# Coulomb GANs: Provably Optimal Nash Equilibria via Potential Fields

arXiv: https://arxiv.org/abs/1708.08819 · HTML: https://mlsanity.com/paper/1708.08819/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Aug 2017.

## Built on by (most cited first, 20 of 20)

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- [Interpretable ODE-style Generative Diffusion Model via Force Field Construction](https://mlsanity.com/paper/2303.08063/) (2023)
- [Local Convergence of Gradient Descent-Ascent for Training Generative Adversarial Networks](https://mlsanity.com/paper/2305.08277/) (2023)
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## Abstract (arXiv)

Generative adversarial networks (GANs) evolved into one of the most successful unsupervised techniques for generating realistic images. Even though it has recently been shown that GAN training converges, GAN models often end up in local Nash equilibria that are associated with mode collapse or otherwise fail to model the target distribution. We introduce Coulomb GANs, which pose the GAN learning problem as a potential field of charged particles, where generated samples are attracted to training set samples but repel each other. The discriminator learns a potential field while the generator decreases the energy by moving its samples along the vector (force) field determined by the gradient of the potential field. Through decreasing the energy, the GAN model learns to generate samples according to the whole target distribution and does not only cover some of its modes. We prove that Coulomb GANs possess only one Nash equilibrium which is optimal in the sense that the model distribution equals the target distribution. We show the efficacy of Coulomb GANs on a variety of image datasets. On LSUN and celebA, Coulomb GANs set a new state of the art and produce a previously unseen variety of different samples.