Since diffusion models (DM) and the more recent Poisson flow generative models (PFGM) are inspired by physical processes, it is reasonable to ask: Can physical processes offer additional new generative models? We show that the answer is yes. We introduce a general family, Generative Models from Physical Processes (GenPhys), where we translate partial differential equations (PDEs) describing physical processes to generative models. We show that generative models can be constructed from s-generative PDEs (s for smooth). GenPhys subsume the two existing generative models (DM and PFGM) and even give rise to new families of generative models, e.g., "Yukawa Generative Models" inspired from weak interactions. On the other hand, some physical processes by default do not belong to the GenPhys family, e.g., the wave equation and the Schr\"{o}dinger equation, but could be made into the GenPhys family with some modifications. Our goal with GenPhys is to explore and expand the design space of generative models.

翻译：由于扩散模型（DM）及更近期的泊松流生成模型（PFGM）均受物理过程启发，因此一个合理的问题是：物理过程能否提供额外的全新生成模型？我们证明答案是肯定的。本文提出一个通用框架——基于物理过程的生成模型（GenPhys），将描述物理过程的偏微分方程（PDE）转化为生成模型。我们证明生成模型可由s-生成型PDE（s代表光滑）构建。GenPhys不仅涵盖了现有的两种生成模型（DM和PFGM），更催生了新的生成模型族，例如受弱相互作用启发的“汤川生成模型”。另一方面，某些物理过程（如波动方程和薛定谔方程）默认不属于GenPhys族，但可通过适当修改纳入该框架。GenPhys的目标是探索并扩展生成模型的设计空间。