Nonequilbrium physics of generative diffusion models

Generative diffusion models apply the concept of Langevin dynamics in physics to machine leaning, attracting a lot of interest from industrial application, but a complete picture about inherent mechanisms is still lacking. In this paper, we provide a transparent physics analysis of the diffusion models, deriving the fluctuation theorem, entropy production, Franz-Parisi potential to understand the intrinsic phase transitions discovered recently. Our analysis is rooted in non-equlibrium physics and concepts from equilibrium physics, i.e., treating both forward and backward dynamics as a Langevin dynamics, and treating the reverse diffusion generative process as a statistical inference, where the time-dependent state variables serve as quenched disorder studied in spin glass theory. This unified principle is expected to guide machine learning practitioners to design better algorithms and theoretical physicists to link the machine learning to non-equilibrium thermodynamics.