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.

翻译：生成扩散模型将物理学中的朗之万动力学概念应用于机器学习，吸引了工程学、统计学和物理学界的广泛关注，但其内在机制的完整图景仍不清晰。本文对扩散模型提供了清晰的物理学分析，通过构建涨落定理、熵产生、平衡测度以及Franz-Parisi势来理解其动态过程与内在相变。我们的分析植根于正向与反向动力学的路径积分表示，并将反向扩散生成过程视为一种统计推断——其中随时间变化的状态变量扮演着类似于自旋玻璃理论中淬火无序的角色。本研究从而将随机热力学、统计推断与基于几何的分析方法相结合，为生成扩散模型的工作原理提供了连贯的理论图景。