DynaFlow: Dynamics-embedded Flow Matching for Physically Consistent Motion Generation from State-only Demonstrations

TL;DR

DynaFlow tackles the challenge of generating physically feasible motion from state-only demonstrations by embedding a differentiable simulator directly into a flow-matching model. By mapping action trajectories through a differentiable rollout, it guarantees dynamic feasibility by construction while learning to infer the underlying actions. The approach is validated with two datasets, including real hardware deployment on a Go1 quadruped, showing that DynaFlow achieves strict physical consistency without sacrificing distributional fidelity. It enables long-horizon, open-loop locomotion and can transform infeasible retargeted demonstrations into dynamically executable, stylistic behaviors, bridging the gap between kinematic data and real-world execution.

Abstract

This paper introduces DynaFlow, a novel framework that embeds a differentiable simulator directly into a flow matching model. By generating trajectories in the action space and mapping them to dynamically feasible state trajectories via the simulator, DynaFlow ensures all outputs are physically consistent by construction. This end-to-end differentiable architecture enables training on state-only demonstrations, allowing the model to simultaneously generate physically consistent state trajectories while inferring the underlying action sequences required to produce them. We demonstrate the effectiveness of our approach through quantitative evaluations and showcase its real-world applicability by deploying the generated actions onto a physical Go1 quadruped robot. The robot successfully reproduces diverse gait present in the dataset, executes long-horizon motions in open-loop control and translates infeasible kinematic demonstrations into dynamically executable, stylistic behaviors. These hardware experiments validate that DynaFlow produces deployable, highly effective motions on real-world hardware from state-only demonstrations, effectively bridging the gap between kinematic data and real-world execution.

Figures (7)

• Figure 1: Schematic illustration of proposed framework. Given state-only demonstrations that are not guaranteed to be physically feasible, DynaFlow generates dynamically consistent trajectories while also inferring deployable action sequences. The entire model is trained end-to-end using analytical gradients provided by the differentiable simulator.
• Figure 2: Comparative analysis of physical consistency and distributional similarity. The SAE (red) and TRE (blue) for each method on two distinct datasets (Sec. \ref{['ssec:dataset']}) are summarized in the box plot. The mean value for each metric is annotated above the corresponding box plots. Notably, DynaFlow produces physically consistent trajectories while preserving high fidelity to the original motion.
• Figure 3: Comparison of tracking performance on the (a) Simulation Rollouts and (b) Retargeted Motion Capture datasets. Each plot shows the resulting state trajectory (base height and pitch angle) after using a numerical inverse dynamics solver to track the original plan from each method. Trajectories are terminated and marked with an 'x' upon failure (body height $<$ 0.2 m or the vertical component of the base's z-axis $<$ 0.5). Most baselines produce untrackable plans that fail due to either the accumulation of physical errors (SAE) or inherent plan instability (high TRE). In contrast, only DynaFlow consistently generates trackable and stable trajectories.
• Figure 4: Performance validation of DynaFlow on the real-world experiment. The robot demonstrates a smooth transition between gaits, robust recovery from an external push, and successful long-horizon open-loop locomotion without any replanning.
• Figure 5: Transfer of an infeasible motion to real-world execution. DynaFlow translates a dynamically infeasible, kinematically retargeted German Shepherd gallop into a feasible trajectory and successfully executes it in simulation and on the Go1 robot.