Patch the Path: Fixed-Budget Post-Sampling Trajectory Upgrade for Flow Matching

We study how to improve a flow-matching sample after sampling is complete, using a small, fixed budget of additional model evaluations. We propose FixUp-FM, a training-free method that revisits the completed Euler trajectory and upgrades steps with large estimated local errors to Heun. A minimum-norm velocity adjustment derived from the trajectory propagates these corrections downstream without additional model evaluations, reserving computation for selected Heun corrections. FixUp-FM also supports incremental refinement across successive requests, with each pass building on the latest corrected trajectory rather than restarting. Under smoothness and bounded-propagation assumptions in the fixed-budget setting, we establish near-oracle defect selection and second-order endpoint agreement with a selective Euler–Heun rerun using exact velocities. Across SD3 Medium, SD3.5 Large, and FLUX.1-dev, FixUp-FM achieves higher mean ImageReward than NFE-matched direct Euler in 111 of 120 tested correction-budget configurations across the main sampling range.