Speed-accuracy relations for diffusion models: Wisdom from nonequilibrium thermodynamics and optimal transport

TL;DR

This paper establishes a theoretical framework linking diffusion models and nonequilibrium thermodynamics, deriving speed-accuracy inequalities that inform optimal data generation strategies, validated through numerical experiments on image datasets.

Contribution

It introduces a novel connection between diffusion models and stochastic thermodynamics, deriving speed-accuracy relations and optimal protocols using optimal transport theory.

Findings

Derived speed-accuracy inequalities for diffusion models.

Validated relations through numerical experiments with various noise schedules.

Demonstrated applicability to real-world image data generation.

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. 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.