# Wasserstein Proximal of GANs

arXiv: https://arxiv.org/abs/2102.06862 · HTML: https://mlsanity.com/paper/2102.06862/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 47 references that are in the map.
- First posted on arXiv 13 Feb 2021.

## Builds on (most cited first, 15 of 15)

- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Wasserstein GAN](https://mlsanity.com/paper/1701.07875/) (2017)
- [A Mean Field View of the Landscape of Two-Layers Neural Networks](https://mlsanity.com/paper/1804.06561/) (2018)
- [Learning with a Wasserstein Loss](https://mlsanity.com/paper/1506.05439/) (2015)
- [Stein Variational Gradient Descent as Gradient Flow](https://mlsanity.com/paper/1704.07520/) (2017)
- [On the regularization of Wasserstein GANs](https://mlsanity.com/paper/1709.08894/) (2017)
- [Banach Wasserstein GAN](https://mlsanity.com/paper/1806.06621/) (2018)
- [Riemannian metrics for neural networks I: feedforward networks](https://mlsanity.com/paper/1303.0818/) (2013)
- [Natural gradient via optimal transport](https://mlsanity.com/paper/1803.07033/) (2018)
- [Approximate inference with Wasserstein gradient flows](https://mlsanity.com/paper/1806.04542/) (2018)
- [Proximal Recursion for Solving the Fokker-Planck Equation](https://mlsanity.com/paper/1809.10844/) (2018)

## Built on by (most cited first, 15 of 15)

- [Optimizing Functionals on the Space of Probabilities with Input Convex Neural Networks](https://mlsanity.com/paper/2106.00774/) (2021)
- [Variational Wasserstein gradient flow](https://mlsanity.com/paper/2112.02424/) (2021)
- [Scalable Wasserstein Gradient Flow for Generative Modeling through Unbalanced Optimal Transport](https://mlsanity.com/paper/2402.05443/) (2024)
- [Efficient Gradient Flows in Sliced-Wasserstein Space](https://mlsanity.com/paper/2110.10972/) (2021)
- [Particle-based Variational Inference with Preconditioned Functional Gradient Flow](https://mlsanity.com/paper/2211.13954/) (2022)
- [Wassmap: Wasserstein Isometric Mapping for Image Manifold Learning](https://mlsanity.com/paper/2204.06645/) (2022)
- [Wasserstein proximal operators describe score-based generative models and resolve memorization](https://mlsanity.com/paper/2402.06162/) (2024)
- [Achieving High Accuracy with PINNs via Energy Natural Gradients](https://mlsanity.com/paper/2302.13163/) (2023)
- [Provably convergent quasistatic dynamics for mean-field two-player zero-sum games](https://mlsanity.com/paper/2202.10947/) (2022)
- [Optimal Neural Network Approximation of Wasserstein Gradient Direction via Convex Optimization](https://mlsanity.com/paper/2205.13098/) (2022)
- [Neural Wasserstein Gradient Flows for Maximum Mean Discrepancies with Riesz Kernels](https://mlsanity.com/paper/2301.11624/) (2023)
- [Efficient Natural Gradient Descent Methods for Large-Scale PDE-Based Optimization Problems](https://mlsanity.com/paper/2202.06236/) (2022)
- [Adaptive Annealed Importance Sampling with Constant Rate Progress](https://mlsanity.com/paper/2306.15283/) (2023)
- [Neural FIM for learning Fisher Information Metrics from point cloud data](https://mlsanity.com/paper/2306.06062/) (2023)
- [Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers](https://mlsanity.com/paper/2607.22004/) (2026)

## Abstract (arXiv)

We introduce a new method for training generative adversarial networks by applying the Wasserstein-2 metric proximal on the generators. The approach is based on Wasserstein information geometry. It defines a parametrization invariant natural gradient by pulling back optimal transport structures from probability space to parameter space. We obtain easy-to-implement iterative regularizers for the parameter updates of implicit deep generative models. Our experiments demonstrate that this method improves the speed and stability of training in terms of wall-clock time and Fr'echet Inception Distance.