Trajectory-Consistent Flow Matching for Robust Visuomotor Policy Learning
For robot learning researchers, this work provides a principled solution to the trajectory drift problem in flow matching policies, enabling reliable long-horizon manipulation.
The paper addresses the train-inference mismatch in flow matching policies for robot manipulation, where pointwise velocity training leads to compounding trajectory errors during inference. By combining auxiliary rectified flow velocity regression, multi-step trajectory consistency training, velocity field regularization, and RK4 inference, the method achieves 70% and 60% success on two long-horizon tasks where baselines score 0%, and 100% on precision tool placement.
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.