arXiv:2407.04495 · v6
Speed-accuracy relations for diffusion models: Wisdom from nonequilibrium thermodynamics and optimal transport
摘要
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. This relation can be interpreted as the speed of the diffusion dynamics in the absence of the non-conservative 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.
作者备注：37 pages, 9 figures. Corrected a coefficient in the score matching objective function that was inconsistent with the result presented in Discussions. The results and conclusions are unchanged
期刊信息：Phys. Rev. X 15, 031031 (2025)