# Stabilizing GANs' Training with Brownian Motion Controller

arXiv: https://arxiv.org/abs/2306.10468 · HTML: https://mlsanity.com/paper/2306.10468/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 50 references that are in the map.
- First posted on arXiv 18 Jun 2023.

## Builds on (most cited first, 23 of 23)

- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [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)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [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)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [MMD GAN: Towards Deeper Understanding of Moment Matching Network](https://mlsanity.com/paper/1705.08584/) (2017)
- [Energy-based Generative Adversarial Network](https://mlsanity.com/paper/1609.03126/) (2016)
- [PacGAN: The power of two samples in generative adversarial networks](https://mlsanity.com/paper/1712.04086/) (2017)
- [Disentangling factors of variation in deep representations using adversarial training](https://mlsanity.com/paper/1611.03383/) (2016)
- [Amortised MAP Inference for Image Super-resolution](https://mlsanity.com/paper/1610.04490/) (2016)
- [Generative Multi-Adversarial Networks](https://mlsanity.com/paper/1611.01673/) (2016)
- [Many Paths to Equilibrium: GANs Do Not Need to Decrease a Divergence At Every Step](https://mlsanity.com/paper/1710.08446/) (2017)
- [Improving GAN Equilibrium by Raising Spatial Awareness](https://mlsanity.com/paper/2112.00718/) (2021)
- [Understanding and Stabilizing GANs' Training Dynamics with Control Theory](https://mlsanity.com/paper/1909.13188/) (2019)

## Built on by (most cited first, 4 of 4)

- [Monotone Generative Modeling via a Gromov-Monge Embedding](https://mlsanity.com/paper/2311.01375/) (2023)
- [C-GAIL: Stabilizing Generative Adversarial Imitation Learning with Control Theory](https://mlsanity.com/paper/2402.16349/) (2024)
- [Performative Drift Resistant Classification Using Generative Domain Adversarial Networks](https://mlsanity.com/paper/2504.01135/) (2025)
- [Controlled-Minimax: Stabilizing Adversarial Optimization via Control Theory](https://mlsanity.com/paper/2610.12915/) (2026)

## Abstract (arXiv)

The training process of generative adversarial networks (GANs) is unstable and does not converge globally. In this paper, we examine the stability of GANs from the perspective of control theory and propose a universal higher-order noise-based controller called Brownian Motion Controller (BMC). Starting with the prototypical case of Dirac-GANs, we design a BMC to retrieve precisely the same but reachable optimal equilibrium. We theoretically prove that the training process of DiracGANs-BMC is globally exponential stable and derive bounds on the rate of convergence. Then we extend our BMC to normal GANs and provide implementation instructions on GANs-BMC. Our experiments show that our GANs-BMC effectively stabilizes GANs' training under StyleGANv2-ada frameworks with a faster rate of convergence, a smaller range of oscillation, and better performance in terms of FID score.