用统一框架重写12种生成模型，让它们共享代码与训练流程。
All in One: Generative Modeling as Mean-Field Game Design
- 将12种生成模型统一为一个变分问题，仅通过四个可组合代价函数定义。
- 提出DI-Flow新设计，用可微熵函数提升模式覆盖能力，效果优于传统方法。
- 开源工具库支持自动共享训练循环与反向ODE采样，适配研究者快速实验。
平均场博弈（MFG）为连续时间生成建模提供了一个统一视角：一个代价元组可恢复十二种主流模型——连续归一化流、OT-Flow、基于得分的模型、薛定谔桥等——作为同一变分问题的特例。然而该框架仍有两个维度未被探索：交互项 $\mathcal{I}$ 在多数现有模型中设为零，且丰富的MFG求解器尚未应用于生成建模。本文通过开发MFGLab——一个基于PyTorch的开源库，其核心接口为代价元组——解决上述空白：所有十二种模型均由四个可组合的代价函数指定，训练循环、对数雅可比行列式及反向常微分方程采样器均自动共享。此外，我们提出DI-Flow，一种利用可微熵泛函鼓励模式覆盖的新代价设计，并提供基于学习的MFG求解器，在随机动力学情形下显著优于神经网络训练。在两个二维基准测试中，统一接口与手写实现相比无损失。
原文摘要 · Abstract (English)
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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