. By eliminating the need for policy retraining for each control mode, our approach improves efficiency and flexibility for future humanoid applications.

In this work, we investigate the data-driven safe control synthesis problem for unknown dynamic systems. We first formulate the safety synthesis problem as a robust convex program (RCP) based on notion of control barrier function. To resolve the issue of unknown system dynamic, we follow the existing approach by converting the RCP to a scenario convex program (SCP) by randomly collecting finite samples of system trajectory. However, to improve the sample efficiency to achieve a desired confidence bound, we provide a new posteriori method with validation tests. Specifically, after collecting a set of data for the SCP, we further collect another set of independent validate data as posterior information to test the obtained solution. We derive a new overall confidence bound for the safety of the controller that connects the original sample data, the support constraints, and the validation data. The efficiency of the proposed approach is illustrated by a case study of room temperature control. We show that, compared with existing methods, the proposed approach can significantly reduce the required number of sample data to achieve a desired confidence bound.

Despite advances in learning-based methods, finding valid Lyapunov functions for nonlinear dynamical systems remains challenging. Current neural network approaches face two main issues: challenges in scalable verification and limited interpretability. To address these, we propose an end-to-end framework using transformers to construct analytical Lyapunov functions (local), which simplifies formal verification, enhances interpretability, and provides valuable insights for control engineers. Our framework consists of a transformer-based trainer that generates candidate Lyapunov functions and a falsifier that verifies candidate expressions and refines the model via risk-seeking policy gradient. Unlike Alfarano et al. (2024), which utilizes pre-training and seeks global Lyapunov functions for low-dimensional systems, our model is trained from scratch via reinforcement learning (RL) and succeeds in finding local Lyapunov functions for high-dimensional and non-polynomial systems. Given the analytical nature of the candidates, we employ efficient optimization methods for falsification during training and formal verification tools for the final verification. We demonstrate the efficiency of our approach on a range of nonlinear dynamical systems with up to ten dimensions and show that it can discover Lyapunov functions not previously identified in the control literature.

We investigate the use of transformer sequence models as dynamics models (TDMs) for control. In a number of experiments in the DeepMind control suite, we find that first, TDMs perform well in a single-environment learning setting when compared to baseline models. Second, TDMs exhibit strong generalization capabilities to unseen environments, both in a few-shot setting, where a generalist model is fine-tuned with small amounts of data from the target environment, and in a zero-shot setting, where a generalist model is applied to an unseen environment without any further training. We further demonstrate that generalizing system dynamics can work much better than generalizing optimal behavior directly as a policy. This makes TDMs a promising ingredient for a foundation model of control.

Recent works exploring deep learning application to dynamical systems modeling have demonstrated that embedding physical priors into neural networks can yield more effective, physically-realistic, and data-efficient models. However, in the absence of complete prior knowledge of a dynamical system's physical characteristics, determining the optimal structure and optimization strategy for these models can be difficult. In this work, we explore methods for discovering neural state space dynamics models for system identification. Starting with a design space of block-oriented state space models and structured linear maps with strong physical priors, we encode these components into a model genome alongside network structure, penalty constraints, and optimization hyperparameters. Demonstrating the overall utility of the design space, we employ an asynchronous genetic search algorithm that alternates between model selection and optimization and obtains accurate physically consistent models of three physical systems: an aerodynamics body, a continuous stirred tank reactor, and a two tank interacting system.

Text-to-image diffusion generative models can generate high quality images at the cost of tedious prompt engineering. Controllability can be improved by introducing layout conditioning, however existing methods lack layout editing ability and fine-grained control over object attributes. The concept of multi-layer generation holds great potential to address these limitations, however generating image instances concurrently to scene composition limits control over fine-grained object attributes, relative positioning in 3D space and scene manipulation abilities. In this work, we propose a novel multi-stage generation paradigm that is designed for fine-grained control, flexibility and interactivity. To ensure control over instance attributes, we devise a novel training paradigm to adapt a diffusion model to generate isolated scene components as RGBA images with transparency information. To build complex images, we employ these pre-generated instances and introduce a multi-layer composite generation process that smoothly assembles components in realistic scenes. Our experiments show that our RGBA diffusion model is capable of generating diverse and high quality instances with precise control over object attributes. Through multi-layer composition, we demonstrate that our approach allows to build and manipulate images from highly complex prompts with fine-grained control over object appearance and location, granting a higher degree of control than competing methods.

The ability to separate signal from noise, and reason with clean abstractions, is critical to intelligence. With this ability, humans can efficiently perform real world tasks without considering all possible nuisance factors.How can artificial agents do the same? What kind of information can agents safely discard as noises? In this work, we categorize information out in the wild into four types based on controllability and relation with reward, and formulate useful information as that which is both controllable and reward-relevant. This framework clarifies the kinds information removed by various prior work on representation learning in reinforcement learning (RL), and leads to our proposed approach of learning a Denoised MDP that explicitly factors out certain noise distractors. Extensive experiments on variants of DeepMind Control Suite and RoboDesk demonstrate superior performance of our denoised world model over using raw observations alone, and over prior works, across policy optimization control tasks as well as the non-control task of joint position regression.

The enduring challenge in the field of artificial intelligence has been the control of systems to achieve desired behaviours. While for systems governed by straightforward dynamics equations, methods like Linear Quadratic Regulation (LQR) have historically proven highly effective, most real-world tasks, which require a general problem-solver, demand world models with dynamics that cannot be easily described by simple equations. Consequently, these models must be learned from data using neural networks. Most model predictive control (MPC) algorithms designed for visual world models have traditionally explored gradient-free population-based optimisation methods, such as Cross Entropy and Model Predictive Path Integral (MPPI) for planning. However, we present an exploration of a gradient-based alternative that fully leverages the differentiability of the world model. In our study, we conduct a comparative analysis between our method and other MPC-based alternatives, as well as policy-based algorithms. In a sample-efficient setting, our method achieves on par or superior performance compared to the alternative approaches in most tasks. Additionally, we introduce a hybrid model that combines policy networks and gradient-based MPC, which outperforms pure policy based methods thereby holding promise for Gradient-based planning with world models in complex real-world tasks.

In this work, we consider the problem of deriving and incorporating accurate dynamic models for model predictive control (MPC) with an application to quadrotor control. MPC relies on precise dynamic models to achieve the desired closed-loop performance. However, the presence of uncertainties in complex systems and the environments they operate in poses a challenge in obtaining sufficiently accurate representations of the system dynamics. In this work, we make use of a deep learning tool, knowledge-based neural ordinary differential equations (KNODE), to augment a model obtained from first principles. The resulting hybrid model encompasses both a nominal first-principle model and a neural network learnt from simulated or real-world experimental data. Using a quadrotor, we benchmark our hybrid model against a state-of-the-art Gaussian Process (GP) model and show that the hybrid model provides more accurate predictions of the quadrotor dynamics and is able to generalize beyond the training data. To improve closed-loop performance, the hybrid model is integrated into a novel MPC framework, known as KNODE-MPC. Results show that the integrated framework achieves 60.2% improvement in simulations and more than 21% in physical experiments, in terms of trajectory tracking performance.

Recent advances in diffusion-based controllable visual generation have led to remarkable improvements in image quality. However, these powerful models are typically deployed on cloud servers due to their large computational demands, raising serious concerns about user data privacy. To enable secure and efficient on-device generation, we explore in this paper controllable diffusion models built upon linear attention architectures, which offer superior scalability and efficiency, even on edge devices. Yet, our experiments reveal that existing controllable generation frameworks, such as ControlNet and OminiControl, either lack the flexibility to support multiple heterogeneous condition types or suffer from slow convergence on such linear-attention models. To address these limitations, we propose a novel controllable diffusion framework tailored for linear attention backbones like SANA. The core of our method lies in a unified gated conditioning module working in a dual-path pipeline, which effectively integrates multi-type conditional inputs, such as spatially aligned and non-aligned cues. Extensive experiments on multiple tasks and benchmarks demonstrate that our approach achieves state-of-the-art controllable generation performance based on linear-attention models, surpassing existing methods in terms of fidelity and controllability.

Realistic and diverse multi-agent driving scenes are crucial for evaluating autonomous vehicles, but safety-critical events which are essential for this task are rare and underrepresented in driving datasets. Data-driven scene generation offers a low-cost alternative by synthesizing complex traffic behaviors from existing driving logs. However, existing models often lack controllability or yield samples that violate physical or social constraints, limiting their usability. We present OMEGA, an optimization-guided, training-free framework that enforces structural consistency and interaction awareness during diffusion-based sampling from a scene generation model. OMEGA re-anchors each reverse diffusion step via constrained optimization, steering the generation towards physically plausible and behaviorally coherent trajectories. Building on this framework, we formulate ego-attacker interactions as a game-theoretic optimization in the distribution space, approximating Nash equilibria to generate realistic, safety-critical adversarial scenarios. Experiments on nuPlan and Waymo show that OMEGA improves generation realism, consistency, and controllability, increasing the ratio of physically and behaviorally valid scenes from 32.35% to 72.27% for free exploration capabilities, and from 11% to 80% for controllability-focused generation. Our approach can also generate 5times more near-collision frames with a time-to-collision under three seconds while maintaining the overall scene realism.

Much has been said about observability in system theory and control; however, it has been recently that observability in complex networks has seriously attracted the attention of researchers. This paper examines the state-of-the-art and discusses some issues raised due to "complexity" and "stochasticity". These unresolved issues call for a new practical methodology. For stochastic systems, a degree of observability may be defined and the observability problem is not a binary (i.e., yes-no) question anymore. Here, we propose to employ a goal-seeking system to play a supervisory role in the network. Hence, improving the degree of observability would be a valid objective for the supervisory system. Towards this goal, the supervisor dynamically optimizes the observation process by reconfiguring the sensory parts in the network. A cognitive dynamic system is suggested as a proper choice for the supervisory system. In this framework, the network itself is viewed as the environment with which the cognitive dynamic system interacts. Computer experiments confirm the potential of the proposed approach for addressing some of the issues raised in networks due to complexity and stochasticity.

We present a comprehensive study on discrete morphological symmetries of dynamical systems, which are commonly observed in biological and artificial locomoting systems, such as legged, swimming, and flying animals/robots/virtual characters. These symmetries arise from the presence of one or more planes/axis of symmetry in the system's morphology, resulting in harmonious duplication and distribution of body parts. Significantly, we characterize how morphological symmetries extend to symmetries in the system's dynamics, optimal control policies, and in all proprioceptive and exteroceptive measurements related to the system's dynamics evolution. In the context of data-driven methods, symmetry represents an inductive bias that justifies the use of data augmentation or symmetric function approximators. To tackle this, we present a theoretical and practical framework for identifying the system's morphological symmetry group G and characterizing the symmetries in proprioceptive and exteroceptive data measurements. We then exploit these symmetries using data augmentation and G-equivariant neural networks. Our experiments on both synthetic and real-world applications provide empirical evidence of the advantageous outcomes resulting from the exploitation of these symmetries, including improved sample efficiency, enhanced generalization, and reduction of trainable parameters.

Diffusion model has demonstrated remarkable capability in video generation, which further sparks interest in introducing trajectory control into the generation process. While existing works mainly focus on training-based methods (e.g., conditional adapter), we argue that diffusion model itself allows decent control over the generated content without requiring any training. In this study, we introduce a tuning-free framework to achieve trajectory-controllable video generation, by imposing guidance on both noise construction and attention computation. Specifically, 1) we first show several instructive phenomenons and analyze how initial noises influence the motion trajectory of generated content. 2) Subsequently, we propose FreeTraj, a tuning-free approach that enables trajectory control by modifying noise sampling and attention mechanisms. 3) Furthermore, we extend FreeTraj to facilitate longer and larger video generation with controllable trajectories. Equipped with these designs, users have the flexibility to provide trajectories manually or opt for trajectories automatically generated by the LLM trajectory planner. Extensive experiments validate the efficacy of our approach in enhancing the trajectory controllability of video diffusion models.

In this paper, we consider a varying terminal time structure for the stochastic optimal control problem under state constraints, in which the terminal time varies with the mean value of the state. In this new stochastic optimal control system, the control domain does not need to be convex and the diffusion coefficient contains the control variable. To overcome the difficulty in the proof of the related Pontryagin's stochastic maximum principle, we develop asymptotic first- and second-order adjoint equations for the varying terminal time, and then establish its variational equation. In the end, two examples are given to verify the main results of this study.

Dyna-style model-based reinforcement learning contains two phases: model rollouts to generate sample for policy learning and real environment exploration using current policy for dynamics model learning. However, due to the complex real-world environment, it is inevitable to learn an imperfect dynamics model with model prediction error, which can further mislead policy learning and result in sub-optimal solutions. In this paper, we propose COPlanner, a planning-driven framework for model-based methods to address the inaccurately learned dynamics model problem with conservative model rollouts and optimistic environment exploration. COPlanner leverages an uncertainty-aware policy-guided model predictive control (UP-MPC) component to plan for multi-step uncertainty estimation. This estimated uncertainty then serves as a penalty during model rollouts and as a bonus during real environment exploration respectively, to choose actions. Consequently, COPlanner can avoid model uncertain regions through conservative model rollouts, thereby alleviating the influence of model error. Simultaneously, it explores high-reward model uncertain regions to reduce model error actively through optimistic real environment exploration. COPlanner is a plug-and-play framework that can be applied to any dyna-style model-based methods. Experimental results on a series of proprioceptive and visual continuous control tasks demonstrate that both sample efficiency and asymptotic performance of strong model-based methods are significantly improved combined with COPlanner.

Nonlinear ordinary differential equations (ODEs) are powerful tools for modeling real-world dynamical systems. However, propagating initial state uncertainty through nonlinear dynamics, especially when the ODE is unknown and learned from data, remains a major challenge. This paper introduces a novel continuum dynamics perspective for model learning that enables formal uncertainty propagation by constructing Taylor series approximations of probabilistic events. We establish sufficient conditions for the soundness of the approach and prove its asymptotic convergence. Empirical results demonstrate the framework's effectiveness, particularly when predicting rare events.

We propose a new method to ensure neural ordinary differential equations (ODEs) satisfy output specifications by using invariance set propagation. Our approach uses a class of control barrier functions to transform output specifications into constraints on the parameters and inputs of the learning system. This setup allows us to achieve output specification guarantees simply by changing the constrained parameters/inputs both during training and inference. Moreover, we demonstrate that our invariance set propagation through data-controlled neural ODEs not only maintains generalization performance but also creates an additional degree of robustness by enabling causal manipulation of the system's parameters/inputs. We test our method on a series of representation learning tasks, including modeling physical dynamics and convexity portraits, as well as safe collision avoidance for autonomous vehicles.

Optimal operation of chemical processes is vital for energy, resource, and cost savings in chemical engineering. The problem of optimal operation can be tackled with reinforcement learning, but traditional reinforcement learning methods face challenges due to hard constraints related to quality and safety that must be strictly satisfied, and the large amount of required training data. Chemical processes often cannot provide sufficient experimental data, and while detailed dynamic models can be an alternative, their complexity makes it computationally intractable to generate the needed data. Optimal control methods, such as model predictive control, also struggle with the complexity of the underlying dynamic models. Consequently, many chemical processes rely on manually defined operation recipes combined with simple linear controllers, leading to suboptimal performance and limited flexibility. In this work, we propose a novel approach that leverages expert knowledge embedded in operation recipes. By using reinforcement learning to optimize the parameters of these recipes and their underlying linear controllers, we achieve an optimized operation recipe. This method requires significantly less data, handles constraints more effectively, and is more interpretable than traditional reinforcement learning methods due to the structured nature of the recipes. We demonstrate the potential of our approach through simulation results of an industrial batch polymerization reactor, showing that it can approach the performance of optimal controllers while addressing the limitations of existing methods.

Recent works in robotic manipulation through reinforcement learning (RL) or imitation learning (IL) have shown potential for tackling a range of tasks e.g., opening a drawer or a cupboard. However, these techniques generalize poorly to unseen objects. We conjecture that this is due to the high-dimensional action space for joint control. In this paper, we take an alternative approach and separate the task of learning 'what to do' from 'how to do it' i.e., whole-body control. We pose the RL problem as one of determining the skill dynamics for a disembodied virtual manipulator interacting with articulated objects. The whole-body robotic kinematic control is optimized to execute the high-dimensional joint motion to reach the goals in the workspace. It does so by solving a quadratic programming (QP) model with robotic singularity and kinematic constraints. Our experiments on manipulating complex articulated objects show that the proposed approach is more generalizable to unseen objects with large intra-class variations, outperforming previous approaches. The evaluation results indicate that our approach generates more compliant robotic motion and outperforms the pure RL and IL baselines in task success rates. Additional information and videos are available at https://kl-research.github.io/decoupskill

Lightweight, controllable, and physically plausible human motion synthesis is crucial for animation, virtual reality, robotics, and human-computer interaction applications. Existing methods often compromise between computational efficiency, physical realism, or spatial controllability. We propose FlexMotion, a novel framework that leverages a computationally lightweight diffusion model operating in the latent space, eliminating the need for physics simulators and enabling fast and efficient training. FlexMotion employs a multimodal pre-trained Transformer encoder-decoder, integrating joint locations, contact forces, joint actuations and muscle activations to ensure the physical plausibility of the generated motions. FlexMotion also introduces a plug-and-play module, which adds spatial controllability over a range of motion parameters (e.g., joint locations, joint actuations, contact forces, and muscle activations). Our framework achieves realistic motion generation with improved efficiency and control, setting a new benchmark for human motion synthesis. We evaluate FlexMotion on extended datasets and demonstrate its superior performance in terms of realism, physical plausibility, and controllability.

To stabilize the periodic operation of a chemical reactor the oscillation period should be determined precisely in real time. The method discussed in the paper is based on adaptive sampling of the state variable with the use of chaotic mapping to itself. It enables precise determination of the oscillation period in real time and could be used for a proper control system, that can successfully control the process and maintain the oscillation period at a set level. The method was applied to a tank reactor and tubular reactor with recycle.

Human motion generation holds significant promise in fields such as animation, film production, and robotics. However, existing methods often fail to produce physically plausible movements that adhere to biomechanical principles. While recent autoregressive and diffusion models have improved visual quality, they frequently overlook essential biodynamic features, such as muscle activation patterns and joint coordination, leading to motions that either violate physical laws or lack controllability. This paper introduces BioMoDiffuse, a novel biomechanics-aware diffusion framework that addresses these limitations. It features three key innovations: (1) A lightweight biodynamic network that integrates muscle electromyography (EMG) signals and kinematic features with acceleration constraints, (2) A physics-guided diffusion process that incorporates real-time biomechanical verification via modified Euler-Lagrange equations, and (3) A decoupled control mechanism that allows independent regulation of motion speed and semantic context. We also propose a set of comprehensive evaluation protocols that combines traditional metrics (FID, R-precision, etc.) with new biomechanical criteria (smoothness, foot sliding, floating, etc.). Our approach bridges the gap between data-driven motion synthesis and biomechanical authenticity, establishing new benchmarks for physically accurate motion generation.

Character animation in real-world scenarios necessitates a variety of constraints, such as trajectories, key-frames, interactions, etc. Existing methodologies typically treat single or a finite set of these constraint(s) as separate control tasks. They are often specialized, and the tasks they address are rarely extendable or customizable. We categorize these as solutions to the close-set motion control problem. In response to the complexity of practical motion control, we propose and attempt to solve the open-set motion control problem. This problem is characterized by an open and fully customizable set of motion control tasks. To address this, we introduce a new paradigm, programmable motion generation. In this paradigm, any given motion control task is broken down into a combination of atomic constraints. These constraints are then programmed into an error function that quantifies the degree to which a motion sequence adheres to them. We utilize a pre-trained motion generation model and optimize its latent code to minimize the error function of the generated motion. Consequently, the generated motion not only inherits the prior of the generative model but also satisfies the required constraints. Experiments show that we can generate high-quality motions when addressing a wide range of unseen tasks. These tasks encompass motion control by motion dynamics, geometric constraints, physical laws, interactions with scenes, objects or the character own body parts, etc. All of these are achieved in a unified approach, without the need for ad-hoc paired training data collection or specialized network designs. During the programming of novel tasks, we observed the emergence of new skills beyond those of the prior model. With the assistance of large language models, we also achieved automatic programming. We hope that this work will pave the way for the motion control of general AI agents.

Visuomotor policies trained via behavior cloning are vulnerable to covariate shift, where small deviations from expert trajectories can compound into failure. Common strategies to mitigate this issue involve expanding the training distribution through human-in-the-loop corrections or synthetic data augmentation. However, these approaches are often labor-intensive, rely on strong task assumptions, or compromise the quality of imitation. We introduce Latent Policy Barrier, a framework for robust visuomotor policy learning. Inspired by Control Barrier Functions, LPB treats the latent embeddings of expert demonstrations as an implicit barrier separating safe, in-distribution states from unsafe, out-of-distribution (OOD) ones. Our approach decouples the role of precise expert imitation and OOD recovery into two separate modules: a base diffusion policy solely on expert data, and a dynamics model trained on both expert and suboptimal policy rollout data. At inference time, the dynamics model predicts future latent states and optimizes them to stay within the expert distribution. Both simulated and real-world experiments show that LPB improves both policy robustness and data efficiency, enabling reliable manipulation from limited expert data and without additional human correction or annotation.

Data-driven model predictive control has two key advantages over model-free methods: a potential for improved sample efficiency through model learning, and better performance as computational budget for planning increases. However, it is both costly to plan over long horizons and challenging to obtain an accurate model of the environment. In this work, we combine the strengths of model-free and model-based methods. We use a learned task-oriented latent dynamics model for local trajectory optimization over a short horizon, and use a learned terminal value function to estimate long-term return, both of which are learned jointly by temporal difference learning. Our method, TD-MPC, achieves superior sample efficiency and asymptotic performance over prior work on both state and image-based continuous control tasks from DMControl and Meta-World. Code and video results are available at https://nicklashansen.github.io/td-mpc.

Emerging video diffusion models achieve high visual fidelity but fundamentally couple scene dynamics with camera motion, limiting their ability to provide precise spatial and temporal control. We introduce a 4D-controllable video diffusion framework that explicitly decouples scene dynamics from camera pose, enabling fine-grained manipulation of both scene dynamics and camera viewpoint. Our framework takes continuous world-time sequences and camera trajectories as conditioning inputs, injecting them into the video diffusion model through a 4D positional encoding in the attention layer and adaptive normalizations for feature modulation. To train this model, we curate a unique dataset in which temporal and camera variations are independently parameterized; this dataset will be made public. Experiments show that our model achieves robust real-world 4D control across diverse timing patterns and camera trajectories, while preserving high generation quality and outperforming prior work in controllability. See our website for video results: https://19reborn.github.io/Bullet4D/

Deep neural networks (DNN) have shown great capacity of modeling a dynamical system; nevertheless, they usually do not obey physics constraints such as conservation laws. This paper proposes a new learning framework named ConCerNet to improve the trustworthiness of the DNN based dynamics modeling to endow the invariant properties. ConCerNet consists of two steps: (i) a contrastive learning method to automatically capture the system invariants (i.e. conservation properties) along the trajectory observations; (ii) a neural projection layer to guarantee that the learned dynamics models preserve the learned invariants. We theoretically prove the functional relationship between the learned latent representation and the unknown system invariant function. Experiments show that our method consistently outperforms the baseline neural networks in both coordinate error and conservation metrics by a large margin. With neural network based parameterization and no dependence on prior knowledge, our method can be extended to complex and large-scale dynamics by leveraging an autoencoder.

Large language models (LLMs) pre-trained on vast internet-scale data have showcased remarkable capabilities across diverse domains. Recently, there has been escalating interest in deploying LLMs for robotics, aiming to harness the power of foundation models in real-world settings. However, this approach faces significant challenges, particularly in grounding these models in the physical world and in generating dynamic robot motions. To address these issues, we introduce a novel paradigm in which we use few-shot prompts collected from the physical environment, enabling the LLM to autoregressively generate low-level control commands for robots without task-specific fine-tuning. Experiments across various robots and environments validate that our method can effectively prompt a robot to walk. We thus illustrate how LLMs can proficiently function as low-level feedback controllers for dynamic motion control even in high-dimensional robotic systems. The project website and source code can be found at: https://prompt2walk.github.io/ .