# Discriminator optimal transport

arXiv: https://arxiv.org/abs/1910.06832 · HTML: https://mlsanity.com/paper/1910.06832/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2019.

## Built on by (most cited first, 25 of 25)

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- [Kantorovich Strikes Back! Wasserstein GANs are not Optimal Transport?](https://mlsanity.com/paper/2206.07767/) (2022)
- [Complexity Matters: Rethinking the Latent Space for Generative Modeling](https://mlsanity.com/paper/2307.08283/) (2023)
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- [Learning Probabilistic Models from Generator Latent Spaces with Hat EBM](https://mlsanity.com/paper/2210.16486/) (2022)
- [BIGRoC: Boosting Image Generation via a Robust Classifier](https://mlsanity.com/paper/2108.03702/) (2021)
- [Variational Schr"odinger Diffusion Models](https://mlsanity.com/paper/2405.04795/) (2024)
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- [Optimal Budgeted Rejection Sampling for Generative Models](https://mlsanity.com/paper/2311.00460/) (2023)
- [Efficient Generative Modeling beyond Memoryless Diffusion via Adjoint Schr"odinger Bridge Matching](https://mlsanity.com/paper/2602.15396/) (2026)
- [Controlling the Fidelity and Diversity of Deep Generative Models via Pseudo Density](https://mlsanity.com/paper/2407.08659/) (2024)
- [Learning High-Dimensional Distributions with Latent Neural Fokker-Planck Kernels](https://mlsanity.com/paper/2105.04538/) (2021)
- [Reparameterized Sampling for Generative Adversarial Networks](https://mlsanity.com/paper/2107.00352/) (2021)
- [A new method for determining Wasserstein 1 optimal transport maps from Kantorovich potentials, with deep learning applications](https://mlsanity.com/paper/2211.00820/) (2022)
- [Structural Adversarial Objectives for Self-Supervised Representation Learning](https://mlsanity.com/paper/2310.00357/) (2023)
- [Deep Generative Quantile Bayes](https://mlsanity.com/paper/2410.08378/) (2024)
- [Sliced L2 Distance for Colour Grading](https://mlsanity.com/paper/2102.09297/) (2021)
- [A Generic Approach for Enhancing GANs by Regularized Latent Optimization](https://mlsanity.com/paper/2112.03502/) (2021)
- [Multisymplectic Formulation of Deep Learning Using Mean--Field Type Control and Nonlinear Stability of Training Algorithm](https://mlsanity.com/paper/2207.12242/) (2022)

## Abstract (arXiv)

Within a broad class of generative adversarial networks, we show that discriminator optimization process increases a lower bound of the dual cost function for the Wasserstein distance between the target distribution p and the generator distribution pG. It implies that the trained discriminator can approximate optimal transport (OT) from pG to p.Based on some experiments and a bit of OT theory, we propose a discriminator optimal transport (DOT) scheme to improve generated images. We show that it improves inception score and FID calculated by un-conditional GAN trained by CIFAR-10, STL-10 and a public pre-trained model of conditional GAN by ImageNet.