A Unifying View of Variational Generative Wasserstein Flows

Paul Caucheteux, Clément Bonet, Anna Korba
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:12079-12134, 2026.

Abstract

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 $f$-divergences 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-caucheteux26a, title = {A Unifying View of Variational Generative {W}asserstein Flows}, author = {Caucheteux, Paul and Bonet, Cl\'{e}ment and Korba, Anna}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {12079--12134}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/caucheteux26a/caucheteux26a.pdf}, url = {https://proceedings.mlr.press/v306/caucheteux26a.html}, abstract = {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 $f$-divergences 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.} }
Endnote
%0 Conference Paper %T A Unifying View of Variational Generative Wasserstein Flows %A Paul Caucheteux %A Clément Bonet %A Anna Korba %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-caucheteux26a %I PMLR %P 12079--12134 %U https://proceedings.mlr.press/v306/caucheteux26a.html %V 306 %X 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 $f$-divergences 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.
APA
Caucheteux, P., Bonet, C. & Korba, A.. (2026). A Unifying View of Variational Generative Wasserstein Flows. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:12079-12134 Available from https://proceedings.mlr.press/v306/caucheteux26a.html.

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