# Wasserstein Variational Inference

arXiv: https://arxiv.org/abs/1805.11284 · HTML: https://mlsanity.com/paper/1805.11284/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2018.

## Built on by (most cited first, 17 of 17)

- [A Survey on Optimal Transport for Machine Learning: Theory and Applications](https://mlsanity.com/paper/2106.01963/) (2021)
- [Wasserstein Unsupervised Reinforcement Learning](https://mlsanity.com/paper/2110.07940/) (2021)
- [f-GAIL: Learning f-Divergence for Generative Adversarial Imitation Learning](https://mlsanity.com/paper/2010.01207/) (2020)
- [Sliced Wasserstein Variational Inference](https://mlsanity.com/paper/2207.13177/) (2022)
- [On the Convergence of Coordinate Ascent Variational Inference](https://mlsanity.com/paper/2306.01122/) (2023)
- [Gromov-Wasserstein Autoencoders](https://mlsanity.com/paper/2209.07007/) (2022)
- [Bayesian brains and the R'enyi divergence](https://mlsanity.com/paper/2107.05438/) (2021)
- [Evaluating Sensitivity to the Stick-Breaking Prior in Bayesian Nonparametrics](https://mlsanity.com/paper/2107.03584/) (2021)
- [Hyperbolic Geometry in Computer Vision: A Survey](https://mlsanity.com/paper/2304.10764/) (2023)
- [Deep Generative Models: Complexity, Dimensionality, and Approximation](https://mlsanity.com/paper/2504.00820/) (2025)
- [Bayesian Distributional Policy Gradients](https://mlsanity.com/paper/2103.11265/) (2021)
- [A Primer on Variational Inference for Physics-Informed Deep Generative Modelling](https://mlsanity.com/paper/2409.06560/) (2024)
- [Bayesian Experimental Design for Model Discrepancy Calibration: An Auto-Differentiable Ensemble Kalman Inversion Approach](https://mlsanity.com/paper/2504.20319/) (2025)
- [Parameter Estimation in DAGs from Incomplete Data via Optimal Transport](https://mlsanity.com/paper/2305.15927/) (2023)
- [Nonlinear Kalman Filtering with Reparametrization Gradients](https://mlsanity.com/paper/2303.04450/) (2023)
- [Streaming Sliced Optimal Transport](https://mlsanity.com/paper/2505.06835/) (2025)
- [Bayesian Experimental Design for Model Discrepancy Calibration: A Rivalry between Kullback--Leibler Divergence and Wasserstein Distance](https://mlsanity.com/paper/2601.16425/) (2026)

## Abstract (arXiv)

This paper introduces Wasserstein variational inference, a new form of approximate Bayesian inference based on optimal transport theory. Wasserstein variational inference uses a new family of divergences that includes both f-divergences and the Wasserstein distance as special cases. The gradients of the Wasserstein variational loss are obtained by backpropagating through the Sinkhorn iterations. This technique results in a very stable likelihood-free training method that can be used with implicit distributions and probabilistic programs. Using the Wasserstein variational inference framework, we introduce several new forms of autoencoders and test their robustness and performance against existing variational autoencoding techniques.