统一了生成模型的变分推导框架，揭示其与最优传输的深层联系。
A Unifying View of Variational Generative Wasserstein Flows
- 基于JKO格式构建统一生成框架，覆盖多种散度优化方法。
- 证明现有算法可视为参数化JKO方案的特例，建立理论等价性。
- 拓展至MMD等度量，揭示生成对抗网络的内在机制，适合理论研究者。
许多现代生成模型可视为最小化概率分布之间的差异，但依赖不同的算法与几何原理。Wasserstein梯度流为分布优化提供了连续时间形式，可通过Jordan-Kinderlehrer-Otto（JKO）方案进行隐式离散化近似。本文提出基于Wasserstein梯度流的统一理论框架，称为生成Wasserstein流（GWF）。我们表明，一大类现有方法可作为 $f$-散度目标下的参数化JKO方案实例，并建立多个近期提出算法间的等价关系。我们将该框架扩展至积分概率度量与平方最大均值差异（squared MMD），推导出新的基于JKO的生成算法，并阐明其与生成对抗网络（GANs）的联系。我们对多种目标下JKO正则化的影响进行了实证研究。最后，分析了参数化Wasserstein流，其中动力学受限于参数映射诱导的分布。
原文摘要 · Abstract (English)
Many modern generative models can be viewed as minimizing divergences between probability distributions, yet they rely on different algorithmic and geometric principles. Wasserstein gradient flows provide a continuous-time formulation for optimizing over distributions, and can be approximated through their implicit discretization via the Jordan-Kinderlehrer-Otto (JKO) scheme. In this work, we present a unified theoretical framework for generative modeling based on Wasserstein gradient flows, which we refer to as Generative Wasserstein Flows (GWF). We show that a broad class of existing methods can be derived as instances of parametric JKO schemes for $f$-divergence objectives, and we establish equivalences between several recently proposed algorithms. We extend this framework beyond f-divergence to Integral Probability Metrics and squared Maximum Mean Discrepancy, deriving new JKO-based generative algorithms, and clarifying their connections with GANs. We study empirically the impact of the JKO regularization for a wide set of objectives. Finally, we analyze parametric Wasserstein flows, where the dynamics are restricted to distributions induced by parametrized maps.
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