Problem
Research questions and friction points this paper is trying to address.
flow matching
marginal velocity field
sample-wise velocities
generation quality
low-density regions
Training-Free Refinement of Flow Matching with Divergence-based Sampling
🤖 AI Summary
This work addresses a critical limitation in flow matching models, where velocity conflicts at intermediate states cause the average velocity field to steer samples toward low-density regions, degrading generation quality. To mitigate this issue, the authors propose Flow Divergence Sampler (FDS), a training-free framework that leverages the divergence of the velocity field to refine intermediate states prior to each ODE solver step, guiding them toward high-confidence, less ambiguous regions. This approach is the first to demonstrate that velocity field divergence can effectively quantify guidance bias, enabling a plug-and-play sampling refinement mechanism that is agnostic to both the underlying model and ODE solver. Experiments show that FDS significantly improves generation fidelity in tasks such as text-to-image synthesis and inverse problems, without requiring any additional training or modifications to existing flow matching models.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
flow matching
divergence-based sampling
training-free refinement
marginal velocity field
plug-and-play framework
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