AI 中文总结
研究旨在填补平均场博弈在生成建模中未探索的维度空白，通过 MFGLab 库统一十二个模型的 API，提出 DI - Flow 成本设计及基于学习的 MFG 求解器，实验验证统一 API 无损，提升了生成建模性能。
AI 中文摘要
平均场博弈（MFGs）为连续时间生成建模提供了一个统一视角：一个成本元组将十二个著名模型——连续归一化流、OT 流、基于得分的模型、薛定谔桥等——作为一个变分问题的特殊情况。然而，该空间的两个维度仍未被探索：许多现有模型中交互项$\mathcal{I}$设为零，且丰富的 MFG 求解器家族从未应用于生成建模。我们用 MFGLab 开源 PyTorch 库填补这两个空白，其主要 API 是成本元组。所有十二个模型由四个可组合成本函数指定，训练循环、对数雅可比和反向 ODE 采样器自动共享。我们还提出 DI - Flow，一种使用可微熵泛函鼓励模式覆盖的新型成本设计，并提供在随机动力学行上显著优于神经训练的基于学习的 MFG 求解器。在两个二维基准上的实验证实统一 API 相对于手工编码实现无损。
英文摘要
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.
