Faster Visuomotor Policy Learning on Action Manifolds via Riemannian MeanFlow

Flow matching policies learn continuous velocity fields that transport noise to actions, enabling fast deterministic inference for robot manipulation. However, standard training optimizes a pointwise velocity objective while inference requires numerical integration of that field -- a mismatch that causes compounding trajectory errors. We propose four complementary remedies: (1) auxiliary rectified flow velocity regression that provides uniform temporal supervision across the full time interval; (2) multi-step trajectory consistency training that supervises the integrated displacement of the velocity field over trajectory segments, directly closing the train-inference gap; (3) velocity field regularization that enforces temporal smoothness, preventing oscillations that destabilize integration; and (4) fourth-order Runge-Kutta (RK4) inference that reduces global discretization error by orders of magnitude over Euler methods. Critically, these components are not independently sufficient -- RK4 without a smooth velocity field fails, and smoothness without trajectory-level supervision still drifts, as our ablation study confirms. We further pair these with a dual-view 3D point cloud encoder using two independent PointNet encoders for complementary spatial perception. On four real-robot tasks across a Franka arm and a Boston Dynamics Spot, our method achieves 70% and 60% overall success on two long-horizon multi-phase tasks where both baselines score 0%, and reaches 100% on precision tool placement. Three MetaWorld simulation tasks confirm consistent improvements, validating that trajectory-level supervision is essential for reliable policy execution.

Flow matching has recently become a new standard for behavior cloning in robotic manipulation. However, state-of-the-art flow matching policies suffer from a systematic structural mismatch: they rely on a globally fixed isotropic source distribution despite the strongly fragmented and heteroscedastic structure of robotic action spaces. This agnostic initialization forces the model to learn highly entangled vector fields, bottlenecking training efficiency and limiting overall policy performance. To address this limitation, we introduce Latent Action Guided Flow Matching (LAFM), a novel framework that replaces the monolithic Gaussian with an adaptive library of learned prior distributions. By grounding these distributions using a latent action model, LAFM maps current observations to discrete motion primitives, selecting a specialized base distribution that provides an informed, structurally aligned initialization for the denoising process. This dynamic adaptivity naturally accommodates heteroscedasticity in human demonstrations and makes transport trajectories shorter and less entangled. Empirically, LAFM substantially outperforms standard flow matching formulations, increasing task success rates by 23.4% in real-world robotic deployments and by 10.4% on the LIBERO-90 benchmark. Furthermore, we demonstrate that LAFM achieves state-of-the-art results, surpassing massively pre-trained vision-language-action models while utilizing significantly smaller architectures.

Generative models such as diffusion and flow matching have become dominant paradigms for visuomotor policy learning, yet their reliance on iterative denoising incurs high inference latency incompatible with real-time robotic control. We present Fast Legendre-polynomial Action policy via Sparse History-anchored flow (FLASH Policy), which replaces discrete action-chunk generation with continuous Legendre polynomial trajectory representation. Specifically, by fitting expert demonstrations under sparse temporal sampling, FLASH enables a single inference to cover a significantly extended action horizon. To further accelerate generation, FLASH initiates the flow matching process from history polynomial coefficients rather than uninformative Gaussian noise, shortening the transport distance and enabling accurate single-step inference. Moreover, analytic polynomial differentiation directly provides desired velocity feed-forward signals to the torque controller without numerical approximation. Extensive experiments on five simulated and two real-world manipulation tasks demonstrate that FLASH achieves state-of-the-art success rates ($\ge 92\%$ across all tasks), a per-episode inference time of $31.40\,ms$ (up to $175\times$ faster than diffusion policies and $18\times$ faster than prior flow matching policies), up to $4\times$ faster training convergence than ACT, and $5\times$ to $7\times$ reduction in controller tracking error compared to discrete-action baselines.