# Banach Wasserstein GAN

arXiv: https://arxiv.org/abs/1806.06621 · HTML: https://mlsanity.com/paper/1806.06621/

## Key facts

- Cited by 56 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jun 2018.

## Built on by (most cited first, 30 of 56)

- [Deep Unsupervised Domain Adaptation: A Review of Recent Advances and Perspectives](https://mlsanity.com/paper/2208.07422/) (2022)
- [Generative Adversarial Neural Operators](https://mlsanity.com/paper/2205.03017/) (2022)
- [Nearly Optimal VC-Dimension and Pseudo-Dimension Bounds for Deep Neural Network Derivatives](https://mlsanity.com/paper/2305.08466/) (2023)
- [SOS: Score-based Oversampling for Tabular Data](https://mlsanity.com/paper/2206.08555/) (2022)
- [Invertible Tabular GANs: Killing Two Birds with OneStone for Tabular Data Synthesis](https://mlsanity.com/paper/2202.03636/) (2022)
- [EHRDiff: Exploring Realistic EHR Synthesis with Diffusion Models](https://mlsanity.com/paper/2303.05656/) (2023)
- [Continuous-Multiple Image Outpainting in One-Step via Positional Query and A Diffusion-based Approach](https://mlsanity.com/paper/2401.15652/) (2024)
- [Wasserstein Proximal of GANs](https://mlsanity.com/paper/2102.06862/) (2021)
- [Deeper or Wider: A Perspective from Optimal Generalization Error with Sobolev Loss](https://mlsanity.com/paper/2402.00152/) (2024)
- [Self-Diagnosing GAN: Diagnosing Underrepresented Samples in Generative Adversarial Networks](https://mlsanity.com/paper/2102.12033/) (2021)
- [Latent Diffusion Model-Enabled Low-Latency Semantic Communication in the Presence of Semantic Ambiguities and Wireless Channel Noises](https://mlsanity.com/paper/2406.06644/) (2024)
- [Graph Edit Distance with General Costs Using Neural Set Divergence](https://mlsanity.com/paper/2409.17687/) (2024)
- [Robust W-GAN-Based Estimation Under Wasserstein Contamination](https://mlsanity.com/paper/2101.07969/) (2021)
- [HIERAMP: Coarse-to-Fine Autoregressive Amplification for Generative Dataset Distillation](https://mlsanity.com/paper/2603.06932/) (2026)
- [Adversarial Constrained Bidding via Minimax Regret Optimization with Causality-Aware Reinforcement Learning](https://mlsanity.com/paper/2306.07106/) (2023)
- [Moreau-Yosida f-divergences](https://mlsanity.com/paper/2102.13416/) (2021)
- [AnyECG: Foundational Models for Multitask Cardiac Analysis in Real-World Settings](https://mlsanity.com/paper/2411.17711/) (2024)
- [Robust Distribution Alignment for Industrial Anomaly Detection under Distribution Shift](https://mlsanity.com/paper/2503.14910/) (2025)
- [Dissipative Gradient Descent Ascent Method: A Control Theory Inspired Algorithm for Min-max Optimization](https://mlsanity.com/paper/2403.09090/) (2024)
- [Straighten Viscous Rectified Flow via Noise Optimization](https://mlsanity.com/paper/2507.10218/) (2025)
- [About exchanging expectation and supremum for conditional Wasserstein GANs](https://mlsanity.com/paper/2103.13906/) (2021)
- [Generative Adversarial Networks for Image Augmentation in Agriculture: A Systematic Review](https://mlsanity.com/paper/2204.04707/) (2022)
- [Assessing Domain Gap for Continual Domain Adaptation in Object Detection](https://mlsanity.com/paper/2302.10396/) (2023)
- [Adaptive Consensus Optimization Method for GANs](https://mlsanity.com/paper/2304.10317/) (2023)
- [Hoeffding's Inequality for Markov Chains under Generalized Concentrability Condition](https://mlsanity.com/paper/2310.02941/) (2023)
- [Style-Adaptive Detection Transformer for Single-Source Domain Generalized Object Detection](https://mlsanity.com/paper/2504.20498/) (2025)
- [Refiner: Data Refining against Gradient Leakage Attacks in Federated Learning](https://mlsanity.com/paper/2212.02042/) (2022)
- [Meta-Learning Enabled Score-Based Generative Model for 1.5T-Like Image Reconstruction from 0.5T MRI](https://mlsanity.com/paper/2305.02509/) (2023)
- [Convex Latent-Optimized Adversarial Regularizers for Imaging Inverse Problems](https://mlsanity.com/paper/2309.09250/) (2023)
- [Socialized Learning: A Survey of the Paradigm Shift for Edge Intelligence in Networked Systems](https://mlsanity.com/paper/2404.13348/) (2024)

## Abstract (arXiv)

Wasserstein Generative Adversarial Networks (WGANs) can be used to generate realistic samples from complicated image distributions. The Wasserstein metric used in WGANs is based on a notion of distance between individual images, which induces a notion of distance between probability distributions of images. So far the community has considered ℓ2 as the underlying distance. We generalize the theory of WGAN with gradient penalty to Banach spaces, allowing practitioners to select the features to emphasize in the generator. We further discuss the effect of some particular choices of underlying norms, focusing on Sobolev norms. Finally, we demonstrate a boost in performance for an appropriate choice of norm on CIFAR-10 and CelebA.