Training-Free Refinement of Flow Matching with Divergence-based Sampling

TL;DR

This paper introduces FDS, a training-free method that refines flow-based model states during inference by using divergence signals to improve generation quality across tasks.

Contribution

The paper proposes a novel, training-free divergence-based sampling method (FDS) that enhances flow model inference without retraining.

Findings

FDS improves fidelity in text-to-image synthesis.

FDS enhances performance in inverse problems.

FDS is compatible with standard solvers and flow backbones.

Abstract

Flow-based models learn a target distribution by modeling a marginal velocity field, defined as the average of sample-wise velocities connecting each sample from a simple prior to the target data. When sample-wise velocities conflict at the same intermediate state, however, this averaged velocity can misguide samples toward low-density regions, degrading generation quality. To address this issue, we propose the Flow Divergence Sampler (FDS), a training-free framework that refines intermediate states before each solver step. Our key finding reveals that the severity of this misguidance is quantified by the divergence of the marginal velocity field that is readily computable during inference with a well-optimized model. FDS exploits this signal to steer states toward less ambiguous regions. As a plug-and-play framework compatible with standard solvers and off-the-shelf flow backbones, FDS consistently improves fidelity across various generation tasks including text-to-image synthesis, and inverse problems.