# A Unifying View of Variational Generative Wasserstein Flows

arXiv: https://arxiv.org/abs/2605.31369 · HTML: https://mlsanity.com/paper/2605.31369/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 103 references that are in the map.
- First posted on arXiv 29 May 2026.

## Builds on (most cited first, 7 of 7)

- [Generative Modeling via Drifting](https://mlsanity.com/paper/2602.04770/) (2026)
- [Statistical optimal transport](https://mlsanity.com/paper/2407.18163/) (2024)
- [The Elements of Differentiable Programming](https://mlsanity.com/paper/2403.14606/) (2024)
- [GAN and VAE from an Optimal Transport Point of View](https://mlsanity.com/paper/1706.01807/) (2017)
- [Proximal optimal transport divergences](https://mlsanity.com/paper/2505.12097/) (2025)
- [Learning Monge maps with constrained drifting models](https://mlsanity.com/paper/2603.25182/) (2026)
- [CKGAN: Training Generative Adversarial Networks Using Characteristic Kernel Integral Probability Metrics](https://mlsanity.com/paper/2504.05945/) (2025)

## Built on by (most cited first, 2 of 2)

- [Three-Body Scattering for Generative Modeling](https://mlsanity.com/paper/2607.18198/) (2026)
- [One-Step Generative Modeling via Unbalanced Optimal Transport](https://mlsanity.com/paper/2609.32708/) (2026)

## Abstract (arXiv)

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.