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

Flow-based models learn a target distribution by modelinga marginal velocity field, defined as the average of sample-wise velocitiesconnecting each sample from a simple prior to the target data. However,when sample-wise velocities conflict at the same intermediate state, thisaveraged velocity can misguide samples toward low-density regions, de-grading generation quality. To address this issue, we propose the FlowDivergence Sampler (FDS), a training-free framework that refines in-termediate states before each solver step. Our key finding reveals thatthe severity of this misguidance is quantified by the divergence of themarginal velocity field that is readily computable during inference witha well-optimized model. FDS exploits this signal to steer states towardless ambiguous regions. As a plug-and-play framework compatible withstandard solvers and off-the-shelf flow backbones, FDS consistently im-proves fidelity across various generation tasks including text-to-imagesynthesis, and inverse problems.