Generative diffusion models have achieved spectacular performance in many areas of generative modeling. While the fundamental ideas behind these models come from non-equilibrium physics, variational inference and stochastic calculus, in this paper we show that many aspects of these models can be understood using the tools of equilibrium statistical mechanics. Using this reformulation, we show that generative diffusion models undergo second-order phase transitions corresponding to symmetry breaking phenomena. We show that these phase-transitions are always in a mean-field universality class, as they are the result of a self-consistency condition in the generative dynamics. We argue that the critical instability that arises from the phase transitions lies at the heart of their generative capabilities, which are characterized by a set of mean field critical exponents. Furthermore, using the statistical physics of disordered systems, we show that memorization can be understood as a form of critical condensation corresponding to a disordered phase transition. Finally, we show that the dynamic equation of the generative process can be interpreted as a stochastic adiabatic transformation that minimizes the free energy while keeping the system in thermal equilibrium.

翻译：生成式扩散模型在生成建模的多个领域取得了显著成就。尽管这些模型的基本原理源于非平衡物理、变分推断和随机微积分，但本文表明，这些模型的诸多方面可以利用平衡统计力学的工具来理解。基于这一重新表述，我们证明生成式扩散模型会经历对应对称破缺现象的二阶相变。我们指出，这些相变始终属于平均场普适类，因为它们是生成动力学中自洽性条件的结果。我们论证，相变所引发的临界不稳定性正是其生成能力的核心，而这些能力由一组平均场临界指数表征。此外，利用无序系统的统计物理，我们证明记忆化可理解为一种对应于无序相变的临界凝聚形式。最后，我们表明生成过程的动力学方程可解释为一种随机绝热变换，该变换在保持系统热平衡的同时最小化自由能。