All in One: Generative Modeling as Mean-Field Game Design

2026/07/25 by Kun Zhao, Xu Chen
#cs.LG #cs.AI

paper · pdf

Abstract

Mean-field games (MFGs) offer a unifying lens on continuous-time generative modeling: a cost tuple recovering twelve prominent models---Continuous Normalizing Flows, OT-Flow, Score-based Models, Schrödinger Bridges, and more---as special cases of one variational problem. Yet two dimensions of this space remain entirely unexplored: the interaction term I is set to zero in many existing models, and the rich family of MFG solvers has never been applied to generative modeling. We address both gaps with MFGLab an open-source PyTorch library whose primary API is the cost tuple: all twelve models are specified by four composable cost functions, and the training loop, log-Jacobian, and reverse-ODE sampler are shared automatically. We additionally propose DI-Flow, a novel cost design that uses a differentiable entropy functional to encourage mode coverage, and provide learning-based MFG solvers that substantially outperform neural training on stochastic-dynamics rows. Experiments on two 2-D benchmarks confirm that the unified API is lossless relative to hand-coded implementations.

Citations

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• Neural Ordinary Differential Equations
• Generative Adversarial Imitation Learning

Related

• A mean-field games laboratory for generative modeling
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• Solving Continuous Mean Field Games: Deep Reinforcement Learning for Non-Stationary Dynamics
• Neural Mean-Field Games: Extending Mean-Field Game Theory with Neural Stochastic Differential Equations
• Signatured Deep Fictitious Play for Mean Field Games with Common Noise