Sharpen Your Flow: Sharpness-Aware Sampling for Flow Matching

TL;DR

SharpEuler is a training-free, profile-based sampler that optimizes timestep allocation in flow matching models, improving sample quality without additional neural network evaluations.

Contribution

It introduces SharpEuler, a novel offline profiling method that estimates where velocity fields change rapidly, guiding efficient sampling in flow models.

Findings

SharpEuler reduces inter-mode leakage in generated samples.

It increases mode coverage at fixed evaluation budgets.

Sample quality improves without additional neural network evaluations.

Abstract

Flow matching models generate samples by numerically integrating a learned velocity field, with each integration step requiring a neural network evaluation. Fast generation therefore requires using a small fixed evaluation budget effectively: the key question is not only how to integrate the flow, but where the sampler should spend its steps. We propose SharpEuler, a training-free sampler that profiles a pretrained model offline by estimating where the learned velocity field changes most rapidly along calibration trajectories. This finite-difference estimate defines a solver-aware sharpness profile, which is smoothed and converted by a quantile transform into a timestep grid for any desired inference budget. At test time, sampling remains ordinary Euler integration with the same number of model evaluations as a uniform schedule. We justify SharpEuler using three principles: a numerical principle identifying trajectory acceleration as the leading source of Euler discretization error, a variational principle deriving sharpness-based power-law timestep densities, and a statistical guarantee showing that the finite-sample calibrated sampler is stable at the terminal distribution level. Our experiments show that SharpEuler improves sample quality at fixed budgets, reducing inter-mode leakage and increasing mode coverage.