Daily Papers

Body deformation caused by muscle contraction plays a vital role in the visual realism of character animation, yet in most 3D animation pipelines artists have to manually specify muscle activations, which is time-consuming and gives no guarantee of physical realism. To address this, we propose a new method in which a reinforcement learning (RL) controller discovers per-muscle activations that track reference motions without manual tuning. Existing RL muscle controllers stop at 1D muscles; we go one step further, keeping the 1D model inside the RL control loop as a fast surrogate, and using a 3D volumetric simulation to produce the final deformation. Because both stages share the very same constitutive law, the muscle deformation is produced by the same activations that generated the motion. We further add a measured electromyography (EMG) prior that steers the redundant activation solution toward real human muscle recruitment. To achieve stable, efficient, and realistic simulation, we propose a novel geometric multigrid for Extended Position-Based Dynamics (XPBD) that is built on a coarse tetrahedral cage with barycentric-coordinate prolongation and closes a V-cycle on tetrahedral meshes. Within this GPU-parallelized solver, we inject the same Hill-type force-length law as an energy-based fiber constraint that turns per-fiber activation into realistic muscle contraction and bulging. We demonstrate volumetric muscle simulation on a 194-muscle human body with a diverse set of motions (walk, kick, swim, overhead-squat, etc.), simulating the full-body model at 18 ms per frame on a single RTX 4090. Our work takes a step toward character animation that is not only visually convincing but also biomechanically grounded. The website with code and videos is at https://chunleili.github.io/project-page-rlmuscle/.

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.

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.

Motion trajectories offer reliable references for physics-based motion learning but suffer from sparsity, particularly in regions that lack sufficient data coverage. To address this challenge, we introduce a self-supervised, structured representation and generation method that extracts spatial-temporal relationships in periodic or quasi-periodic motions. The motion dynamics in a continuously parameterized latent space enable our method to enhance the interpolation and generalization capabilities of motion learning algorithms. The motion learning controller, informed by the motion parameterization, operates online tracking of a wide range of motions, including targets unseen during training. With a fallback mechanism, the controller dynamically adapts its tracking strategy and automatically resorts to safe action execution when a potentially risky target is proposed. By leveraging the identified spatial-temporal structure, our work opens new possibilities for future advancements in general motion representation and learning algorithms.

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.

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.

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.

Planning has been very successful for control tasks with known environment dynamics. To leverage planning in unknown environments, the agent needs to learn the dynamics from interactions with the world. However, learning dynamics models that are accurate enough for planning has been a long-standing challenge, especially in image-based domains. We propose the Deep Planning Network (PlaNet), a purely model-based agent that learns the environment dynamics from images and chooses actions through fast online planning in latent space. To achieve high performance, the dynamics model must accurately predict the rewards ahead for multiple time steps. We approach this using a latent dynamics model with both deterministic and stochastic transition components. Moreover, we propose a multi-step variational inference objective that we name latent overshooting. Using only pixel observations, our agent solves continuous control tasks with contact dynamics, partial observability, and sparse rewards, which exceed the difficulty of tasks that were previously solved by planning with learned models. PlaNet uses substantially fewer episodes and reaches final performance close to and sometimes higher than strong model-free algorithms.

Joint-embedding predictive architectures (JEPAs) learn latent dynamics for planning and avoid representation collapse by matching features to maximum-entropy distributions such as isotropic Gaussians, yielding dense representations. However, it is unclear whether dense representations are the most favorable geometry for modeling dynamics. In this work, we ask whether a different geometry, sparse representations, can make action-conditioned latent dynamics easier to model, and what dynamical structure emerges from such representations. We first show that nonlinear Lipschitz dynamics can be approximated arbitrarily well by action-conditioned linear dynamics in a sufficiently high-dimensional one-hot latent space, with rollout error vanishing as the dimension grows. This motivates distributed sparse representations as a practical relaxation of one-hot sparsity. We introduce LpWorldModel (LpWM), a JEPA model regularized with Rectified Distribution Matching Regularization (RDMReg) to match encoder features to a Rectified Generalized Gaussian distribution, yielding non-negative sparse codes. Empirically, sparsity lowers the predictor complexity required for successful planning: on PushT, sparse LpWM outperforms dense LeWM by up to 57% in planning success at intermediate predictor capacities. This advantage also extends beyond Gaussian distribution matching, with LpWM outperforming dense VICReg representations across multiple predictor families. We further find that the learned sparse representations are mode-factored, with support encoding discrete dynamical regimes and feature magnitudes capturing continuous within-regime state. Together, these results suggest that sparse representations can reduce the predictor complexity required for control while revealing interpretable structure.

Offline reinforcement learning aims to train agents from pre-collected datasets. However, this comes with the added challenge of estimating the value of behaviors not covered in the dataset. Model-based methods offer a potential solution by training an approximate dynamics model, which then allows collection of additional synthetic data via rollouts in this model. The prevailing theory treats this approach as online RL in an approximate dynamics model, and any remaining performance gap is therefore understood as being due to dynamics model errors. In this paper, we analyze this assumption and investigate how popular algorithms perform as the learned dynamics model is improved. In contrast to both intuition and theory, if the learned dynamics model is replaced by the true error-free dynamics, existing model-based methods completely fail. This reveals a key oversight: The theoretical foundations assume sampling of full horizon rollouts in the learned dynamics model; however, in practice, the number of model-rollout steps is aggressively reduced to prevent accumulating errors. We show that this truncation of rollouts results in a set of edge-of-reach states at which we are effectively ``bootstrapping from the void.'' This triggers pathological value overestimation and complete performance collapse. We term this the edge-of-reach problem. Based on this new insight, we fill important gaps in existing theory, and reveal how prior model-based methods are primarily addressing the edge-of-reach problem, rather than model-inaccuracy as claimed. Finally, we propose Reach-Aware Value Learning (RAVL), a simple and robust method that directly addresses the edge-of-reach problem and hence - unlike existing methods - does not fail as the dynamics model is improved. Code open-sourced at: github.com/anyasims/edge-of-reach.

We present a Learning from Demonstration method for teaching robots to perform search strategies imitated from humans in scenarios where alignment tasks fail due to position uncertainty. The method utilizes human demonstrations to learn both a state invariant dynamics model and an exploration distribution that captures the search area covered by the demonstrator. We present two alternative algorithms for computing a search trajectory from the exploration distribution, one based on sampling and another based on deterministic ergodic control. We augment the search trajectory with forces learnt through the dynamics model to enable searching both in force and position domains. An impedance controller with superposed forces is used for reproducing the learnt strategy. We experimentally evaluate the method on a KUKA LWR4+ performing a 2D peg-in-hole and a 3D electricity socket task. Results show that the proposed method can, with only few human demonstrations, learn to complete the search task.

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.

The world evolves following its dynamics, i.e., its laws of motion. However, leading video diffusion models largely fit the pixels without modeling how the pixels transit over time. Thus, they render visually plausible frames but may not accurately obey the laws. To capture the dynamics purely from pixels, we introduce Latent Dynamics Reasoning (LDR). LDR casts the latent transition as an explicit kinematic integration, where the lower-order dynamics are integrated numerically and the model regresses only the third- and higher-order residual that drives the rollout. For this integration to extrapolate better, LDR runs it on a structured latent rather than dense convolutional features. Following PhyWorld, we validate LDR on a controlled white-box physics benchmark spanning five tasks (uniform motion, parabola, collision, bouncing, looming), focusing on out-of-distribution scenarios that reveal whether a model has truly learned the underlying dynamics. LDR extrapolates the learned dynamics far better: the gap between its in- and out-of-distribution error is over 20times smaller than the video diffusion baseline's, under both single- and joint-task training at 256^2 resolution, while using 26times fewer parameters and running 143times faster. LDR can even generalize under severe shift: for example, trained only on red balls moving left-to-right, it correctly predicts the motion of a blue square moving right-to-left. To our knowledge, this is the first video world model that extrapolates learned dynamics beyond its training distribution. Project page: https://lat-dyn-reason.github.io/

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.

In the physical world we inhabit, space and time are fundamentally continuous. However, existing machine learning paradigms for world modeling are largely confined to discrete-time prediction, thereby exhibiting significant inefficiency in capturing the dynamics of physical world. We introduce Physical-Time Flow (PT-Flow), a novel approach that learns a continuous latent velocity field operating in physical time. Crucially, the underlying dynamics of sequential data are parameterized by an ordinary differential equation (ODE) embedded in a well-structured representation space. Under this paradigm, the prediction of future can be recast as temporal integration via an ODE solver in the compressed latent space. Building upon PT-Flow, we construct ODEWorld, a continuous-time latent world model that is both efficient and versatile. By extracting time-variant features and enforcing ODE properties on both the dynamical representation space and the latent velocity field, ODEWorld effectively addresses the long-standing representation collapse issue in latent world model literature. This also enables high-quality image reconstruction even after long-horizon prediction. Moreover, its continuous nature allows for arbitrary temporal resolution and even backward prediction, which is impossible for most discrete-time models. Lastly, ODEWorld can provide rich planning-oriented information to facilitate downstream policy learning. Comprehensive experiments demonstrate that ODEWorld successfully reconciles planning-conducive dynamics abstraction with visual realism, excelling in both video generation and robotic control. https://dstate.github.io/odeworld_website/{Project Website}.

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.

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/

Accurate dynamics models are critical for informed decision-making in robotic systems, particularly for agile aerial vehicles operating under uncertainty. Neural network dynamics models are attractive for capturing complex nonlinear effects, but existing predictive approaches struggle with long-horizon forecasting because their autoregressive rollout mechanism amplifies errors over time. Joint Embedding Predictive Architectures (JEPAs) offer a compelling alternative by modeling dynamics in latent space, yet prior JEPA-style methods for robot navigation have been studied primarily for kinematic-level planning, with limited investigation in high-frequency control. In this work, we introduce the JEPA-style model for real-time quadrotor control. The proposed approach combines a latent dynamics model with a novel physics-inspired prober that maps frozen latents to interpretable state, enabling physically grounded long-horizon prediction. Additionally, we combine the learned model with a sampling-based optimal control solution to take advantage of its predictive capabilities for real-time control on embedded hardware. Finally, to reduce the dependence on expensive and unsafe real-world data collection, we develop a structured pipeline for automated dataset generation. Extensive open-loop and outdoor closed-loop experiments demonstrate accurate prediction, robust zero-shot sim-to-real transfer, and strong generalization across diverse operating conditions.

We develop a novel policy synthesis algorithm, RMPflow, based on geometrically consistent transformations of Riemannian Motion Policies (RMPs). RMPs are a class of reactive motion policies designed to parameterize non-Euclidean behaviors as dynamical systems in intrinsically nonlinear task spaces. Given a set of RMPs designed for individual tasks, RMPflow can consistently combine these local policies to generate an expressive global policy, while simultaneously exploiting sparse structure for computational efficiency. We study the geometric properties of RMPflow and provide sufficient conditions for stability. Finally, we experimentally demonstrate that accounting for the geometry of task policies can simplify classically difficult problems, such as planning through clutter on high-DOF manipulation systems.

Learning domain adaptive policies that can generalize to unseen transition dynamics, remains a fundamental challenge in learning-based control. Substantial progress has been made through domain representation learning to capture domain-specific information, thus enabling domain-aware decision making. We analyze the process of learning domain representations through dynamical prediction and find that selecting contexts adjacent to the current step causes the learned representations to entangle static domain information with varying dynamical properties. Such mixture can confuse the conditioned policy, thereby constraining zero-shot adaptation. To tackle the challenge, we propose DADP (Domain Adaptive Diffusion Policy), which achieves robust adaptation through unsupervised disentanglement and domain-aware diffusion injection. First, we introduce Lagged Context Dynamical Prediction, a strategy that conditions future state estimation on a historical offset context; by increasing this temporal gap, we unsupervisedly disentangle static domain representations by filtering out transient properties. Second, we integrate the learned domain representations directly into the generative process by biasing the prior distribution and reformulating the diffusion target. Extensive experiments on challenging benchmarks across locomotion and manipulation demonstrate the superior performance, and the generalizability of DADP over prior methods. More visualization results are available on the https://outsider86.github.io/DomainAdaptiveDiffusionPolicy/.

We propose a data augmentation method for offline reinforcement learning, motivated by active positioning problems. Particularly, our approach enables the training of off-policy models from a limited number of suboptimal trajectories. We introduce a trajectory-based augmentation technique that exploits task structure and the geometric relationship between rewards, value functions, and mathematical properties of logging policies. During data collection, our augmentation supports suboptimal logging policies, leading to higher data quality and improved offline reinforcement learning performance. We provide theoretical justification for these strategies and validate them empirically across positioning tasks of varying dimensionality and under partial observability.

Temporal abstraction and efficient planning pose significant challenges in offline reinforcement learning, mainly when dealing with domains that involve temporally extended tasks and delayed sparse rewards. Existing methods typically plan in the raw action space and can be inefficient and inflexible. Latent action spaces offer a more flexible paradigm, capturing only possible actions within the behavior policy support and decoupling the temporal structure between planning and modeling. However, current latent-action-based methods are limited to discrete spaces and require expensive planning. This paper presents a unified framework for continuous latent action space representation learning and planning by leveraging latent, score-based diffusion models. We establish the theoretical equivalence between planning in the latent action space and energy-guided sampling with a pretrained diffusion model and incorporate a novel sequence-level exact sampling method. Our proposed method, LatentDiffuser, demonstrates competitive performance on low-dimensional locomotion control tasks and surpasses existing methods in higher-dimensional tasks.

We present a novel approach for generating motion primitives for kinodynamic motion planning using diffusion models. The motions generated by our approach are adapted to each problem instance by utilizing problem-specific parameters, allowing for finding solutions faster and of better quality. The diffusion models used in our approach are trained on randomly cut solution trajectories. These trajectories are created by solving randomly generated problem instances with a kinodynamic motion planner. Experimental results show significant improvements up to 30 percent in both computation time and solution quality across varying robot dynamics such as second-order unicycle or car with trailer.

Diffusion-based world models can generate and predict trajectories in high-dimensional dynamical systems, but predictive accuracy does not imply that their latent coordinates recover the underlying state variables or causal interactions. We ask whether a frozen pretrained diffusion model can be equipped with identifiable coordinates without retraining its generative backbone. We show that auxiliary-variable nonlinear ICA guarantees can be transferred to Contrastive Diffusion Alignment (ConDA), which learns only a lightweight alignment map on top of frozen diffusion latents. Under standard TCL/GCL assumptions, the aligned representation identifies latent dynamical states up to permutation and componentwise invertible transformations, preserves the latent dynamic structural causal model, and reduces lagged graph recovery to transition-Jacobian sparsity. We evaluate TCL-, GCL-, and CEBRA-based ConDA against TDRL, CaRiNG, IDOL, temporal SuaVE, and iVAE across physical and robotic video systems. TCL and GCL achieve near-perfect blockwise state recovery and competitive lagged graph recovery, including exact recovery in a simulated falling-body system. In a simulated bipedal robot, learned dynamics recover the sign and temporal structure of responses to held-out control perturbations. These results show that a frozen generative diffusion model can be equipped with coordinates that are identifiable, structurally interpretable, and useful for analyzing intervention-relevant dynamics.

Dynamics models learned from visual observations have shown to be effective in various robotic manipulation tasks. One of the key questions for learning such dynamics models is what scene representation to use. Prior works typically assume representation at a fixed dimension or resolution, which may be inefficient for simple tasks and ineffective for more complicated tasks. In this work, we investigate how to learn dynamic and adaptive representations at different levels of abstraction to achieve the optimal trade-off between efficiency and effectiveness. Specifically, we construct dynamic-resolution particle representations of the environment and learn a unified dynamics model using graph neural networks (GNNs) that allows continuous selection of the abstraction level. During test time, the agent can adaptively determine the optimal resolution at each model-predictive control (MPC) step. We evaluate our method in object pile manipulation, a task we commonly encounter in cooking, agriculture, manufacturing, and pharmaceutical applications. Through comprehensive evaluations both in the simulation and the real world, we show that our method achieves significantly better performance than state-of-the-art fixed-resolution baselines at the gathering, sorting, and redistribution of granular object piles made with various instances like coffee beans, almonds, corn, etc.

Imitation learning (IL) enables efficient skill acquisition from demonstrations but often struggles with long-horizon tasks and high-precision control due to compounding errors. Residual policy learning offers a promising, model-agnostic solution by refining a base policy through closed-loop corrections. However, existing approaches primarily focus on local corrections to the base policy, lacking a global understanding of state evolution, which limits robustness and generalization to unseen scenarios. To address this, we propose incorporating global dynamics modeling to guide residual policy updates. Specifically, we leverage Koopman operator theory to impose linear time-invariant structure in a learned latent space, enabling reliable state transitions and improved extrapolation for long-horizon prediction and unseen environments. We introduce KORR (Koopman-guided Online Residual Refinement), a simple yet effective framework that conditions residual corrections on Koopman-predicted latent states, enabling globally informed and stable action refinement. We evaluate KORR on long-horizon, fine-grained robotic furniture assembly tasks under various perturbations. Results demonstrate consistent gains in performance, robustness, and generalization over strong baselines. Our findings further highlight the potential of Koopman-based modeling to bridge modern learning methods with classical control theory.

We develop data-driven methods incorporating geometric and topological information to learn parsimonious representations of nonlinear dynamics from observations. The approaches learn nonlinear state-space models of the dynamics for general manifold latent spaces using training strategies related to Variational Autoencoders (VAEs). Our methods are referred to as Geometric Dynamic (GD) Variational Autoencoders (GD-VAEs). We learn encoders and decoders for the system states and evolution based on deep neural network architectures that include general Multilayer Perceptrons (MLPs), Convolutional Neural Networks (CNNs), and other architectures. Motivated by problems arising in parameterized PDEs and physics, we investigate the performance of our methods on tasks for learning reduced dimensional representations of the nonlinear Burgers Equations, Constrained Mechanical Systems, and spatial fields of Reaction-Diffusion Systems. GD-VAEs provide methods that can be used to obtain representations in manifold latent spaces for diverse learning tasks involving dynamics.

In this paper, we address the task of interacting with dynamic environments where the changes in the environment are independent of the agent. We study this through the context of trapping a moving ball with a UR5 robotic arm. Our key contribution is an approach to utilize a static planner for dynamic tasks using a Dynamic Planning add-on; that is, if we can successfully solve a task with a static target, then our approach can solve the same task when the target is moving. Our approach has three key components: an off-the-shelf static planner, a trajectory forecasting network, and a network to predict robot's estimated time of arrival at any location. We demonstrate the generalization of our approach across environments. More information and videos at https://mlevy2525.github.io/DynamicAddOn.

Text-conditioned human motion generation, which allows for user interaction through natural language, has become increasingly popular. Existing methods typically generate short, isolated motions based on a single input sentence. However, human motions are continuous and can extend over long periods, carrying rich semantics. Creating long, complex motions that precisely respond to streams of text descriptions, particularly in an online and real-time setting, remains a significant challenge. Furthermore, incorporating spatial constraints into text-conditioned motion generation presents additional challenges, as it requires aligning the motion semantics specified by text descriptions with geometric information, such as goal locations and 3D scene geometry. To address these limitations, we propose DartControl, in short DART, a Diffusion-based Autoregressive motion primitive model for Real-time Text-driven motion control. Our model effectively learns a compact motion primitive space jointly conditioned on motion history and text inputs using latent diffusion models. By autoregressively generating motion primitives based on the preceding history and current text input, DART enables real-time, sequential motion generation driven by natural language descriptions. Additionally, the learned motion primitive space allows for precise spatial motion control, which we formulate either as a latent noise optimization problem or as a Markov decision process addressed through reinforcement learning. We present effective algorithms for both approaches, demonstrating our model's versatility and superior performance in various motion synthesis tasks. Experiments show our method outperforms existing baselines in motion realism, efficiency, and controllability. Video results are available on the project page: https://zkf1997.github.io/DART/.

In this paper, we study robust decision-making in the latent space of world models (WMs). Robust optimization is a mathematical framework where, given explicitly specified dynamics and physically meaningful disturbances, a robot can select actions that remain effective even under worst-case disturbances. However, applying this principle to the learned latent space of WMs introduces a fundamental challenge: because WMs have fully learned state spaces and dynamics inferred from high-dimensional observations, it is unclear how to define latent-space disturbances that faithfully represent uncertainty in the underlying system. Our key idea is to model a latent-space disturbance as a perturbation to the learned latent dynamics that induces pessimistic but plausible transitions. Specifically, we construct a set of plausible latent dynamics by combining a dynamics-aware similarity metric that captures plausible transitions with out-of-distribution detection that excludes implausible latent states. We calibrate this uncertainty set over latent dynamics using conformal prediction, ensuring that WM imaginations induced by the latent disturbance remain plausible without becoming overly pessimistic. We then jointly optimize robust robot actions and the worst-case latent disturbances through game-theoretic optimization. We leverage this latent-space robust optimization to robustify policy steering, considering two paradigms: latent safety filtering and sample-and-verify steering of a generative control policy. Our controlled simulation experiments show that our latent disturbance enables robust decision-making directly in WM latent spaces, and hardware experiments with a Franka manipulator show that modeling latent disturbances enables robust policy steering, reducing failures by 70% in safety filtering and 54% in sampling-based policy steering. Project website: https://junwon.me/LatentDisturbance/.

Learning the continuous dynamics of a system from snapshots of its temporal marginals is a problem which appears throughout natural sciences and machine learning, including in quantum systems, single-cell biological data, and generative modeling. In these settings, we assume access to cross-sectional samples that are uncorrelated over time, rather than full trajectories of samples. In order to better understand the systems under observation, we would like to learn a model of the underlying process that allows us to propagate samples in time and thereby simulate entire individual trajectories. In this work, we propose Action Matching, a method for learning a rich family of dynamics using only independent samples from its time evolution. We derive a tractable training objective, which does not rely on explicit assumptions about the underlying dynamics and does not require back-propagation through differential equations or optimal transport solvers. Inspired by connections with optimal transport, we derive extensions of Action Matching to learn stochastic differential equations and dynamics involving creation and destruction of probability mass. Finally, we showcase applications of Action Matching by achieving competitive performance in a diverse set of experiments from biology, physics, and generative modeling.

With the rapid advancement of large language models (LLMs) and vision-language models (VLMs), significant progress has been made in developing open-vocabulary robotic manipulation systems. However, many existing approaches overlook the importance of object dynamics, limiting their applicability to more complex, dynamic tasks. In this work, we introduce KUDA, an open-vocabulary manipulation system that integrates dynamics learning and visual prompting through keypoints, leveraging both VLMs and learning-based neural dynamics models. Our key insight is that a keypoint-based target specification is simultaneously interpretable by VLMs and can be efficiently translated into cost functions for model-based planning. Given language instructions and visual observations, KUDA first assigns keypoints to the RGB image and queries the VLM to generate target specifications. These abstract keypoint-based representations are then converted into cost functions, which are optimized using a learned dynamics model to produce robotic trajectories. We evaluate KUDA on a range of manipulation tasks, including free-form language instructions across diverse object categories, multi-object interactions, and deformable or granular objects, demonstrating the effectiveness of our framework. The project page is available at http://kuda-dynamics.github.io.

Path-velocity decomposition is an intuitive yet powerful approach to address the complexity of kinodynamic motion planning. The difficult trajectory planning problem is solved in two separate, simpler, steps: first, find a path in the configuration space that satisfies the geometric constraints (path planning), and second, find a time-parameterization of that path satisfying the kinodynamic constraints. A fundamental requirement is that the path found in the first step should be time-parameterizable. Most existing works fulfill this requirement by enforcing quasi-static constraints in the path planning step, resulting in an important loss in completeness. We propose a method that enables path-velocity decomposition to discover truly dynamic motions, i.e. motions that are not quasi-statically executable. At the heart of the proposed method is a new algorithm -- Admissible Velocity Propagation -- which, given a path and an interval of reachable velocities at the beginning of that path, computes exactly and efficiently the interval of all the velocities the system can reach after traversing the path while respecting the system kinodynamic constraints. Combining this algorithm with usual sampling-based planners then gives rise to a family of new trajectory planners that can appropriately handle kinodynamic constraints while retaining the advantages associated with path-velocity decomposition. We demonstrate the efficiency of the proposed method on some difficult kinodynamic planning problems, where, in particular, quasi-static methods are guaranteed to fail.

Reinforcement learning is able to solve complex sequential decision-making tasks but is currently limited by sample efficiency and required computation. To improve sample efficiency, recent work focuses on model-based RL which interleaves model learning with planning. Recent methods further utilize policy learning, value estimation, and, self-supervised learning as auxiliary objectives. In this paper we show that, surprisingly, a simple representation learning approach relying only on a latent dynamics model trained by latent temporal consistency is sufficient for high-performance RL. This applies when using pure planning with a dynamics model conditioned on the representation, but, also when utilizing the representation as policy and value function features in model-free RL. In experiments, our approach learns an accurate dynamics model to solve challenging high-dimensional locomotion tasks with online planners while being 4.1 times faster to train compared to ensemble-based methods. With model-free RL without planning, especially on high-dimensional tasks, such as the DeepMind Control Suite Humanoid and Dog tasks, our approach outperforms model-free methods by a large margin and matches model-based methods' sample efficiency while training 2.4 times faster.

Recent Vision-Language-Action models show potential to generalize across embodiments but struggle to quickly align with a new robot's action space when high-quality demonstrations are scarce, especially for bipedal humanoids. We present TrajBooster, a cross-embodiment framework that leverages abundant wheeled-humanoid data to boost bipedal VLA. Our key idea is to use end-effector trajectories as a morphology-agnostic interface. TrajBooster (i) extracts 6D dual-arm end-effector trajectories from real-world wheeled humanoids, (ii) retargets them in simulation to Unitree G1 with a whole-body controller trained via a heuristic-enhanced harmonized online DAgger to lift low-dimensional trajectory references into feasible high-dimensional whole-body actions, and (iii) forms heterogeneous triplets that couple source vision/language with target humanoid-compatible actions to post-pre-train a VLA, followed by only 10 minutes of teleoperation data collection on the target humanoid domain. Deployed on Unitree G1, our policy achieves beyond-tabletop household tasks, enabling squatting, cross-height manipulation, and coordinated whole-body motion with markedly improved robustness and generalization. Results show that TrajBooster allows existing wheeled-humanoid data to efficiently strengthen bipedal humanoid VLA performance, reducing reliance on costly same-embodiment data while enhancing action space understanding and zero-shot skill transfer capabilities. For more details, For more details, please refer to our https://jiachengliu3.github.io/TrajBooster/.

We introduce Adaptive Filter Attention (AFA), a novel attention mechanism that incorporates a learnable dynamics model directly into the computation of attention weights. Rather than comparing queries and keys directly, we model the input sequence as discrete observations of a linear stochastic differential equation (SDE). By imposing a linear dynamics model with simultaneously diagonalizable state matrices and noise covariances, we can make use of a closed-form solution to the differential Lyapunov equation to efficiently propagate pairwise uncertainties through the dynamics. Attention naturally arises as the maximum likelihood solution for this linear SDE, with attention weights corresponding to robust residual-based reweightings of the propagated pairwise precisions. Imposing an additional constraint on the state matrix's eigenvalues leads to a simplified variant with the same computational and memory complexity as standard attention. In the limit of vanishing dynamics and process noise, and using a small-angle approximation, we recover ordinary dot-product attention.

Robots capable of learning from demonstration (LfD) must exhibit stability while executing learned motion skills. To be effective in the real world, they should also remember multiple skills over time -- a capability lacking in current stable-LfD methods. We propose an approach to stable, continual LfD, and highlight the role of stability in improving continual learning. Our proposed hypernetwork generates the parameters of two neural networks: a trajectory learning dynamics model, and a trajectory-stabilizing Lyapunov function. These generated networks form a clock-augmented stable neural ODE solver (sNODE), a stable dynamics model that offers a superior stability-accuracy trade-off compared to the state-of-the-art. We further propose stochastic hypernetwork regularization with a single, uniformly-sampled task embedding, reducing the cumulative training time for N tasks from O(N^2) to O(N) without degrading performance on real-world tasks. We introduce high-dimensional variants of the popular LASA dataset to assess scalability and extend a dataset of robotic LfD tasks to assess real-world performance. We empirically evaluate our approach on multiple LfD datasets of varying complexity, including sequences of 7--26 tasks, trajectories of 2--32 dimensions, and real-world tasks involving position and orientation. Our thorough evaluation on multiple LfD datasets demonstrates that our approach sequentially learns and retains multiple motion skills without retraining on past demonstrations, and outperforms other relevant baselines in terms of trajectory errors, continual learning scores, and stability metrics. Notably, we show that stability greatly enhances continual learning performance, particularly in size-efficient chunked hypernetworks. Our code is available at https://github.com/sayantanauddy/clfd-snode.

World models enable model-based planning through learned latent dynamics, but imagined rollouts become unstable as the planning horizon grows or the dynamics distribution shifts. We argue that this instability reflects two missing structures in planner-facing latents: history-conditioned memory for approximate Markov completeness, and geometric organization that separates configuration, momentum, and task semantics. We propose HaM-World (HMW), a structured world model that decomposes the latent state into a canonical (q, p) subspace and a context subspace c, while using Mamba selective state-space memory as the history-conditioned input to the same latent dynamics. Within this interface, (q, p) evolves through an energy-derived Hamiltonian vector field plus learnable residual/control dynamics, while c captures semantic, dissipative, and non-conservative factors. This gives the planner a single latent state shared by dynamics prediction, reward/value estimation, imagined rollouts, and CEM action search. On four DeepMind Control Suite tasks, HaM-World reaches the highest Avg. AUC (117.9, +9.5%), reduces long-horizon rollout error to 45% of a strong baseline model, and wins 11/12 k in {3,5,7} MSE cells. Under 12 OOD perturbations spanning dynamics shifts, action delay, and observation masking, HaM-World achieves the highest return in every condition, with average OOD-return gains of 10.2% on Finger Spin and 13.6% on Reacher Easy. Mechanism diagnostics further show bounded action-free Hamiltonian-energy drift, structured energy variation under policy rollouts, and coherent control-induced energy transfer, supporting the intended Soft-Hamiltonian dynamics design.

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.

Joint embedding predictive architectures (JEPAs) predict future latent representations without reconstructing observations, enabling world models to focus on high-level semantic dynamics. However, a JEPA can preserve high dimensional visual information while discarding information about the physical consequences of actions. We call this failure mode causal dynamics information collapse and propose action-grounded vision-invariance latent (AVL) to prevent this collapse. We first use the executed action as an auxiliary dynamics anchor that encourages the model to preserve dynamics information, and then use a vision-invariance pathway which aligns perturbed and clean latent predictions without discarding dynamics information, forcing the model to fully understand and utilize causal dynamics information. We validate AVL on four robotic control tasks (TwoRoom, PushT, OGBench Cube, and Reacher), showing that it substantially improves success rates under visual perturbations while preserving clean-environment performance. We further evaluate physical consequence alignment, clean-noisy dynamics consistency, and the causal effect of targeted transition subspace erasure. Collectively, these results indicate that dynamic information causally relevant to planning is preserved from collapse under AVL.

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.

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.

Operating effectively in complex environments while complying with specified constraints is crucial for the safe and successful deployment of robots that interact with and operate around people. In this work, we focus on generating long-horizon trajectories that adhere to novel static and temporally-extended constraints/instructions at test time. We propose a data-driven diffusion-based framework, LTLDoG, that modifies the inference steps of the reverse process given an instruction specified using finite linear temporal logic (LTL_f). LTLDoG leverages a satisfaction value function on LTL_f and guides the sampling steps using its gradient field. This value function can also be trained to generalize to new instructions not observed during training, enabling flexible test-time adaptability. Experiments in robot navigation and manipulation illustrate that the method is able to generate trajectories that satisfy formulae that specify obstacle avoidance and visitation sequences. Code and supplementary material are available online at https://github.com/clear-nus/ltldog.

With the great success of diffusion models (DMs) in generating realistic synthetic vision data, many researchers have investigated their potential in decision-making and control. Most of these works utilized DMs to sample directly from the trajectory space, where DMs can be viewed as a combination of dynamics models and policies. In this work, we explore how to decouple DMs' ability as dynamics models in fully offline settings, allowing the learning policy to roll out trajectories. As DMs learn the data distribution from the dataset, their intrinsic policy is actually the behavior policy induced from the dataset, which results in a mismatch between the behavior policy and the learning policy. We propose Dynamics Diffusion, short as DyDiff, which can inject information from the learning policy to DMs iteratively. DyDiff ensures long-horizon rollout accuracy while maintaining policy consistency and can be easily deployed on model-free algorithms. We provide theoretical analysis to show the advantage of DMs on long-horizon rollout over models and demonstrate the effectiveness of DyDiff in the context of offline reinforcement learning, where the rollout dataset is provided but no online environment for interaction.

Graph Neural Networks (GNNs) with equivariant properties have emerged as powerful tools for modeling complex dynamics of multi-object physical systems. However, their generalization ability is limited by the inadequate consideration of physical inductive biases: (1) Existing studies overlook the continuity of transitions among system states, opting to employ several discrete transformation layers to learn the direct mapping between two adjacent states; (2) Most models only account for first-order velocity information, despite the fact that many physical systems are governed by second-order motion laws. To incorporate these inductive biases, we propose the Second-order Equivariant Graph Neural Ordinary Differential Equation (SEGNO). Specifically, we show how the second-order continuity can be incorporated into GNNs while maintaining the equivariant property. Furthermore, we offer theoretical insights into SEGNO, highlighting that it can learn a unique trajectory between adjacent states, which is crucial for model generalization. Additionally, we prove that the discrepancy between this learned trajectory of SEGNO and the true trajectory is bounded. Extensive experiments on complex dynamical systems including molecular dynamics and motion capture demonstrate that our model yields a significant improvement over the state-of-the-art baselines.

Rapidly-exploring Random Trees (RRT) and its variations have emerged as a robust and efficient tool for finding collision-free paths in robotic systems. However, adding dynamic constraints makes the motion planning problem significantly harder, as it requires solving two-value boundary problems (computationally expensive) or propagating random control inputs (uninformative). Alternatively, Iterative Discontinuity Bounded A* (iDb-A*), introduced in our previous study, combines search and optimization iteratively. The search step connects short trajectories (motion primitives) while allowing a bounded discontinuity between the motion primitives, which is later repaired in the trajectory optimization step. Building upon these foundations, in this paper, we present iDb-RRT, a sampling-based kinodynamic motion planning algorithm that combines motion primitives and trajectory optimization within the RRT framework. iDb-RRT is probabilistically complete and can be implemented in forward or bidirectional mode. We have tested our algorithm across a benchmark suite comprising 30 problems, spanning 8 different systems, and shown that iDb-RRT can find solutions up to 10x faster than previous methods, especially in complex scenarios that require long trajectories or involve navigating through narrow passages.

General-purpose navigation in challenging environments remains a significant problem in robotics, with current state-of-the-art approaches facing myriad limitations. Classical approaches struggle with cluttered settings and require extensive tuning, while learning-based methods face difficulties generalizing to out-of-distribution environments. This paper introduces X-Mobility, an end-to-end generalizable navigation model that overcomes existing challenges by leveraging three key ideas. First, X-Mobility employs an auto-regressive world modeling architecture with a latent state space to capture world dynamics. Second, a diverse set of multi-head decoders enables the model to learn a rich state representation that correlates strongly with effective navigation skills. Third, by decoupling world modeling from action policy, our architecture can train effectively on a variety of data sources, both with and without expert policies: off-policy data allows the model to learn world dynamics, while on-policy data with supervisory control enables optimal action policy learning. Through extensive experiments, we demonstrate that X-Mobility not only generalizes effectively but also surpasses current state-of-the-art navigation approaches. Additionally, X-Mobility also achieves zero-shot Sim2Real transferability and shows strong potential for cross-embodiment generalization.

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

Accurately anticipating how complex, diverse scenes will evolve requires models that represent uncertainty, simulate along extended interaction chains, and efficiently explore many plausible futures. Yet most existing approaches rely on dense video or latent-space prediction, expending substantial capacity on dense appearance rather than on the underlying sparse trajectories of points in the scene. This makes large-scale exploration of future hypotheses costly and limits performance when long-horizon, multi-modal motion is essential. We address this by formulating the prediction of open-set future scene dynamics as step-wise inference over sparse point trajectories. Our autoregressive diffusion model advances these trajectories through short, locally predictable transitions, explicitly modeling the growth of uncertainty over time. This dynamics-centric representation enables fast rollout of thousands of diverse futures from a single image, optionally guided by initial constraints on motion, while maintaining physical plausibility and long-range coherence. We further introduce OWM, a benchmark for open-set motion prediction based on diverse in-the-wild videos, to evaluate accuracy and variability of predicted trajectory distributions under real-world uncertainty. Our method matches or surpasses dense simulators in predictive accuracy while achieving orders-of-magnitude higher sampling speed, making open-set future prediction both scalable and practical. Project page: http://compvis.github.io/myriad.

We propose a novel parameterized skill-learning algorithm that aims to learn transferable parameterized skills and synthesize them into a new action space that supports efficient learning in long-horizon tasks. We propose to leverage off-policy Meta-RL combined with a trajectory-centric smoothness term to learn a set of parameterized skills. Our agent can use these learned skills to construct a three-level hierarchical framework that models a Temporally-extended Parameterized Action Markov Decision Process. We empirically demonstrate that the proposed algorithms enable an agent to solve a set of difficult long-horizon (obstacle-course and robot manipulation) tasks.

Leveraging diverse robotic data for pretraining remains a critical challenge. Existing methods typically model the dataset's action distribution using simple observations as inputs. However, these inputs are often incomplete, resulting in a dispersed conditional action distribution-an issue we refer to as coordinate system chaos and state chaos. This inconsistency significantly hampers pretraining efficiency. To address this, we propose 4D-VLA, a novel approach that effectively integrates 4D information into the input to mitigate these sources of chaos. Our model introduces depth and temporal information into visual features with sequential RGB-D inputs, aligning the coordinate systems of the robot and the scene. This alignment endows the model with strong spatiotemporal reasoning capabilities while minimizing training overhead. Additionally, we introduce memory bank sampling, a frame sampling strategy designed to extract informative frames from historical images, further improving effectiveness and efficiency. Experimental results demonstrate that our pretraining method and architectural components substantially enhance model performance. In both simulated and real-world experiments, our model achieves a significant increase in success rate over OpenVLA. To further assess spatial perception and generalization to novel views, we introduce MV-Bench, a multi-view simulation benchmark. Our model consistently outperforms existing methods, demonstrating stronger spatial understanding and adaptability.

End-to-end autonomous driving has emerged as a compelling paradigm for learning planning directly from sensor observations, while recent world-model-based approaches further enrich this paradigm by enabling explicit reasoning about how the scene may evolve in the future. Yet future prediction alone does not guarantee better planning unless the predicted evolution can be converted into planning-relevant trajectory updates. Many current methods still forecast future scene states without explicitly decoding the motion implications hidden in state transitions. As a result, future reasoning often remains descriptively useful but only weakly coupled to executable motion generation. To address this limitation, we propose IDOL, an inverse-dynamics-guided future prediction framework for world-model-based end-to-end planning in latent BEV space, where inverse dynamics serves as the key bridge between future prediction and trajectory optimization. IDOL first predicts multiple future latent scene states with a BEV world model, then applies an inverse dynamics model to adjacent latent futures to decode transition-aware trajectory features and recover planning-relevant motion deltas that explain how the latent world evolves over time. These inverse-dynamics-derived signals are used to optimize the planned trajectory, turning future forecasting from passive scene anticipation into actionable planning guidance. A lightweight closed-loop refinement module further improves long-horizon consistency by reusing the optimized trajectory for another round of future-aware reasoning. By introducing inverse dynamics into latent future reasoning, IDOL tightens the coupling between world modeling and planning. Extensive experiments on the NAVSIM v1 and NAVSIM v2 benchmarks show that IDOL achieves state-of-the-art performance among comparable methods.

The goal of a world model is to capture the dynamics of an environment. This has the great appeal that it allows agents to plan and simulate a course of actions with the help of a world model. For these uses to be reliable, however, the learned dynamics must behave well beyond the specific state-action combinations observed in expert rollouts. Despite this, the relationship between data coverage, dynamics generalization, and downstream planning performance remains underexplored. We study this relationship through the lens of compositional generalization: can a world model recombine familiar state and action factors into valid dynamics? To answer this, we introduce AnyGoal, a benchmark of goal-shifted task variants built from widely used world-model environments, together with an open-source library. Each task is designed to be within reach of a world model that has learned the underlying dynamics: individual state factors and actions remain within their training support, but their combinations are underrepresented in expert trajectories. Across multiple environments and world model families, we find that current models consistently exhibit failures under these recombinations. By examining dynamics and representation failures across model families, interaction regimes, and evaluation metrics, we study where current world models generalize and where challenges remain for goal-shifted prediction and planning. Together, this framework, benchmark, and analysis provide a basis for evaluating progress toward world models that generalize to new planning tasks.

World models have recently re-emerged as a central paradigm for embodied intelligence, robotics, autonomous driving, and model-based reinforcement learning. However, current world model research is often dominated by three partially separated routes: 2D video-generative models that emphasize visual future synthesis, 3D scene-centric models that emphasize spatial reconstruction, and JEPA-like latent models that emphasize abstract predictive representations. While each route has made important progress, they still struggle to provide physically reliable, action-controllable, and long-horizon stable predictions for embodied decision making. In this paper, we argue that the bottleneck of world models is no longer only whether they can generate realistic futures, but whether those futures are physically meaningful and useful for action. We propose Hamiltonian World Models as a physically grounded perspective on world modeling. The key idea is to encode observations into a structured latent phase space, evolve the latent state through Hamiltonian-inspired dynamics with control, dissipation, and residual terms, decode the predicted trajectory into future observations, and use the resulting rollouts for planning. We discuss how Hamiltonian structure may improve interpretability, data efficiency, and long-horizon stability, while also noting practical challenges in real-world robotic scenes involving friction, contact, non-conservative forces, and deformable objects.

World models are essential for autonomous robotic planning. However, the substantial computational overhead of existing dense Transformerbased models significantly hinders real-time deployment. To address this efficiency-performance bottleneck, we introduce DDP-WM, a novel world model centered on the principle of Disentangled Dynamics Prediction (DDP). We hypothesize that latent state evolution in observed scenes is heterogeneous and can be decomposed into sparse primary dynamics driven by physical interactions and secondary context-driven background updates. DDP-WM realizes this decomposition through an architecture that integrates efficient historical processing with dynamic localization to isolate primary dynamics. By employing a crossattention mechanism for background updates, the framework optimizes resource allocation and provides a smooth optimization landscape for planners. Extensive experiments demonstrate that DDP-WM achieves significant efficiency and performance across diverse tasks, including navigation, precise tabletop manipulation, and complex deformable or multi-body interactions. Specifically, on the challenging Push-T task, DDP-WM achieves an approximately 9 times inference speedup and improves the MPC success rate from 90% to98% compared to state-of-the-art dense models. The results establish a promising path for developing efficient, high-fidelity world models. Codes will be available at https://github.com/HCPLab-SYSU/DDP-WM.

The rapid progress of artificial intelligence is reshaping robotics and accelerating the adoption of learning-based approaches. While purely data-driven methods have achieved remarkable success in computer vision and natural language processing, robotics remains constrained by limited data, complex real-world interactions, and the need for reliable operation. These challenges have motivated the exploration of physics-embedded robot learning, which embeds physics priors into learning algorithms. By encoding the underlying physical laws and constraints, physics priors can complement limited data with robotics-specific inductive biases, potentially improving generalization, interpretability, and sample efficiency. However, the literature on physics-embedded robot learning remains fragmented across terminology, methodologies, and application domains, making it difficult to assess this growing body of work. This survey reviews physics-embedded robot learning across a broad range of physics priors, robotics applications, and machine learning models, from single-layer perceptrons to generative foundation models. We adopt a unified taxonomy that classifies existing approaches according to their physics embedding: physics-guided inputs, data, and representations; physics-encoded model architectures; and physics-informed training loss functions. Building on this taxonomy, we review methods for robot dynamics learning, trajectory planning, prediction, control, and estimation, together with the corresponding open-source software ecosystem. We identify key open challenges, and outline promising future research directions. Overall, we argue that physics priors provide a particularly relevant robotics-specific inductive bias, complementing rather than replacing data-driven learning, and paving the way toward more generalizable, data-efficient, and trustworthy robotic systems.

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.

Learning to simulate complex physical systems from data has emerged as a promising way to overcome the limitations of traditional numerical solvers, which often require prohibitive computational costs for high-fidelity solutions. Recent Graph Neural Simulators (GNSs) accelerate simulations by learning dynamics on graph-structured data, yet often struggle to capture long-range interactions and suffer from error accumulation under autoregressive rollouts. To address these challenges, we propose Information-preserving Graph Neural Simulators (IGNS), a graph-based neural simulator built on the principles of Hamiltonian dynamics. This structure guarantees preservation of information across the graph, while extending to port-Hamiltonian systems allows the model to capture a broader class of dynamics, including non-conservative effects. IGNS further incorporates a warmup phase to initialize global context, geometric encoding to handle irregular meshes, and a multi-step training objective that facilitates PDE matching, where the trajectory produced by integrating the port-Hamiltonian core aligns with the ground-truth trajectory, thereby reducing rollout error. To evaluate these properties systematically, we introduce new benchmarks that target long-range dependencies and challenging external forcing scenarios. Across all tasks, IGNS consistently outperforms state-of-the-art GNSs, achieving higher accuracy and stability under challenging and complex dynamical systems. Our project page: https://thobotics.github.io/neural_pde_matching.

Visual navigation requires agents to reach goals in complex environments through perception and planning. World models address this task by simulating action-conditioned state transitions to predict future observations. Current navigation world models typically learn state evolution under actions within the compressed latent space of a Variational Autoencoder, where spatial compression often discards fine-grained structural information and hinders precise control. To better understand the propagation characteristics of different representations, we conduct a linear dynamics probe and observe that dense DINOv2 features exhibit stronger linear predictability for action-conditioned transitions. Motivated by this observation, we propose the Representation Autoencoder-based Navigation World Model (RAE-NWM), which models navigation dynamics in a dense visual representation space. We employ a Conditional Diffusion Transformer with Decoupled Diffusion Transformer head (CDiT-DH) to model continuous transitions, and introduce a separate time-driven gating module for dynamics conditioning to regulate action injection strength during generation. Extensive evaluations show that modeling sequential rollouts in this space improves structural stability and action accuracy, benefiting downstream planning and navigation.

Preference-based reinforcement learning (PbRL) aligns a robot behavior with human preferences via a reward function learned from binary feedback over agent behaviors. We show that dynamics-aware reward functions improve the sample efficiency of PbRL by an order of magnitude. In our experiments we iterate between: (1) learning a dynamics-aware state-action representation (z^{sa}) via a self-supervised temporal consistency task, and (2) bootstrapping the preference-based reward function from (z^{sa}), which results in faster policy learning and better final policy performance. For example, on quadruped-walk, walker-walk, and cheetah-run, with 50 preference labels we achieve the same performance as existing approaches with 500 preference labels, and we recover 83\% and 66\% of ground truth reward policy performance versus only 38\% and 21\%. The performance gains demonstrate the benefits of explicitly learning a dynamics-aware reward model. Repo: https://github.com/apple/ml-reed.

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.

Data-driven approaches have revolutionized 3D vision, enabling transformers to effectively reconstruct and generate static 3D objects. However, generating simulative 4D dynamics -- realistic temporal deformations of static objects under various physical conditions -- remains challenging and often ad hoc, despite its importance in building comprehensive 3D world models. Most existing methods assume a predefined physical model and use system identification to estimate parameters, restricting these methods to specific categories and small-scale datasets. We propose that these restrictions can be overcome by learning a data-driven kinematic state parameterization for object-centric physical systems. Specifically, we learn both a latent space representing all possible states of the object and a decoder that maps any sampled latent to a plausibly deformed shape of the object. We refer to this parameterization as Neural Object Kinematics (NeuROK), and learn a transformer-based encoder-decoder model on a curated large-scale 4D dataset. This formulation and the learned model significantly simplify the generation of simulative dynamics since we only need to consider the dynamics within a low-dimensional latent space from the Lagrangian mechanics' perspective in classical physics. We demonstrate the effectiveness and generality of this neural simulation framework across diverse dynamic object types, showing clear advantages over prior works. Project page: https://chen-geng.com/neurok

Joint Embedding Predictive Architectures (JEPAs) have shown promising world modeling capabilities, enabling planning in latent space by optimizing action trajectories using methods like the Cross-Entropy Method (CEM). These methods are, however, too computationally expensive and ineffective for long-horizon planning. Furthermore, these methods typically require an explicit image of the goal state, which is not always possible in real-world tasks. In this work, we tackle these limitations by proposing Forward-Forward-JEPA (FF-JEPA), a hierarchical approach leveraging two forward dynamics models. Alongside a standard action-conditioned forward model, we introduce an action-free latent planner that predicts the next subgoal given the current state. This approach removes the need for goal images and enables long-horizon planning by decomposing complex trajectories into a sequence of tractable, short-term optimization problems. Preliminary results on PushT demonstrate that FF-JEPA successfully overcomes flat world models' long-horizon collapse, highlighting this approach as a promising direction for goal-free planning.

Koopman representations aim to learn features of nonlinear dynamical systems (NLDS) which lead to linear dynamics in the latent space. Theoretically, such features can be used to simplify many problems in modeling and control of NLDS. In this work we study autoencoder formulations of this problem, and different ways they can be used to model dynamics, specifically for future state prediction over long horizons. We discover several limitations of predicting future states in the latent space and propose an inference-time mechanism, which we refer to as Periodic Reencoding, for faithfully capturing long term dynamics. We justify this method both analytically and empirically via experiments in low and high dimensional NLDS.

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.

Deep generative models such as flow matching and diffusion models have shown great potential in learning complex distributions and dynamical systems, but often act as black-boxes, neglecting underlying physics. In contrast, physics-based simulation models described by ODEs/PDEs remain interpretable, but may have missing or unknown terms, unable to fully describe real-world observations. We bridge this gap with a novel grey-box method that integrates incomplete physics models directly into generative models. Our approach learns dynamics from observational trajectories alone, without ground-truth physics parameters, in a simulation-free manner that avoids scalability and stability issues of Neural ODEs. The core of our method lies in modelling a structured variational distribution within the flow matching framework, by using two latent encodings: one to model the missing stochasticity and multi-modal velocity, and a second to encode physics parameters as a latent variable with a physics-informed prior. Furthermore, we present an adaptation of the framework to handle second-order dynamics. Our experiments on representative ODE/PDE problems show that our method performs on par with or superior to fully data-driven approaches and previous grey-box baselines, while preserving the interpretability of the physics model. Our code is available at https://github.com/DMML-Geneva/VGB-DM.

Modeling stochastic dynamics from discrete observations is a key interdisciplinary challenge. Existing methods often fail to estimate the continuous evolution of probability densities from trajectories or face the curse of dimensionality. To address these limitations, we presents a novel paradigm: modeling dynamics directly in the weight space of a neural network by projecting the evolving probability distribution. We first theoretically establish the connection between dynamic optimal transport in measure space and an equivalent energy functional in weight space. Subsequently, we design WeightFlow, which constructs the neural network weights into a graph and learns its evolution via a graph controlled differential equation. Experiments on interdisciplinary datasets demonstrate that WeightFlow improves performance by an average of 43.02\% over state-of-the-art methods, providing an effective and scalable solution for modeling high-dimensional stochastic dynamics.

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.

World models enable agents to predict future dynamics conditioned on actions, making the choice of latent representation central to planning and control. Such representations are often either learned directly from pixels with limited semantic structure or inherited from frozen visual foundation models with excessive task-irrelevant detail, yielding state spaces that are poorly matched to downstream planning and control. This is especially challenging in reward-free offline settings, where the model must learn from fixed trajectories without reward supervision or online interaction. To address this, we propose TC-WM, a framework for turning foundation-model embeddings into compact, task-sufficient world representations. The key design is to treat the pretrained embedding space as a semantic scaffold rather than as the final state space: TC-WM linearly projects high-dimensional visual embeddings into a compact latent as the dynamic space, aligns a subspace with the agent's physical state via contrastive learning, and reconstructs embeddings to preserve useful visual structure. This combines the generality of foundation features with the controllability of task-centric dynamics. Theoretically, we show that TC-WM suffices to identify the underlying task-centric latent factors up to a simple transformation. Empirically, TC-WM enables test-time planning across diverse environments (e.g., Robomimic and D4RL), achieving better world-modeling quality and more precise control than state-of-the-art approaches.

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.

Imitation learning method has shown immense promise for robotic manipulation, yet its practical deployment is fundamentally constrained by the data scarcity. Despite prior work on collecting large-scale datasets, there still remains a significant gap to robust spatial generalization. We identify a key limitation: individual trajectories, regardless of their length, are typically collected from a single, static spatial configuration of the environment. This includes fixed object and target spatial positions as well as unchanging camera viewpoints, which significantly restricts the diversity of spatial information available for learning. To address this critical bottleneck in data efficiency, we propose MOtion-Based Variability Enhancement (MOVE), a simple yet effective data collection paradigm that enables the acquisition of richer spatial information from dynamic demonstrations. Our core contribution is an augmentation strategy that injects motion into any movable objects within the environment for each demonstration. This process implicitly generates a dense and diverse set of spatial configurations within a single trajectory. We conduct extensive experiments in both simulation and real-world environments to validate our approach. For example, in simulation tasks requiring strong spatial generalization, MOVE achieves an average success rate of 39.1\%, a 76.1\% relative improvement over the static data collection paradigm (22.2\%), and yields up to 2--5times gains in data efficiency on certain tasks. Our code is available at https://github.com/lucywang720/MOVE.

High-fidelity embodied AI simulators provide realistic evaluation of complex robotic systems, but their computational cost limits their direct use for large-scale reinforcement learning campaigns. We advocate the use of less accurate but more expeditious simulations, which might draw on data-driven, e.g., neural dynamics, models. This contribution argues that the practical value of a neural dynamics model for complex robot control lies in learning the right abstraction: a reduced state that preserves the control-relevant physics of the high-fidelity system while enabling high-throughput policy learning. We develop a neural reduced dynamics (NRD) framework that separates the state the model propagates from what can be supplied as an input or recovered analytically, trains policies entirely inside the frozen learned model, and validates them back in the high-fidelity simulator. Two case studies instantiate it across three control tasks: terrain-aware HMMWV trajectory tracking on rigid, bumpy and deformable Continuum Representation Model (CRM) terrain; and goal reaching for a stock tracked vehicle and its front-mounted articulated arm. Every policy transfers back to the high-fidelity simulator. A single policy trained inside the terrain-conditioned dynamics model, and given no terrain input of its own, attains lower median and mean tracking error than both single-terrain specialists on all three terrains, including zero-shot bumpy terrain. Quantitatively, the tracked vehicle reaches 100 of 100 goals and the arm 97 of 100, with zero contacts or joint-limit violations. The NRD models advance roughly four orders of magnitude faster in simulated time than the high-fidelity simulator scenes they replace, making iterative on-policy learning practical and supporting neural reduced dynamics as a bridge between accurate but expensive physics simulation and scalable robot learning.

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.

Modeling the dynamics of deformable objects is challenging due to their diverse physical properties and the difficulty of estimating states from limited visual information. We address these challenges with a neural dynamics framework that combines object particles and spatial grids in a hybrid representation. Our particle-grid model captures global shape and motion information while predicting dense particle movements, enabling the modeling of objects with varied shapes and materials. Particles represent object shapes, while the spatial grid discretizes the 3D space to ensure spatial continuity and enhance learning efficiency. Coupled with Gaussian Splattings for visual rendering, our framework achieves a fully learning-based digital twin of deformable objects and generates 3D action-conditioned videos. Through experiments, we demonstrate that our model learns the dynamics of diverse objects -- such as ropes, cloths, stuffed animals, and paper bags -- from sparse-view RGB-D recordings of robot-object interactions, while also generalizing at the category level to unseen instances. Our approach outperforms state-of-the-art learning-based and physics-based simulators, particularly in scenarios with limited camera views. Furthermore, we showcase the utility of our learned models in model-based planning, enabling goal-conditioned object manipulation across a range of tasks. The project page is available at https://kywind.github.io/pgnd .

Accurate physical simulation is crucial for the development and validation of control algorithms in robotic systems. Recent works in Reinforcement Learning (RL) take notably advantage of extensive simulations to produce efficient robot control. State-of-the-art servo actuator models generally fail at capturing the complex friction dynamics of these systems. This limits the transferability of simulated behaviors to real-world applications. In this work, we present extended friction models that allow to more accurately simulate servo actuator dynamics. We propose a comprehensive analysis of various friction models, present a method for identifying model parameters using recorded trajectories from a pendulum test bench, and demonstrate how these models can be integrated into physics engines. The proposed friction models are validated on four distinct servo actuators and tested on 2R manipulators, showing significant improvements in accuracy over the standard Coulomb-Viscous model. Our results highlight the importance of considering advanced friction effects in the simulation of servo actuators to enhance the realism and reliability of robotic simulations.

Learning control from action-free recordings is challenging because intervention effects are unobserved and policies may exploit errors in reconstructed dynamics. We present a hierarchical model-based reinforcement learning framework that uses shared structure across related systems to learn system-specific control policies from action-free recordings. A hierarchical dynamical system reconstruction model captures shared dynamics and individual variation through low-dimensional embeddings. These embeddings are then reused to parameterize shared policy and value networks, linking differences in reconstructed dynamics to differences in control. Policies are trained entirely via simulation under an explicit intervention model with additive latent perturbations. Piecewise-linear recurrent neural networks enable mechanistic analyses of the controlled dynamics, while decoder-based constraints make the immediate effects of interventions interpretable in observation space and permit interventions on one modality while protecting another from direct manipulation. On Lorenz-63 and double-pendulum systems, hierarchical policies improve transfer over independently trained policies. On Lorenz-63, they also achieve a higher mean reward than repeated planning with the same reconstructed models, perform comparably to methods trained with controlled interactions, and generalize to systems absent from policy training after embedding inference alone. Applications to neural-behavioral recordings demonstrate suppression of predicted movement under constrained neural perturbations. Together, these findings show how shared dynamical representations support transferable control and mechanistic hypothesis generation from action-free recordings.

Online decision-making faces a tension between efficient inference and long-horizon reasoning. Value-based methods rely on short-horizon bootstrapping that limits the propagation of long-term information, while trajectory optimization methods plan explicitly but must solve a high-dimensional optimization problem at every decision step. We propose Generative Trajectory Planning (GTP), a model-based framework that addresses this tension by learning a generative model as a proposal distribution over action sequences. Instead of optimizing sequences from scratch, GTP samples candidate sequences from a diffusion prior and refines them using learned dynamics, reward, and value models, enabling efficient trajectory-level reasoning. Across continuous control and long-horizon manipulation tasks, GTP matches or exceeds state-of-the-art model-free, diffusion-policy, and model-based baselines, and remains stable in regimes where strong baselines degrade. Our results suggest that generative models are best understood not as policies, but as structured proposal distributions for planning, offering a new perspective on how to integrate generative modeling with model-based decision-making.

Humanoid robots can suffer significant performance drops under small changes in dynamics, task specifications, or environment setup. We propose HoRD, a two-stage learning framework for robust humanoid control under domain shift. First, we train a high-performance teacher policy via history-conditioned reinforcement learning, where the policy infers latent dynamics context from recent state--action trajectories to adapt online to diverse randomized dynamics. Second, we perform online distillation to transfer the teacher's robust control capabilities into a transformer-based student policy that operates on sparse root-relative 3D joint keypoint trajectories. By combining history-conditioned adaptation with online distillation, HoRD enables a single policy to adapt zero-shot to unseen domains without per-domain retraining. Extensive experiments show HoRD outperforms strong baselines in robustness and transfer, especially under unseen domains and external perturbations. Code and project page are available at https://tonywang-0517.github.io/hord/.

Dynamical systems theory and reinforcement learning view world evolution as latent-state dynamics driven by actions, with visual observations providing partial information about the state. Recent video world models attempt to learn this action-conditioned dynamics from data. However, existing datasets rarely match the requirement: they typically lack diverse and semantically meaningful action spaces, and actions are directly tied to visual observations rather than mediated by underlying states. As a result, actions are often entangled with pixel-level changes, making it difficult for models to learn structured world dynamics and maintain consistent evolution over long horizons. In this paper, we propose WildWorld, a large-scale action-conditioned world modeling dataset with explicit state annotations, automatically collected from a photorealistic AAA action role-playing game (Monster Hunter: Wilds). WildWorld contains over 108 million frames and features more than 450 actions, including movement, attacks, and skill casting, together with synchronized per-frame annotations of character skeletons, world states, camera poses, and depth maps. We further derive WildBench to evaluate models through Action Following and State Alignment. Extensive experiments reveal persistent challenges in modeling semantically rich actions and maintaining long-horizon state consistency, highlighting the need for state-aware video generation. The project page is https://shandaai.github.io/wildworld-project/.

Reinforcement Learning with Verifiable Rewards (RLVR) has recently demonstrated remarkable potential in enhancing the reasoning capability of Large Reasoning Models (LRMs). However, RLVR often leads to entropy collapse, resulting in premature policy convergence and performance saturation. While manipulating token-level entropy has proven effective for promoting policy exploration, we argue that the latent dynamics underlying token generation encode a far richer computational structure for steering policy optimization toward a more effective exploration-exploitation tradeoff. To enable tractable analysis and intervention of the latent dynamics of LRMs, we leverage Koopman operator theory to obtain a linearized representation of their hidden-state dynamics. This enables us to introduce Dynamic Spectral Dispersion (DSD), a new metric to quantify the heterogeneity of the model's latent dynamics, serving as a direct indicator of policy exploration. Building upon these foundations, we propose Reasoning with Latent eXploration (ReLaX), a paradigm that explicitly incorporates latent dynamics to regulate exploration and exploitation during policy optimization. Comprehensive experiments across a wide range of multimodal and text-only reasoning benchmarks show that ReLaX significantly mitigates premature convergence and consistently achieves state-of-the-art performance.

Joint-embedding world models enable visual planning by learning action-conditioned dynamics in latent space. Yet they are commonly trained for one-step prediction on encoded states, while planning recursively applies the learned transition to its own predictions. One-step accuracy therefore does not capture how prediction errors propagate under recursive rollout. We decompose multi-step rollout error into the errors introduced at individual steps and their propagation through subsequent transitions. We show that state-affine dynamics are precisely the differentiable transitions with state-independent Jacobians, eliminating the nonlinear propagation residual and making the error propagation operators depend only on the action sequence. Guided by this result, we introduce SALT (State-Affine Latent Transition), an action-conditioned state-affine dynamics model in which the action modulates both the state transformation and the additive update. We train SALT through recursive multi-step rollout supervision, feeding each predicted latent state back into the transition so that training matches how the model is used during planning. Across four visual planning environments, SALT exhibits 1.48--2.19times higher one-step prediction error than the matched LeWM baseline, yet improves closed-loop success in every environment by 10.0 percentage points on average. On OGBench-Cube, the fraction of episodes that fail with a sharp rise in model-predicted cost after execution decreases from 23.3% to 2.0%.

Selective state space models (SSM), such as Mamba, have gained prominence for their effectiveness in modeling sequential data. Despite their outstanding empirical performance, a comprehensive theoretical understanding of deep selective SSM remains elusive, hindering their further development and adoption for applications that need high fidelity. In this paper, we investigate the dynamical properties of tokens in a pre-trained Mamba model. In particular, we derive the dynamical system governing the continuous-time limit of the Mamba model and characterize the asymptotic behavior of its solutions. In the one-dimensional case, we prove that only one of the following two scenarios happens: either all tokens converge to zero, or all tokens diverge to infinity. We provide criteria based on model parameters to determine when each scenario occurs. For the convergent scenario, we empirically verify that this scenario negatively impacts the model's performance. For the divergent scenario, we prove that different tokens will diverge to infinity at different rates, thereby contributing unequally to the updates during model training. Based on these investigations, we propose two refinements for the model: excluding the convergent scenario and reordering tokens based on their importance scores, both aimed at improving practical performance. Our experimental results validate these refinements, offering insights into enhancing Mamba's effectiveness in real-world applications.

Scalable simulation is essential for robot data generation, policy training, evaluation, and safe iteration, yet real-world interaction is costly and conventional simulators require labor-intensive construction. We present Uranus, a data-driven robot simulator built around a joint-trajectory-conditioned autoregressive diffusion model. Uranus offers three key capabilities: (1) streaming, open-ended rollout, which receives future joint-position trajectories online and autoregressively generates one latent frame per step, corresponding to four RGB frames, without a fixed horizon; (2) low-latency generation, achieving 24 FPS after inference optimization; and (3) scalable, extensible robot control, providing a unified interface for synchronized multi-view generation across diverse robot embodiments and camera configurations. We conduct comprehensive quantitative and qualitative evaluations on both in-distribution and out-of-distribution data, providing an objective assessment of Uranus and clearly identifying its current limitations. We release the code and model weights to empower the community with practical tools and insights.

In many domains generating variable length sequences through insertions provides greater flexibility over autoregressive models. However, the action space of insertion models is much larger than that of autoregressive models (ARMs) making the learning challenging. To address this, we incorporate trainable order dynamics into the target rates for discrete flow matching, and show that with suitable choices of parameterizations, joint training of the target order dynamics and the generator is tractable without the need for numerical simulation. As the generative insertion model, we use a variable length masked diffusion model, which generates by inserting and filling mask tokens. On graph traversal tasks for which a locally optimal insertion order is known, we explore the choices of parameterization empirically and demonstrate the trade-offs between flexibility, training stability and generation quality. On de novo small molecule generation, we find that the learned order dynamics leads to an increase in the number of valid molecules generated and improved quality, when compared to uniform order dynamics.

This work explores the in-context learning capabilities of State Space Models (SSMs) and presents, to the best of our knowledge, the first theoretical explanation of a possible underlying mechanism. We introduce a novel weight construction for SSMs, enabling them to predict the next state of any dynamical system after observing previous states without parameter fine-tuning. This is accomplished by extending the HiPPO framework to demonstrate that continuous SSMs can approximate the derivative of any input signal. Specifically, we find an explicit weight construction for continuous SSMs and provide an asymptotic error bound on the derivative approximation. The discretization of this continuous SSM subsequently yields a discrete SSM that predicts the next state. Finally, we demonstrate the effectiveness of our parameterization empirically. This work should be an initial step toward understanding how sequence models based on SSMs learn in context.

We propose DynVLA, a driving VLA model that introduces a new CoT paradigm termed Dynamics CoT. DynVLA forecasts compact world dynamics before action generation, enabling more informed and physically grounded decision-making. To obtain compact dynamics representations, DynVLA introduces a Dynamics Tokenizer that compresses future evolution into a small set of dynamics tokens. Considering the rich environment dynamics in interaction-intensive driving scenarios, DynVLA decouples ego-centric and environment-centric dynamics, yielding more accurate world dynamics modeling. We then train DynVLA to generate dynamics tokens before actions through SFT and RFT, improving decision quality while maintaining latency-efficient inference. Compared to Textual CoT, which lacks fine-grained spatiotemporal understanding, and Visual CoT, which introduces substantial redundancy due to dense image prediction, Dynamics CoT captures the evolution of the world in a compact, interpretable, and efficient form. Extensive experiments on NAVSIM, Bench2Drive, and a large-scale in-house dataset demonstrate that DynVLA consistently outperforms Textual CoT and Visual CoT methods, validating the effectiveness and practical value of Dynamics CoT. Project Page: https://yaoyao-jpg.github.io/dynvla.

Effective interaction modeling and behavior prediction of dynamic agents play a significant role in interactive motion planning for autonomous robots. Although existing methods have improved prediction accuracy, few research efforts have been devoted to enhancing prediction model interpretability and out-of-distribution (OOD) generalizability. This work addresses these two challenging aspects by designing a variational auto-encoder framework that integrates graph-based representations and time-sequence models to efficiently capture spatio-temporal relations between interactive agents and predict their dynamics. Our model infers dynamic interaction graphs in a latent space augmented with interpretable edge features that characterize the interactions. Moreover, we aim to enhance model interpretability and performance in OOD scenarios by disentangling the latent space of edge features, thereby strengthening model versatility and robustness. We validate our approach through extensive experiments on both simulated and real-world datasets. The results show superior performance compared to existing methods in modeling spatio-temporal relations, motion prediction, and identifying time-invariant latent features.

Robotic systems often exhibit unstable modes, along which small perturbations and disturbances can cause unbounded growth unless corrected through feedback. Controlling such systems from high-dimensional visual observations requires representations that preserve these modes. Joint-embedding predictive architectures (JEPAs) provide a natural framework for learning such representations and their dynamics from visual data. However, we demonstrate that next step prediction combined with anti-collapse regularization does not guarantee that controllable unstable modes are preserved: the training loss can be minimized while these modes are collapsed, making stabilization from the learned representation impossible. To address this, we augment world-model training with an action reconstruction objective (i.e., an inverse dynamics loss) that encourages control-aware representations, namely, visual representations that preserve crucial features for control. We prove that exact action reconstruction makes the encoder injective on the finite-horizon reachable subspace. Thus, the encoder cannot discard any state direction reachable by an action sequence within H steps. Moreover, we show that, as H grows, the dominant eigenspace of the finite-horizon controllability Gramian converges to the controllable unstable subspace. We establish our theoretical results for linear systems and demonstrate empirically that our findings extend to nonlinear visual control tasks (CartPole, Walker2D, and PointMaze), highlighting the benefits of control-aware representation learning.

Reduced-order modeling (ROM) of time-dependent and parameterized differential equations aims to accelerate the simulation of complex high-dimensional systems by learning a compact latent manifold representation that captures the characteristics of the solution fields and their time-dependent dynamics. Although high-fidelity numerical solvers generate the training datasets, they have thus far been excluded from the training process, causing the learned latent dynamics to drift away from the discretized governing physics. This mismatch often limits generalization and forecasting capabilities. In this work, we propose Physics-informed ROM (Φ-ROM) by incorporating differentiable PDE solvers into the training procedure. Specifically, the latent space dynamics and its dependence on PDE parameters are shaped directly by the governing physics encoded in the solver, ensuring a strong correspondence between the full and reduced systems. Our model outperforms state-of-the-art data-driven ROMs and other physics-informed strategies by accurately generalizing to new dynamics arising from unseen parameters, enabling long-term forecasting beyond the training horizon, maintaining continuity in both time and space, and reducing the data cost. Furthermore, Φ-ROM learns to recover and forecast the solution fields even when trained or evaluated with sparse and irregular observations of the fields, providing a flexible framework for field reconstruction and data assimilation. We demonstrate the framework's robustness across various PDE solvers and highlight its broad applicability by providing an open-source JAX implementation that is readily extensible to other PDE systems and differentiable solvers, available at https://phi-rom.github.io.

Accurate and efficient simulation of modern robots remains challenging due to their high degrees of freedom and intricate mechanisms. Neural simulators have emerged as a promising alternative to traditional analytical simulators, capable of efficiently predicting complex dynamics and adapting to real-world data; however, existing neural simulators typically require application-specific training and fail to generalize to novel tasks and/or environments, primarily due to inadequate representations of the global state. In this work, we address the problem of learning generalizable neural simulators for robots that are structured as articulated rigid bodies. We propose NeRD (Neural Robot Dynamics), learned robot-specific dynamics models for predicting future states for articulated rigid bodies under contact constraints. NeRD uniquely replaces the low-level dynamics and contact solvers in an analytical simulator and employs a robot-centric and spatially-invariant simulation state representation. We integrate the learned NeRD models as an interchangeable backend solver within a state-of-the-art robotics simulator. We conduct extensive experiments to show that the NeRD simulators are stable and accurate over a thousand simulation steps; generalize across tasks and environment configurations; enable policy learning exclusively in a neural engine; and, unlike most classical simulators, can be fine-tuned from real-world data to bridge the gap between simulation and reality.

Generating continuous-time, continuous-space stochastic processes (e.g., videos, weather forecasts) conditioned on partial observations (e.g., first and last frames) is a fundamental challenge. Existing approaches, (e.g., diffusion models), suffer from key limitations: (1) noise-to-data evolution fails to capture structural similarity between states close in physical time and has unstable integration in low-step regimes; (2) random noise injected is insensitive to the physical process's time elapsed, resulting in incorrect dynamics; (3) they overlook conditioning on arbitrary subsets of states (e.g., irregularly sampled timesteps, future observations). We propose ABC: Any-Subset Autoregressive Models via Non-Markovian Diffusion Bridges in Continuous Time and Space. Crucially, we model the process with one continual SDE whose time variable and intermediate states track the real time and process states. This has provable advantages: (1) the starting point for generating future states is the already-close previous state, rather than uninformative noise; (2) random noise injection scales with physical time elapsed, encouraging physically plausible dynamics with similar time-adjacent states. We derive SDE dynamics via changes-of-measure on path space, yielding another advantage: (3) path-dependent conditioning on arbitrary subsets of the state history and/or future. To learn these dynamics, we derive a path- and time-dependent extension of denoising score matching. Our experiments show ABC's superiority to competing methods on multiple domains, including video generation and weather forecasting.

Learning dexterous manipulation skills presents significant challenges due to complex nonlinear dynamics that underlie the interactions between objects and multi-fingered hands. Koopman operators have emerged as a robust method for modeling such nonlinear dynamics within a linear framework. However, current methods rely on runtime access to ground-truth (GT) object states, making them unsuitable for vision-based practical applications. Unlike image-to-action policies that implicitly learn visual features for control, we use a dynamics model, specifically the Koopman operator, to learn visually interpretable object features critical for robotic manipulation within a scene. We construct a Koopman operator using object features predicted by a feature extractor and utilize it to auto-regressively advance system states. We train the feature extractor to embed scene information into object features, thereby enabling the accurate propagation of robot trajectories. We evaluate our approach on simulated and real-world robot tasks, with results showing that it outperformed the model-based imitation learning NDP by 1.08times and the image-to-action Diffusion Policy by 1.16times. The results suggest that our method maintains task success rates with learned features and extends applicability to real-world manipulation without GT object states.

Demonstration augmentation is proposed for cost-efficient data acquisition, but existing methods are fundamentally limited in deformable manipulation due to two challenges: (1) the state space is high-dimensional with physics-induced constraints, making valid configurations impossible to reach via low-dimensional pose perturbations; and (2) trajectory transfer is non-equivariant, as material points no longer move rigidly together under deformation. We present DeformGen, a dynamics-based augmentation framework that achieves topological diversity for deformable objects. For the state challenge, DeformGen expands the valid state distribution by applying localized physical disturbances and forward-simulating the dynamics to obtain topology-coherent, physically plausible deformable states. For the trajectory challenge, DeformGen transfers source manipulation trajectories via deformation-field warping, which lifts per-particle displacements into a continuous spatial function to adapt the end-effector trajectory consistently with the deformed geometry. In this way, our method jointly augments the state distribution and its associated manipulation behavior. Experiments on high-fidelity deformable manipulation benchmarks show that DeformGen generally improves policy learning compared with training on the original demonstrations alone and with rigid-style augmentation baselines.

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.

Recent advances in reinforcement learning (RL) have shown much promise across a variety of applications. However, issues such as scalability, explainability, and Markovian assumptions limit its applicability in certain domains. We observe that many of these shortcomings emanate from the simulator as opposed to the RL training algorithms themselves. As such, we propose a semantic proxy for simulation based on a temporal extension to annotated logic. In comparison with two high-fidelity simulators, we show up to three orders of magnitude speed-up while preserving the quality of policy learned. In addition, we show the ability to model and leverage non-Markovian dynamics and instantaneous actions while providing an explainable trace describing the outcomes of the agent actions.

General-purpose robot policies should be modeled as dynamical systems, yet many VLA and generative imitation policies still rely on present observations or short windows. This Markovian shortcut fails in memory-dependent manipulation: identical observations can demand different actions after different histories. We present Chronos, a physics-informed full-history framework for non-Markovian long-horizon manipulation. The key idea is to elevate observation history from auxiliary context to the latent state of the policy dynamics. At each physical control step, Chronos forms one state-representative token by fusing observation and proprioception, so the token sequence is aligned one-to-one with physical time. A selective state space model propagates this causal historical state, which conditions a multimodal coarse action prior through implicit maximum likelihood estimation (IMLE). This prior is then refined by a second-order Schrodinger-inspired bridge that predicts acceleration fields, yielding smoother and more physically grounded robot motion. Across 16 simulated tasks and 4 real-world experiments, Chronos is evaluated on precision insertion, general manipulation, and memory-dependent long-horizon control. On RMBench, where success requires remembering task phase, Chronos achieves 73.6% average success, outperforming Markovian VLA baseline pi0.5 by +62.4 percentage points, a 6.6x relative gain, while using 10x fewer parameters. It also surpasses the memory VLA Mem-0 by 22.8 points while using over 30x fewer parameters. In real-world dual-arm experiments using a single RGB camera, Chronos achieves 78% average success over four tasks, including 72% on the three memory-dependent tasks, whereas pi0.5 achieves 7% overall and 0% on the memory-dependent subset. These results suggest that history should not be treated as auxiliary context, but as the latent state of the manipulation policy.

Large language models (LLMs) are shown to possess a wealth of actionable knowledge that can be extracted for robot manipulation in the form of reasoning and planning. Despite the progress, most still rely on pre-defined motion primitives to carry out the physical interactions with the environment, which remains a major bottleneck. In this work, we aim to synthesize robot trajectories, i.e., a dense sequence of 6-DoF end-effector waypoints, for a large variety of manipulation tasks given an open-set of instructions and an open-set of objects. We achieve this by first observing that LLMs excel at inferring affordances and constraints given a free-form language instruction. More importantly, by leveraging their code-writing capabilities, they can interact with a visual-language model (VLM) to compose 3D value maps to ground the knowledge into the observation space of the agent. The composed value maps are then used in a model-based planning framework to zero-shot synthesize closed-loop robot trajectories with robustness to dynamic perturbations. We further demonstrate how the proposed framework can benefit from online experiences by efficiently learning a dynamics model for scenes that involve contact-rich interactions. We present a large-scale study of the proposed method in both simulated and real-robot environments, showcasing the ability to perform a large variety of everyday manipulation tasks specified in free-form natural language. Project website: https://voxposer.github.io

Vision-based robotic policies often struggle with even minor viewpoint changes, underscoring the need for view-invariant visual representations. This challenge becomes more pronounced in real-world settings, where viewpoint variability is unavoidable and can significantly disrupt policy performance. Existing methods typically learn invariance from multi-view observations at the scene level, but such approaches rely on visual appearance and fail to incorporate the physical dynamics essential for robust generalization. We propose View-Invariant Latent Action (VILA), which models a latent action capturing transition patterns across trajectories to learn view-invariant representations grounded in physical dynamics. VILA aligns these latent actions across viewpoints using an action-guided objective based on ground-truth action sequences. Experiments in both simulation and the real world show that VILA-based policies generalize effectively to unseen viewpoints and transfer well to new tasks, establishing VILA as a strong pretraining framework that improves robustness and downstream learning performance.

Robots in dynamic, human-centric environments must follow language instructions while maintaining real-time reactive control. Vision-language-action (VLA) models offer a promising framework, but they assume temporally aligned reasoning and control, despite semantic inference being inherently delayed relative to real-time action. We introduce Think-in-Control (TIC)-VLA, a latency-aware framework that explicitly models delayed semantic reasoning during action generation. TIC-VLA defines a delayed semantic-control interface that conditions action generation on delayed vision-language semantic states and explicit latency metadata, in addition to current observations, enabling policies to compensate for asynchronous reasoning. We further propose a latency-consistent training pipeline that injects reasoning inference delays during imitation learning and online reinforcement learning, aligning training with asynchronous deployment. To support realistic evaluation, we present DynaNav, a physics-accurate, photo-realistic simulation suite for language-guided navigation in dynamic environments. Extensive experiments in simulation and on a real robot show that TIC-VLA consistently outperforms prior VLA models while maintaining robust real-time control under multi-second reasoning latency. Project website: https://ucla-mobility.github.io/TIC-VLA/

We introduce PACOH-RL, a novel model-based Meta-Reinforcement Learning (Meta-RL) algorithm designed to efficiently adapt control policies to changing dynamics. PACOH-RL meta-learns priors for the dynamics model, allowing swift adaptation to new dynamics with minimal interaction data. Existing Meta-RL methods require abundant meta-learning data, limiting their applicability in settings such as robotics, where data is costly to obtain. To address this, PACOH-RL incorporates regularization and epistemic uncertainty quantification in both the meta-learning and task adaptation stages. When facing new dynamics, we use these uncertainty estimates to effectively guide exploration and data collection. Overall, this enables positive transfer, even when access to data from prior tasks or dynamic settings is severely limited. Our experiment results demonstrate that PACOH-RL outperforms model-based RL and model-based Meta-RL baselines in adapting to new dynamic conditions. Finally, on a real robotic car, we showcase the potential for efficient RL policy adaptation in diverse, data-scarce conditions.

Learning predictive world models from raw visual observations is a central challenge in reinforcement learning (RL), especially for robotics and continuous control. Conventional model-based RL frameworks directly condition future predictions on absolute actions, which makes optimization unstable: the optimal action distributions are task-dependent, unknown a priori, and often lead to oscillatory or inefficient control. To address this, we introduce the Residual-Action World Model (ResWM), a new framework that reformulates the control variable from absolute actions to residual actions -- incremental adjustments relative to the previous step. This design aligns with the inherent smoothness of real-world control, reduces the effective search space, and stabilizes long-horizon planning. To further strengthen the representation, we propose an Observation Difference Encoder that explicitly models the changes between adjacent frames, yielding compact latent dynamics that are naturally coupled with residual actions. ResWM is integrated into a Dreamer-style latent dynamics model with minimal modifications and no extra hyperparameters. Both imagination rollouts and policy optimization are conducted in the residual-action space, enabling smoother exploration, lower control variance, and more reliable planning. Empirical results on the DeepMind Control Suite demonstrate that ResWM achieves consistent improvements in sample efficiency, asymptotic returns, and control smoothness, significantly surpassing strong baselines such as Dreamer and TD-MPC. Beyond performance, ResWM produces more stable and energy-efficient action trajectories, a property critical for robotic systems deployed in real-world environments. These findings suggest that residual action modeling provides a simple yet powerful principle for bridging algorithmic advances in RL with the practical requirements of robotics.

Action-conditioned world models (ACWMs) have shown strong promise for video prediction and decision-making. However, existing benchmarks are largely restricted to egocentric navigation or narrow, task-specific robotics datasets, offering only limited coverage of the rich physical interactions required for generalized world understanding. We introduce ACWM-Phys, a new benchmark for evaluating action-conditioned prediction under diverse physical dynamics in a clean, controllable simulation environment with a carefully designed action space. ACWM-Phys contains training and evaluation data spanning rigid-body dynamics, kinematics, deformable-object interactions, and particle dynamics. To evaluate both interpolation and generalization, we design in-distribution and out-of-distribution protocols with controlled shifts in interaction patterns or scene configurations. By building the benchmark in a fully controllable simulator, ACWM-Phys enables precise data collection, reproducible evaluation, and systematic analysis of model capabilities for physically grounded world modeling. Through systematic experiments on ACWM-DiT, we find that OoD generalization depends not only on the physical regime but also on effective task complexity: models generalize well on visually simple, low-dimensional interactions with clear geometric structure, but suffer larger drops on deformable contacts, high-dimensional control, and complex articulated motion. This suggests that the model still relies heavily on visual appearance patterns instead of fully learning the underlying physics. Ablations show that cross-attention improves high-dimensional action conditioning, causal VAEs outperform frame-wise encoders, and larger action spaces are harder to model but can improve generalization by providing richer control signals. These findings guide the design of physically grounded world models.

World models aim to capture environmental dynamics and predict future trajectories, showing growing potential for embodied intelligence. Physics-informed 4D generation integrates physical simulation to predict 3D object interactions, offering a promising pathway toward world models. However, this paradigm relies on manually imposed dynamical assumptions rather than internalizing world dynamics, and thus still leaves a gap toward a true world model. To bridge this gap, we propose NeuIDO, a novel world dynamics modeling framework that learns a unified intrinsic dynamics representation from visual observations, advancing physics-informed 4D generation toward a world model. Specifically, we formulate world modeling as a neural operator learning problem and introduce a two-stage training strategy to learn a generalizable mapping from the visual observation distribution to the intrinsic dynamics distribution. Building on this observation-dynamics mapping, NeuIDO enables zero-shot dynamics inference directly from videos and can be further aligned with complex real-world dynamics via few-shot adaptation. Extensive experiments demonstrate that NeuIDO effectively unifies the intrinsic dynamics underlying diverse visual observations into a shared representation and rapidly infers dynamics in novel scenes.

Ropes, cables, and other deformable linear objects appear in tasks from untangling to cable routing and suturing, yet controlling their shape remains a challenge in robot manipulation. We study model-based shape control in a general setting: the object lies unfixated on a support surface and two arms may grasp and move it anywhere along its length. Because each arm chooses a grasp point, direction, and magnitude, the joint action space is combinatorially large, and the dynamics model's per-prediction cost bounds how much of it a planner can search. We present ForwardDLO, a recurrent latent dynamics model for this unfixated bimanual setting that predicts per-segment displacements grounded in the observed rope state at every step. Our model reaches accuracy comparable to more expensive baselines while containing no explicit segment-to-segment operations, which makes batched evaluation of candidate actions cheap. On open-loop prediction of real rope motion it reaches the lowest error of the learned models we evaluate, 13% below the strongest baseline. Within a fixed time budget it scores 8 to 22 times more candidate actions than models of comparable accuracy while matching them in real-world shape matching; and on a simulated routing task at a 30Hz control rate, this throughput converts into 98% task success versus at most 30% for the baselines at their own budgets. We release the model, code, and a dataset of 2.42 million simulated and 14,107 real rope transitions at https://anonymous.4open.science/r/ForwardDLO/

The massive overactuation in the human musculoskeletal system makes it challenging to train musculoskeletal models to generate human-like motion via reinforcement learning, primarily because exploration in the resulting high-dimensional and redundant action space is extremely inefficient. To address this problem, we propose the λ-hold controller, inspired by the equilibrium-point (EP) hypothesis, which has been widely supported by extensive evidence from human motor control studies. The policy's control variable is the per-muscle EP threshold length λ, from which a stretch-reflex recruitment law computes the muscle excitations automatically. Holding each λ over an interval of the gait phase also sharply reduces the frequency at which the policy must be queried. Consequently, the controller, to our knowledge for the first time, enables a muscle-actuated skeletal model to learn human-like sprinting using only a minimal reward within an hour of training. The efficient exploration through the proposed λ-hold controller is not merely an engineering trick but an approach grounded in physiology, bringing together the EP hypothesis, intermittent control, and optimal feedback control. Beyond encapsulating human-like behavior in predictive simulation, this achievement contributes to developing a learnable model of the human motor controller.

Real-world time series are often governed by complex nonlinear dynamics. Understanding these underlying dynamics is crucial for precise future prediction. While deep learning has achieved major success in time series forecasting, many existing approaches do not explicitly model the dynamics. To bridge this gap, we introduce DeepEDM, a framework that integrates nonlinear dynamical systems modeling with deep neural networks. Inspired by empirical dynamic modeling (EDM) and rooted in Takens' theorem, DeepEDM presents a novel deep model that learns a latent space from time-delayed embeddings, and employs kernel regression to approximate the underlying dynamics, while leveraging efficient implementation of softmax attention and allowing for accurate prediction of future time steps. To evaluate our method, we conduct comprehensive experiments on synthetic data of nonlinear dynamical systems as well as real-world time series across domains. Our results show that DeepEDM is robust to input noise, and outperforms state-of-the-art methods in forecasting accuracy. Our code is available at: https://abrarmajeedi.github.io/deep_edm.

The symbolic discovery of Ordinary Differential Equations (ODEs) from trajectory data plays a pivotal role in AI-driven scientific discovery. Existing symbolic methods predominantly rely on fixed, pre-collected training datasets, which often result in suboptimal performance, as demonstrated in our case study in Figure 1. Drawing inspiration from active learning, we investigate strategies to query informative trajectory data that can enhance the evaluation of predicted ODEs. However, the butterfly effect in dynamical systems reveals that small variations in initial conditions can lead to drastically different trajectories, necessitating the storage of vast quantities of trajectory data using conventional active learning. To address this, we introduce Active Symbolic Discovery of Ordinary Differential Equations via Phase Portrait Sketching (APPS). Instead of directly selecting individual initial conditions, our APPS first identifies an informative region within the phase space and then samples a batch of initial conditions from this region. Compared to traditional active learning methods, APPS mitigates the gap of maintaining a large amount of data. Extensive experiments demonstrate that APPS consistently discovers more accurate ODE expressions than baseline methods using passively collected datasets.

Simulations are attractive environments for training agents as they provide an abundant source of data and alleviate certain safety concerns during the training process. But the behaviours developed by agents in simulation are often specific to the characteristics of the simulator. Due to modeling error, strategies that are successful in simulation may not transfer to their real world counterparts. In this paper, we demonstrate a simple method to bridge this "reality gap". By randomizing the dynamics of the simulator during training, we are able to develop policies that are capable of adapting to very different dynamics, including ones that differ significantly from the dynamics on which the policies were trained. This adaptivity enables the policies to generalize to the dynamics of the real world without any training on the physical system. Our approach is demonstrated on an object pushing task using a robotic arm. Despite being trained exclusively in simulation, our policies are able to maintain a similar level of performance when deployed on a real robot, reliably moving an object to a desired location from random initial configurations. We explore the impact of various design decisions and show that the resulting policies are robust to significant calibration error.

Diffusion models offer flexible motion generation, but translating this flexibility into feedback-responsive humanoid control remains challenging. Hierarchical systems steer motion through references that may exceed a separate tracker's capabilities, leaving recovery and physical execution largely to the tracker. Action-only diffusion generates actions directly but lacks an explicit future-state trajectory for test-time motion objectives. Joint state-action diffusion provides this representation, yet representative controllers often depend on privileged full-body states, and support for learned behavior selection and test-time motion steering remains fragmented. We present PredActor, a predictive action diffusion policy that brings these complementary steering capabilities into one directly executed policy using proprioceptive observations. Conditioned on proprioceptive history and optional task context, PredActor jointly generates executable actions and an internal future-state trajectory. Classifier-free guidance strengthens text-conditioned behavior, while classifier guidance steers predicted states toward test-time objectives. Only actions are executed, without a separate motion-reference tracker or externally estimated full-body states as policy inputs. In simulation, PredActor reaches all 15 destination targets and achieves a text retrieval score of 0.580, compared with 0.373 for conditional action diffusion, with similar observed disturbance survival. To make this guided policy practical onboard, rolling denoising and computation-preserving runtime optimizations reduce the complete callback to 16.790 ms median and 19.383 ms p95 on a Jetson Orin NX, both below the 20 ms control period. We deploy PredActor on a Unitree G1; evaluations across simulation and physical hardware demonstrate text-conditioned motion, disturbance response, joystick control, and semantic interpolation.

Interactive traffic simulation is a vital world model for autonomous driving. A central challenge in long-horizon simulation is modeling sustained multi-agent interactions, which is further exacerbated by dynamic token cardinality as agents continuously enter and exit the scene. In this work, we propose that the solution lies in the synergy between the architectural inductive biases and statistical priors of large-scale sequence models, e.g., Large Language Models (LLMs). Our probing experiments reveal that the transferability of attention mechanisms and the distributional consistency between motion tokens and natural language enable small-scale, heavily frozen LLMs to rapidly adapt to traffic modeling. Building on this insight, we introduce RosettaSim, a unified framework that projects scene topology, agent states, and spawning intents into a structured autoregressive stream with variable length, achieving both strong short-term accuracy and stable long-horizon simulation fidelity. Furthermore, evaluating extended rollouts presents yet another hurdle, as one-to-one agent correspondence inevitably fades over time. To address this, we introduce Retrieval-based Traffic Evaluation (RTE), which retrieves semantically similar real-world scenarios as context-aware reference anchors. Experiments on the Waymo Open Sim Agent Challenge (WOSAC) demonstrate that RosettaSim achieves state-of-the-art performance in both short- and long-term simulation. Furthermore, RTE exhibits a stronger correlation with standard metrics (r=0.83) than existing approaches (r=0.74), indicating improved alignment with long-horizon simulation fidelity.

Dynamic objects in our physical 4D (3D + time) world are constantly evolving, deforming, and interacting with other objects, leading to diverse 4D scene dynamics. In this paper, we present a universal generative pipeline, CHORD, for CHOReographing Dynamic objects and scenes and synthesizing this type of phenomena. Traditional rule-based graphics pipelines to create these dynamics are based on category-specific heuristics, yet are labor-intensive and not scalable. Recent learning-based methods typically demand large-scale datasets, which may not cover all object categories in interest. Our approach instead inherits the universality from the video generative models by proposing a distillation-based pipeline to extract the rich Lagrangian motion information hidden in the Eulerian representations of 2D videos. Our method is universal, versatile, and category-agnostic. We demonstrate its effectiveness by conducting experiments to generate a diverse range of multi-body 4D dynamics, show its advantage compared to existing methods, and demonstrate its applicability in generating robotics manipulation policies. Project page: https://yanzhelyu.github.io/chord

Recent robot foundation models largely rely on large-scale behavior cloning, which imitates expert actions but discards transferable dynamics knowledge embedded in heterogeneous embodied data. While the Unified World Model (UWM) formulation has the potential to leverage such diverse data, existing instantiations struggle to scale to foundation-level due to coarse data usage and fragmented datasets. We introduce LDA-1B, a robot foundation model that scales through universal embodied data ingestion by jointly learning dynamics, policy, and visual forecasting, assigning distinct roles to data of varying quality. To support this regime at scale, we assemble and standardize EI-30k, an embodied interaction dataset comprising over 30k hours of human and robot trajectories in a unified format. Scalable dynamics learning over such heterogeneous data is enabled by prediction in a structured DINO latent space, which avoids redundant pixel-space appearance modeling. Complementing this representation, LDA-1B employs a multi-modal diffusion transformer to handle asynchronous vision and action streams, enabling stable training at the 1B-parameter scale. Experiments in simulation and the real world show LDA-1B outperforms prior methods (e.g., π_{0.5}) by up to 21\%, 48\%, and 23\% on contact-rich, dexterous, and long-horizon tasks, respectively. Notably, LDA-1B enables data-efficient fine-tuning, gaining 10\% by leveraging 30\% low-quality trajectories typically harmful and discarded.

Joint Embedding Predictive Architectures (JEPAs) are a promising paradigm for learning task-agnostic latent world models without visual reconstruction. However, standard JEPA training exhibits a strong inductive bias towards slow features, causing feature suppression and the collapse of latent representation. While inverse dynamics provides temporal anti-collapse, it relies on action labels and offers little incentive to embed general, unlabeled dynamics. We introduce Difference Image and Single image embedding Regularization (DISReg), a novel regularizer that builds on an inverse-dynamics-style module that predicts temporal difference image embeddings without any pixel reconstruction loss, encouraging balanced static and dynamic feature learning. DISReg consists of a static term that shapes the distribution of the image embedding and encourages slow features, and a dynamic term, which, unlike direct regularization on the embedding, imposes no constraint on the image embedding's shape or distribution and instead only incentivizes that dynamic features be present. By integrating this regularizer into a standard JEPA, we establish our new architecture, MotionJEPA. Latent probing demonstrates that MotionJEPA produces more complete representations than other methods, and our trajectory analysis shows it maintains geometrically simple latent embeddings with low curvature. We further show that MotionJEPA improves downstream planning success under static-background distractors across four environments.

Progress in Embodied AI has made it possible for end-to-end-trained agents to navigate in photo-realistic environments with high-level reasoning and zero-shot or language-conditioned behavior, but benchmarks are still dominated by simulation. In this work, we focus on the fine-grained behavior of fast-moving real robots and present a large-scale experimental study involving navigation episodes in a real environment with a physical robot, where we analyze the type of reasoning emerging from end-to-end training. In particular, we study the presence of realistic dynamics which the agent learned for open-loop forecasting, and their interplay with sensing. We analyze the way the agent uses latent memory to hold elements of the scene structure and information gathered during exploration. We probe the planning capabilities of the agent, and find in its memory evidence for somewhat precise plans over a limited horizon. Furthermore, we show in a post-hoc analysis that the value function learned by the agent relates to long-term planning. Put together, our experiments paint a new picture on how using tools from computer vision and sequential decision making have led to new capabilities in robotics and control. An interactive tool is available at europe.naverlabs.com/research/publications/reasoning-in-visual-navigation-of-end-to-end-trained-agents.

Large discrete action spaces (LDAS) remain a central challenge in reinforcement learning. Existing solution approaches can handle unstructured LDAS with up to a few million actions. However, many real-world applications in logistics, production, and transportation systems have combinatorial action spaces, whose size grows well beyond millions of actions, even on small instances. Fortunately, such action spaces exhibit structure, e.g., equally spaced discrete resource units. With this work, we focus on handling structured LDAS (SLDAS) with sizes that cannot be handled by current benchmarks: we propose Dynamic Neighborhood Construction (DNC), a novel exploitation paradigm for SLDAS. We present a scalable neighborhood exploration heuristic that utilizes this paradigm and efficiently explores the discrete neighborhood around the continuous proxy action in structured action spaces with up to 10^{73} actions. We demonstrate the performance of our method by benchmarking it against three state-of-the-art approaches designed for large discrete action spaces across two distinct environments. Our results show that DNC matches or outperforms state-of-the-art approaches while being computationally more efficient. Furthermore, our method scales to action spaces that so far remained computationally intractable for existing methodologies.

Learning generalizable manipulation policies hinges on data, yet robot manipulation data is scarce and often entangled with specific embodiments, making both cross-task and cross-platform transfer difficult. We tackle this challenge with task-agnostic embodiment modeling, which learns embodiment dynamics directly from task-agnostic action data and decouples them from high-level policy learning. By focusing on exploring all feasible actions of the embodiment to capture what is physically feasible and consistent, task-agnostic data takes the form of independent image-action pairs with the potential to cover the entire embodiment workspace, unlike task-specific data, which is sequential and tied to concrete tasks. This data-driven perspective bypasses the limitations of traditional dynamics-based modeling and enables scalable reuse of action data across different tasks. Building on this principle, we introduce AnyPos, a unified pipeline that integrates large-scale automated task-agnostic exploration with robust embodiment modeling through inverse dynamics learning. AnyPos generates diverse yet safe trajectories at scale, then learns embodiment representations by decoupling arm and end-effector motions and employing a direction-aware decoder to stabilize predictions under distribution shift, which can be seamlessly coupled with diverse high-level policy models. In comparison to the standard baseline, AnyPos achieves a 51% improvement in test accuracy. On manipulation tasks such as operating a microwave, toasting bread, folding clothes, watering plants, and scrubbing plates, AnyPos raises success rates by 30-40% over strong baselines. These results highlight data-driven embodiment modeling as a practical route to overcoming data scarcity and achieving generalization across tasks and platforms in visuomotor control. Project page: https://embodiedfoundation.github.io/vidar_anypos.

Achieving general-purpose humanoid control requires a delicate balance between the precise execution of commanded motions and the flexible, anthropomorphic adaptability needed to recover from unpredictable environmental perturbations. Current general controllers predominantly formulate motion control as a rigid reference-tracking problem. While effective in nominal conditions, these trackers often exhibit brittle, non-anthropomorphic failure modes under severe disturbances, lacking the generative adaptability inherent to human motor control. To overcome this limitation, we propose Heracles, a novel state-conditioned diffusion middleware that bridges precise motion tracking and generative synthesis. Rather than relying on rigid tracking paradigms or complex explicit mode-switching, Heracles operates as an intermediary layer between high-level reference motions and low-level physics trackers. By conditioning on the robot's real-time state, the diffusion model implicitly adapts its behavior: it approximates an identity map when the state closely aligns with the reference, preserving zero-shot tracking fidelity. Conversely, when encountering significant state deviations, it seamlessly transitions into a generative synthesizer to produce natural, anthropomorphic recovery trajectories. Our framework demonstrates that integrating generative priors into the control loop not only significantly enhances robustness against extreme perturbations but also elevates humanoid control from a rigid tracking paradigm to an open-ended, generative general-purpose architecture.

Imitation learning from human motion capture (MoCap) data provides a promising way to train humanoid robots. However, due to differences in morphology, such as varying degrees of joint freedom and force limits, exact replication of human behaviors may not be feasible for humanoid robots. Consequently, incorporating physically infeasible MoCap data in training datasets can adversely affect the performance of the robot policy. To address this issue, we propose a bi-level optimization-based imitation learning framework that alternates between optimizing both the robot policy and the target MoCap data. Specifically, we first develop a generative latent dynamics model using a novel self-consistent auto-encoder, which learns sparse and structured motion representations while capturing desired motion patterns in the dataset. The dynamics model is then utilized to generate reference motions while the latent representation regularizes the bi-level motion imitation process. Simulations conducted with a realistic model of a humanoid robot demonstrate that our method enhances the robot policy by modifying reference motions to be physically consistent.

We present a new technique to enhance the robustness of imitation learning methods by generating corrective data to account for compounding errors and disturbances. While existing methods rely on interactive expert labeling, additional offline datasets, or domain-specific invariances, our approach requires minimal additional assumptions beyond access to expert data. The key insight is to leverage local continuity in the environment dynamics to generate corrective labels. Our method first constructs a dynamics model from the expert demonstration, encouraging local Lipschitz continuity in the learned model. In locally continuous regions, this model allows us to generate corrective labels within the neighborhood of the demonstrations but beyond the actual set of states and actions in the dataset. Training on this augmented data enhances the agent's ability to recover from perturbations and deal with compounding errors. We demonstrate the effectiveness of our generated labels through experiments in a variety of robotics domains in simulation that have distinct forms of continuity and discontinuity, including classic control problems, drone flying, navigation with high-dimensional sensor observations, legged locomotion, and tabletop manipulation.

Kinodynamic motion planning is concerned with computing collision-free trajectories while abiding by the robot's dynamic constraints. This critical problem is often tackled using sampling-based planners (SBPs) that explore the robot's high-dimensional state space by constructing a search tree via action propagations. Although SBPs can offer global guarantees on completeness and solution quality, their performance is often hindered by slow exploration due to uninformed action sampling. Learning-based approaches can yield significantly faster runtimes, yet they fail to generalize to out-of-distribution (OOD) scenarios and lack critical guarantees, e.g., safety, thus limiting their deployment on physical robots. We present Diffusion Tree (DiTree): a provably-generalizable framework leveraging diffusion policies (DPs) as informed samplers to efficiently guide state-space search within SBPs. DiTree combines DP's ability to model complex distributions of expert trajectories, conditioned on local observations, with the completeness of SBPs to yield provably-safe solutions within a few action propagation iterations for complex dynamical systems. We demonstrate DiTree's power with an implementation combining the popular RRT planner with a DP action sampler trained on a single environment. In comprehensive evaluations on OOD scenarios, % DiTree has comparable runtimes to a standalone DP (3x faster than classical SBPs), while improving the average success rate over DP and SBPs. DiTree is on average 3x faster than classical SBPs, and outperforms all other approaches by achieving roughly 30\% higher success rate. Project webpage: https://sites.google.com/view/ditree.