Correcting Trajectory Drift in Flow Matching Models

Flow-matching generative models are typically sampled by numerically integrating a learned velocity field using a small number of deterministic steps. In this regime, fixed-timestep solvers can drive inference trajectories away from the continuous learned trajectory, causing the learned velocity field to be evaluated at increasingly shifted states and potentially compounding error. We study this inference trajectory drift and propose a training-free sampler that combines cached finite-difference acceleration with discrepancy-guided online control. At each step, the method forms an Euler update and a finite-difference acceleration update from consecutive velocity evaluations, and conservatively shrinks the timestep when their magnitude and angular disagreement is large. The sampler uses one network evaluation per step, stores only the previous velocity, and requires no retraining. A scalar gain $\lambda$ modulates the acceleration correction, while discrepancy-guided step control provides complementary online stabilization; their relative contributions depend on the model and sampling regime. The strongest gains occur in low-NFE RectFlow sampling, where the method outperforms Euler, standard multistep baselines, flow-prediction DPM-Solver++ 2M, and Flow-UniPC across the tested NFE range. Full-vector trajectory diagnostics further show reduced state deviation and learned-field discrepancy relative to AB2 at matched NFE. These findings highlight that sampler design for learned generative models should account not only for nominal integration order, but also for the behavior of the realized inference trajectory.