# Improving GANs Using Optimal Transport

arXiv: https://arxiv.org/abs/1803.05573 · HTML: https://mlsanity.com/paper/1803.05573/

## Key facts

- Cited by 123 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2018.

## Built on by (most cited first, 30 of 123)

- [Cross-Modal Contrastive Learning for Text-to-Image Generation](https://mlsanity.com/paper/2101.04702/) (2021)
- [SE(3)-Stochastic Flow Matching for Protein Backbone Generation](https://mlsanity.com/paper/2310.02391/) (2023)
- [Proximal Optimal Transport Modeling of Population Dynamics](https://mlsanity.com/paper/2106.06345/) (2021)
- [Ambiguous Medical Image Segmentation using Diffusion Models](https://mlsanity.com/paper/2304.04745/) (2023)
- [Simulation-free Schr"odinger bridges via score and flow matching](https://mlsanity.com/paper/2307.03672/) (2023)
- [Minibatch optimal transport distances; analysis and applications](https://mlsanity.com/paper/2101.01792/) (2021)
- [PLOT: Prompt Learning with Optimal Transport for Vision-Language Models](https://mlsanity.com/paper/2210.01253/) (2022)
- [Generative Multiplane Images: Making a 2D GAN 3D-Aware](https://mlsanity.com/paper/2207.10642/) (2022)
- [Don't Generate Me: Training Differentially Private Generative Models with Sinkhorn Divergence](https://mlsanity.com/paper/2111.01177/) (2021)
- [Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projections](https://mlsanity.com/paper/2107.01718/) (2021)
- [Unbalanced Optimal Transport, from Theory to Numerics](https://mlsanity.com/paper/2211.08775/) (2022)
- [Effective Neural Topic Modeling with Embedding Clustering Regularization](https://mlsanity.com/paper/2306.04217/) (2023)
- [Improving Mini-batch Optimal Transport via Partial Transportation](https://mlsanity.com/paper/2108.09645/) (2021)
- [SoK: Privacy-Preserving Data Synthesis](https://mlsanity.com/paper/2307.02106/) (2023)
- [Data Efficient Language-supervised Zero-shot Recognition with Optimal Transport Distillation](https://mlsanity.com/paper/2112.09445/) (2021)
- [A Survey on Optimal Transport for Machine Learning: Theory and Applications](https://mlsanity.com/paper/2106.01963/) (2021)
- [FASTopic: Pretrained Transformer is a Fast, Adaptive, Stable, and Transferable Topic Model](https://mlsanity.com/paper/2405.17978/) (2024)
- [The Monge Gap: A Regularizer to Learn All Transport Maps](https://mlsanity.com/paper/2302.04953/) (2023)
- [Imitation Learning with Sinkhorn Distances](https://mlsanity.com/paper/2008.09167/) (2020)
- [A Unified Framework for Implicit Sinkhorn Differentiation](https://mlsanity.com/paper/2205.06688/) (2022)
- [AWT: Transferring Vision-Language Models via Augmentation, Weighting, and Transportation](https://mlsanity.com/paper/2407.04603/) (2024)
- [Distributional Diffusion Models with Scoring Rules](https://mlsanity.com/paper/2502.02483/) (2025)
- [A Survey on Training Challenges in Generative Adversarial Networks for Biomedical Image Analysis](https://mlsanity.com/paper/2201.07646/) (2022)
- [Sinkhorn-Drifting Generative Models](https://mlsanity.com/paper/2603.12366/) (2026)
- [Hierarchical Sliced Wasserstein Distance](https://mlsanity.com/paper/2209.13570/) (2022)
- [Quasi-Monte Carlo for 3D Sliced Wasserstein](https://mlsanity.com/paper/2309.11713/) (2023)
- [Optimal transport map estimation in general function spaces](https://mlsanity.com/paper/2212.03722/) (2022)
- [Sampling via Gradient Flows in the Space of Probability Measures](https://mlsanity.com/paper/2310.03597/) (2023)
- [Tyche: Stochastic In-Context Learning for Medical Image Segmentation](https://mlsanity.com/paper/2401.13650/) (2024)
- [Generative Drifting is Secretly Score Matching: a Spectral and Variational Perspective](https://mlsanity.com/paper/2603.09936/) (2026)

## Abstract (arXiv)

We present Optimal Transport GAN (OT-GAN), a variant of generative adversarial nets minimizing a new metric measuring the distance between the generator distribution and the data distribution. This metric, which we call mini-batch energy distance, combines optimal transport in primal form with an energy distance defined in an adversarially learned feature space, resulting in a highly discriminative distance function with unbiased mini-batch gradients. Experimentally we show OT-GAN to be highly stable when trained with large mini-batches, and we present state-of-the-art results on several popular benchmark problems for image generation.