非平衡熱力学の知見から拡散モデルの最適手法を提案～熱力学的散逸と生成誤差をつなぐ関係式を導出～

2025-08-01 東京大学

非平衡熱力学と最適輸送理論を用いて拡散モデルを解析

＜関連情報＞

• https://www.s.u-tokyo.ac.jp/ja/press/10887/
• https://journals.aps.org/prx/abstract/10.1103/x5vj-8jq9

拡散モデルにおける速度-精度関係：非平衡熱力学と最適輸送からの知見 Speed-Accuracy Relations for Diffusion Models: Wisdom from Nonequilibrium Thermodynamics and Optimal Transport

Kotaro Ikeda, Tomoya Uda, Daisuke Okanohara, and Sosuke Ito
Physical Review X  Published 30 July, 2025
DOI: https://doi.org/10.1103/x5vj-8jq9

Abstract

We discuss a connection between a generative model, called the diffusion model, and nonequilibrium thermodynamics for the Fokker-Planck equation, called stochastic thermodynamics. Using techniques from stochastic thermodynamics, we derive the speed-accuracy relations for diffusion models, which are inequalities that relate the accuracy of data generation to the entropy production rate. These relations can be interpreted as the relations between accuracy and the speed of the diffusion dynamics in the absence of the nonconservative force. From a stochastic thermodynamic perspective, our results provide quantitative insight into how best to generate data in diffusion models. The optimal learning protocol is introduced by the geodesic of space of the 2-Wasserstein distance in optimal transport theory. We numerically illustrate the validity of the speed-accuracy relations for diffusion models with different noise schedules and different data. We numerically discuss our results for optimal and suboptimal learning protocols. We also demonstrate the applicability of our results to data generation from the real-world image datasets.