# Analyzing and Improving Optimal-Transport-based Adversarial Networks

arXiv: https://arxiv.org/abs/2310.02611 · HTML: https://mlsanity.com/paper/2310.02611/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 69 references that are in the map.
- First posted on arXiv 4 Oct 2023.

## Builds on (most cited first, 30 of 53)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [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)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Score-Based Generative Modeling with Critically-Damped Langevin Diffusion](https://mlsanity.com/paper/2112.07068/) (2021)
- [Optimal transport mapping via input convex neural networks](https://mlsanity.com/paper/1908.10962/) (2019)
- [Geometric Dataset Distances via Optimal Transport](https://mlsanity.com/paper/2002.02923/) (2020)
- [Adversarial Latent Autoencoders](https://mlsanity.com/paper/2004.04467/) (2020)
- [StyleSwin: Transformer-based GAN for High-resolution Image Generation](https://mlsanity.com/paper/2112.10762/) (2021)
- [Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measures](https://mlsanity.com/paper/1508.07941/) (2015)
- [Neural Optimal Transport](https://mlsanity.com/paper/2201.12220/) (2022)

## Built on by (most cited first, 8 of 8)

- [Robust Barycenter Estimation using Semi-Unbalanced Neural Optimal Transport](https://mlsanity.com/paper/2410.03974/) (2024)
- [Improving Neural Optimal Transport via Displacement Interpolation](https://mlsanity.com/paper/2410.03783/) (2024)
- [Overcoming Spurious Solutions in Semi-Dual Neural Optimal Transport: A Smoothing Approach for Learning the Optimal Transport Plan](https://mlsanity.com/paper/2502.04583/) (2025)
- [Scalable Simulation-free Entropic Unbalanced Optimal Transport](https://mlsanity.com/paper/2410.02656/) (2024)
- [A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solvers](https://mlsanity.com/paper/2502.01310/) (2025)
- [Unsupervised Point Cloud Completion through Unbalanced Optimal Transport](https://mlsanity.com/paper/2410.02671/) (2024)
- [Conditional Unbalanced Optimal Transport Maps: An Outlier-Robust Framework for Conditional Generative Modeling](https://mlsanity.com/paper/2603.06972/) (2026)
- [UOTIP: Unbalanced Optimal Transport Map for Unpaired Inverse Problems](https://mlsanity.com/paper/2605.21094/) (2026)

## Abstract (arXiv)

Optimal Transport (OT) problem aims to find a transport plan that bridges two distributions while minimizing a given cost function. OT theory has been widely utilized in generative modeling. In the beginning, OT distance has been used as a measure for assessing the distance between data and generated distributions. Recently, OT transport map between data and prior distributions has been utilized as a generative model. These OT-based generative models share a similar adversarial training objective. In this paper, we begin by unifying these OT-based adversarial methods within a single framework. Then, we elucidate the role of each component in training dynamics through a comprehensive analysis of this unified framework. Moreover, we suggest a simple but novel method that improves the previously best-performing OT-based model. Intuitively, our approach conducts a gradual refinement of the generated distribution, progressively aligning it with the data distribution. Our approach achieves a FID score of 2.51 on CIFAR-10 and 5.99 on CelebA-HQ-256, outperforming unified OT-based adversarial approaches.