Nonequilbrium physics of generative diffusion models
This work addresses a foundational problem for researchers in machine learning, physics, and statistics by offering a theoretical framework to understand diffusion models, though it is incremental in building on existing physics concepts.
The paper tackles the lack of a complete understanding of the mechanisms behind generative diffusion models by providing a physics-based analysis using concepts like the fluctuation theorem and entropy production. The result is a coherent picture linking stochastic thermodynamics, statistical inference, and geometry to explain how these models work.
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.