Speed-accuracy relations for diffusion models: Wisdom from nonequilibrium thermodynamics and optimal transport
Department of Mathematical Engineering and Information Physics, School of Engineering, The University of Tokyo（数学工程与信息物理系，工学院，东京大学）；Department of Earth and Planetary Physics, School of Science, The University of Tokyo（地球与行星物理系，理学院，东京大学）；Preferred Networks Inc.（Preferred Networks公司）；Universal Biology Institute, Graduate School of Science, The University of Tokyo（生物科学研究所，研究生院，东京大学）
Kotaro Ikeda, Tomoya Uda, Daisuke Okanohara, Sosuke Ito
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
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.
We build a rigorous nonequilibrium thermodynamic description for open chemical reaction networks of elementary reactions. Their dynamics is described by deterministic rate equations satisfying mass action law. Our most general framework considers open networks driven by time-dependent chemostats. The energy and entropy balances are established and a nonequilibrium Gibbs free energy is introduced. The difference between this latter and its equilibrium form represents the minimal work done by the chemostats to bring the network in its nonequilibrium state. It is minimized in nondriven detailed-b…
The thermodynamics is studied with the thermodynamic parameter of the lifetime, first-passage time, generalizing the equilibrium thermodynamics. Various ways of describing several stationary nonequilibrium states in the system are considered. The possibilities of increasing the lifetime of the system under external influences on it are investigated.
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Universidade Federal Rural de Pernambuco（伯南布哥联邦农村大学）
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