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, 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 argue that this lead to a form of instability that lies at the heart of their generative capabilities and that can be described by a set of mean field critical exponents. We conclude by analyzing recent work connecting diffusion models and associative memory networks in view of the thermodynamic formulations.

翻译：生成扩散模型在生成建模的许多领域取得了显著的性能。尽管这些模型的基本思想源于非平衡态物理，但在本文中，我们展示这些模型的诸多方面可以利用平衡态统计力学的工具来理解。通过这种重新表述，我们表明生成扩散模型会经历对应于对称性破缺现象的二阶相变。我们论证，这导致了一种不稳定性形式，它正是其生成能力的核心，且可由一组平均场临界指数来描述。最后，我们基于热力学表述，分析了近期将扩散模型与联想记忆网络联系起来的研究工作。