Test-time scaling of diffusions with flow maps

TL;DR

This paper introduces Flow Map Trajectory Tilting (FMTT), a novel test-time method for improving diffusion model samples by directly using flow maps to optimize for user-defined rewards, enabling better ascent and complex image editing.

Contribution

The paper proposes a new algorithm, FMTT, that leverages flow maps for better reward optimization in diffusion models at test-time, outperforming existing methods.

Findings

FMTT improves reward ascent over standard methods.

The approach enables exact sampling and reward maximization.

It facilitates complex image editing with vision-language models.

Abstract

A common recipe to improve diffusion models at test-time so that samples score highly against a user-specified reward is to introduce the gradient of the reward into the dynamics of the diffusion itself. This procedure is often ill posed, as user-specified rewards are usually only well defined on the data distribution at the end of generation. While common workarounds to this problem are to use a denoiser to estimate what a sample would have been at the end of generation, we propose a simple solution to this problem by working directly with a flow map. By exploiting a relationship between the flow map and velocity field governing the instantaneous transport, we construct an algorithm, Flow Map Trajectory Tilting (FMTT), which provably performs better ascent on the reward than standard test-time methods involving the gradient of the reward. The approach can be used to either perform exact sampling via importance weighting or principled search that identifies local maximizers of the reward-tilted distribution. We demonstrate the efficacy of our approach against other look-ahead techniques, and show how the flow map enables engagement with complicated reward functions that make possible new forms of image editing, e.g. by interfacing with vision language models.