Integrating Mean-Field Game Theory with Diffusion Model
Weimin Yuan, Weilong Chen, Hien Van Nguyen, Yifei Zhu, Dan Wang, Zhu Han · 2025
Diffusion probabilistic models can be interpreted as a sequence of distribution transformations, wherein the inverse diffusion trajectory plays a pivotal role in applications ranging from image generation to wireless communication. Meanwhile, Mean Field Game (MFG) theory offers an effective framework for multi-agent control, enabling the regulation of distribution transitions while compressing the data and thereby reducing computational complexity. In this paper, we propose a novel framework, Mean Field Game Diffusion Model (MDM) that synergistically integrates MFG theory with diffusion models to improve both the efficiency and quality of image generation. Specifically, we formulate the reverse diffusion process as an MFG problem by treating the image as a data distribution and each pixel as an individual agent, thereby deriving governing equations to regulate their interactions. This approach optimizes the evolution trajectory of the data distribution by minimizing information-theoretic measures, such as the discrepancy between the generated and target distributions, thereby achieving high- quality generation while minimizing information loss. Comparative experiments across multiple datasets and diverse evaluation metrics demonstrate the effectiveness of MDM, providing a novel perspective that unifies generative modeling, game-theoretic optimization, and information theory.