Trajectory-Consistent Flow Matching for Robust Visuomotor Policy Learning

TL;DR

This paper introduces a set of techniques to improve flow matching policies for robot manipulation, addressing trajectory errors caused by training-inference mismatches and enhancing robustness in real-world tasks.

Contribution

The authors propose four complementary methods—velocity supervision, trajectory consistency, regularization, and RK4 inference—to significantly improve flow matching policy robustness and accuracy.

Findings

Achieved 70% and 60% success rates on long-horizon tasks where baselines failed.

Reached 100% success on precision tool placement tasks.

Validated improvements across four real-robot tasks and three simulation benchmarks.

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.