# Multi-marginal Wasserstein GAN

arXiv: https://arxiv.org/abs/1911.00888 · HTML: https://mlsanity.com/paper/1911.00888/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Nov 2019.

## Built on by (most cited first, 30 of 32)

- [Video Super-Resolution Transformer](https://mlsanity.com/paper/2106.06847/) (2021)
- [Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmark](https://mlsanity.com/paper/2106.01954/) (2021)
- [On amortizing convex conjugates for optimal transport](https://mlsanity.com/paper/2210.12153/) (2022)
- [Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey](https://mlsanity.com/paper/2305.05080/) (2023)
- [Conditional Denoising Diffusion for Sequential Recommendation](https://mlsanity.com/paper/2304.11433/) (2023)
- [The Multimarginal Optimal Transport Formulation of Adversarial Multiclass Classification](https://mlsanity.com/paper/2204.12676/) (2022)
- [One-Shot Diffusion Mimicker for Handwritten Text Generation](https://mlsanity.com/paper/2409.04004/) (2024)
- [AGTGAN: Unpaired Image Translation for Photographic Ancient Character Generation](https://mlsanity.com/paper/2303.07012/) (2023)
- [Deep Equilibrium Diffusion Restoration with Parallel Sampling](https://mlsanity.com/paper/2311.11600/) (2023)
- [HiPA: Enabling One-Step Text-to-Image Diffusion Models via High-Frequency-Promoting Adaptation](https://mlsanity.com/paper/2311.18158/) (2023)
- [A survey on GANs for computer vision: Recent research, analysis and taxonomy](https://mlsanity.com/paper/2203.11242/) (2022)
- [Unaligned Image-to-Image Translation by Learning to Reweight](https://mlsanity.com/paper/2109.11736/) (2021)
- [An Optimal Transport Approach to Personalized Federated Learning](https://mlsanity.com/paper/2206.02468/) (2022)
- [Robust W-GAN-Based Estimation Under Wasserstein Contamination](https://mlsanity.com/paper/2101.07969/) (2021)
- [AdaXpert: Adapting Neural Architecture for Growing Data](https://mlsanity.com/paper/2107.00254/) (2021)
- [Brain Multigraph Prediction using Topology-Aware Adversarial Graph Neural Network](https://mlsanity.com/paper/2105.02565/) (2021)
- [Unbalanced CO-Optimal Transport](https://mlsanity.com/paper/2205.14923/) (2022)
- [Sliced Multi-Marginal Optimal Transport](https://mlsanity.com/paper/2102.07115/) (2021)
- [AV-GAN: Attention-Based Varifocal Generative Adversarial Network for Uneven Medical Image Translation](https://mlsanity.com/paper/2404.10714/) (2024)
- [How to Train Your Agent to Read and Write](https://mlsanity.com/paper/2101.00916/) (2021)
- [Projected Statistical Methods for Distributional Data on the Real Line with the Wasserstein Metric](https://mlsanity.com/paper/2101.09039/) (2021)
- [Factored couplings in multi-marginal optimal transport via difference of convex programming](https://mlsanity.com/paper/2110.00629/) (2021)
- [Neural Estimation for Scaling Entropic Multimarginal Optimal Transport](https://mlsanity.com/paper/2506.00573/) (2025)
- [Guided Trajectory Optimization with Sparse Scaling for Test-Time Diffusion](https://mlsanity.com/paper/2605.21907/) (2026)
- [DiffuPT: Class Imbalance Mitigation for Glaucoma Detection via Diffusion Based Generation and Model Pretraining](https://mlsanity.com/paper/2412.03629/) (2024)
- [Quantized Adaptive Subgradient Algorithms and Their Applications](https://mlsanity.com/paper/2208.05631/) (2022)
- [Tighter Learning Guarantees on Digital Computers via Concentration of Measure on Finite Spaces](https://mlsanity.com/paper/2402.05576/) (2024)
- [Mean and Variance Estimation Complexity in Arbitrary Distributions via Wasserstein Minimization](https://mlsanity.com/paper/2501.10172/) (2025)
- [Generative Model-Based Feature Attention Module for Video Action Analysis](https://mlsanity.com/paper/2508.13565/) (2025)
- [A Unified Kantorovich Duality for Multimarginal Optimal Transport](https://mlsanity.com/paper/2601.17171/) (2026)

## Abstract (arXiv)

Multiple marginal matching problem aims at learning mappings to match a source domain to multiple target domains and it has attracted great attention in many applications, such as multi-domain image translation. However, addressing this problem has two critical challenges: (i) Measuring the multi-marginal distance among different domains is very intractable; (ii) It is very difficult to exploit cross-domain correlations to match the target domain distributions. In this paper, we propose a novel Multi-marginal Wasserstein GAN (MWGAN) to minimize Wasserstein distance among domains. Specifically, with the help of multi-marginal optimal transport theory, we develop a new adversarial objective function with inner- and inter-domain constraints to exploit cross-domain correlations. Moreover, we theoretically analyze the generalization performance of MWGAN, and empirically evaluate it on the balanced and imbalanced translation tasks. Extensive experiments on toy and real-world datasets demonstrate the effectiveness of MWGAN.