GenPhys: From Physical Processes to Generative Models

TL;DR

GenPhys introduces a broad family of generative models derived from physical process-inspired PDEs, unifying existing models like DM and PFGM and enabling new model families such as Yukawa Generative Models.

Contribution

The paper presents a novel framework translating physical PDEs into generative models, expanding the design space beyond existing diffusion and Poisson flow models.

Findings

GenPhys subsumes diffusion models and PFGM.

Yukawa Generative Models inspired by weak interactions.

Physical processes like wave and Schrödinger equations can be adapted into GenPhys.

Abstract

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.