Mean-Field Games Unify Generative Modeling Frameworks

Generative modeling, a rapidly evolving field in AI, encompasses a diverse array of models, each with its own theoretical underpinnings and practical applications. This paper introduces Mean-Field Games (MFGs) as a powerful, unifying theoretical lens through which to view continuous-time generative modeling. The authors demonstrate that a single cost tuple can recover twelve well-known generative models, including Continuous Normalizing Flows, OT-Flow, Score-based Models, and Schrödinger Bridges, as specific instances of one variational problem. The research addresses two previously unexplored aspects within this unified space: the interaction term, often set to zero in existing models, and the application of rich MFG solvers to generative modeling. To facilitate exploration, they developed MFGLab, an open-source PyTorch library. This library allows users to specify all twelve models using just four composable cost functions, with a shared training loop, log-Jacobian, and reverse-ODE sampler, significantly streamlining development. Furthermore, the paper proposes DI-Flow, a novel cost design that incorporates a differentiable entropy functional to encourage better mode coverage in generated samples. Experiments on two 2-D benchmarks confirm that the unified API maintains performance comparable to hand-coded implementations. Additionally, learning-based MFG solvers are shown to substantially outperform neural training methods on stochastic-dynamics rows, highlighting the potential of this new framework.