# Wasserstein Divergence for GANs

arXiv: https://arxiv.org/abs/1712.01026 · HTML: https://mlsanity.com/paper/1712.01026/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Dec 2017.

## Built on by (most cited first, 22 of 22)

- [Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmark](https://mlsanity.com/paper/2106.01954/) (2021)
- [Attentive Eraser: Unleashing Diffusion Model's Object Removal Potential via Self-Attention Redirection Guidance](https://mlsanity.com/paper/2412.12974/) (2024)
- [Imitation Learning for Human Pose Prediction](https://mlsanity.com/paper/1909.03449/) (2019)
- [On amortizing convex conjugates for optimal transport](https://mlsanity.com/paper/2210.12153/) (2022)
- [Gradient Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/2109.02235/) (2021)
- [Adversarial Score Distillation: When score distillation meets GAN](https://mlsanity.com/paper/2312.00739/) (2023)
- [Generative Flows with Invertible Attentions](https://mlsanity.com/paper/2106.03959/) (2021)
- [AQ-GT: a Temporally Aligned and Quantized GRU-Transformer for Co-Speech Gesture Synthesis](https://mlsanity.com/paper/2305.01241/) (2023)
- [Warfare:Breaking the Watermark Protection of AI-Generated Content](https://mlsanity.com/paper/2310.07726/) (2023)
- [Bundle Networks: Fiber Bundles, Local Trivializations, and a Generative Approach to Exploring Many-to-one Maps](https://mlsanity.com/paper/2110.06983/) (2021)
- [Mandarin Singing Voice Synthesis with Denoising Diffusion Probabilistic Wasserstein GAN](https://mlsanity.com/paper/2209.10446/) (2022)
- [Monotone Generative Modeling via a Gromov-Monge Embedding](https://mlsanity.com/paper/2311.01375/) (2023)
- [Time-domain Speech Enhancement with Generative Adversarial Learning](https://mlsanity.com/paper/2103.16149/) (2021)
- [Manifold-preserved GANs](https://mlsanity.com/paper/2109.08955/) (2021)
- [On Deep Learning in Password Guessing, a Survey](https://mlsanity.com/paper/2208.10413/) (2022)
- [VFLGAN: Vertical Federated Learning-based Generative Adversarial Network for Vertically Partitioned Data Publication](https://mlsanity.com/paper/2404.09722/) (2024)
- [Measuring Time-Series Dataset Similarity using Wasserstein Distance](https://mlsanity.com/paper/2507.22189/) (2025)
- [Inference-InfoGAN: Inference Independence via Embedding Orthogonal Basis Expansion](https://mlsanity.com/paper/2110.00788/) (2021)
- [Fair mapping](https://mlsanity.com/paper/2209.00617/) (2022)
- [On Unsupervised Image-to-image translation and GAN stability](https://mlsanity.com/paper/2403.09646/) (2023)
- [Bridging GANs and Bayesian Neural Networks via Partial Stochasticity](https://mlsanity.com/paper/2507.00651/) (2025)
- [Conveying Meaning through Gestures: An Investigation into Semantic Co-Speech Gesture Generation](https://mlsanity.com/paper/2510.17599/) (2025)

## Abstract (arXiv)

In many domains of computer vision, generative adversarial networks (GANs) have achieved great success, among which the family of Wasserstein GANs (WGANs) is considered to be state-of-the-art due to the theoretical contributions and competitive qualitative performance. However, it is very challenging to approximate the k-Lipschitz constraint required by the Wasserstein-1 metric~(W-met). In this paper, we propose a novel Wasserstein divergence~(W-div), which is a relaxed version of W-met and does not require the k-Lipschitz constraint. As a concrete application, we introduce a Wasserstein divergence objective for GANs~(WGAN-div), which can faithfully approximate W-div through optimization. Under various settings, including progressive growing training, we demonstrate the stability of the proposed WGAN-div owing to its theoretical and practical advantages over WGANs. Also, we study the quantitative and visual performance of WGAN-div on standard image synthesis benchmarks of computer vision, showing the superior performance of WGAN-div compared to the state-of-the-art methods.