Test-time scaling of diffusions with flow maps
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.
692d0ac14397b1ec214f67b9
Amirmojtaba Sabour
692d0ac14397b1ec214f67ba
Michael S. Albergo
692d0ac14397b1ec214f67bb
Carles Domingo-Enrich
692d0ac14397b1ec214f67bc
Nicholas M. Boffi
692d0ac14397b1ec214f67bd
Sanja Fidler
692d0ac14397b1ec214f67be
Karsten Kreis
692d0ac14397b1ec214f67bf
Eric Vanden-Eijnden
Test-time scaling of diffusions with flow maps
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.
The proposed Flow Map Trajectory Tilting (FMTT) algorithm improves diffusion models at test-time by leveraging flow maps to better align with user-specified rewards, enabling more effective sampling and image editing.
diffusion models gradient of the reward flow map velocity field Flow Map Trajectory Tilting (FMTT) importance weighting reward-tilted distribution vision language models