Sharpen Your Flow: Sharpness-Aware Sampling for Flow Matching

2026-05-12

AI Summary

This work addresses the challenge of efficiently allocating integration timesteps for flow-matching models under a fixed computational budget to enhance generation quality. The authors propose SharpEuler, a training-free sampler that, for the first time, identifies trajectory acceleration as the dominant source of Euler discretization error. Leveraging this insight, they offline estimate a sharpness profile of the pretrained velocity field and derive a sharpness-based power-law timestep density. By combining finite-difference estimation, profile smoothing, and quantile transformation, SharpEuler constructs a solver-aware timestep grid that enables stable and efficient Euler integration at any inference budget. Experiments demonstrate that SharpEuler significantly improves sample quality, reduces mode leakage, and enhances multimodal coverage.

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.

Problem

• flow matching
• sampling efficiency
• numerical integration
• sharpness-aware
• generation budget

Innovation

• sharpness-aware sampling
• flow matching
• non-uniform timesteps
• Euler integration
• solver-aware profiling