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

• URL: http://arxiv.org/abs/2607.23026v1
• Date: Sat, 25 Jul 2026 03:57:31 GMT
• Title: All in One: Generative Modeling as Mean-Field Game Design
• Abstract summary: Mean-field games (MFGs) offer a unifying lens on continuous-time generative modeling.<n>We develop an open-source library whose primary API is the cost, all twelve models are specified by four composable cost functions, and the training loop, log-Jacobian, and reverse-ODE sampler are shared automatically.<n>We additionally propose DI-Flow, a novel cost functional to encourage mode coverage, and provide learning-based solvers that substantially outperform neural training on MFG-dynamics rows.
• Score: 9.305417960678357
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\mathcal{I}$ 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.

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