Nonequilbrium physics of generative diffusion models

TL;DR

This paper offers a physics-based analysis of generative diffusion models, revealing their underlying thermodynamic and statistical mechanics principles to better understand their dynamics and phase transitions.

Contribution

It introduces a comprehensive physics framework, including fluctuation theorem and entropy production, to analyze the intrinsic mechanisms of diffusion models.

Findings

Formulates a path integral representation of diffusion dynamics

Links stochastic thermodynamics with generative modeling

Identifies phase transitions in diffusion processes

Abstract

Generative diffusion models apply the concept of Langevin dynamics in physics to machine leaning, attracting a lot of interests from engineering, statistics and physics, but a complete picture about inherent mechanisms is still lacking. In this paper, we provide a transparent physics analysis of diffusion models, formulating the fluctuation theorem, entropy production, equilibrium measure, and Franz-Parisi potential to understand the dynamic process and intrinsic phase transitions. Our analysis is rooted in a path integral representation of both forward and backward dynamics, and in treating the reverse diffusion generative process as a statistical inference, where the time-dependent state variables serve as quenched disorder akin to that in spin glass theory. Our study thus links stochastic thermodynamics, statistical inference and geometry based analysis together to yield a coherent picture about how the generative diffusion models work.