Trajectory-Consistent Flow Matching for Robust Visuomotor Policy Learning

• URL: http://arxiv.org/abs/2605.08511v1
• Date: Fri, 08 May 2026 21:44:10 GMT
• Title: Trajectory-Consistent Flow Matching for Robust Visuomotor Policy Learning
• Abstract summary: Flow matching policies learn continuous velocity fields that transport noise to actions, enabling deterministic inference for robot manipulation.<n>Standard training optimize a pointwise velocity objective while inference requires numerical integration of that field -- a mismatch that causes compounding trajectory errors.<n>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; and (3) velocity field regularization that enforces temporal smoothness.
• Score: 1.7616042687330642
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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