# Smoothness and Stability in GANs

arXiv: https://arxiv.org/abs/2002.04185 · HTML: https://mlsanity.com/paper/2002.04185/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2020.

## Built on by (most cited first, 27 of 27)

- [A Closer Look at Smoothness in Domain Adversarial Training](https://mlsanity.com/paper/2206.08213/) (2022)
- [Diffusion Models for Time Series Applications: A Survey](https://mlsanity.com/paper/2305.00624/) (2023)
- [Generative Adversarial Registration for Improved Conditional Deformable Templates](https://mlsanity.com/paper/2105.04349/) (2021)
- [CarveMix: A Simple Data Augmentation Method for Brain Lesion Segmentation](https://mlsanity.com/paper/2108.06883/) (2021)
- [Diagnosing and Fixing Manifold Overfitting in Deep Generative Models](https://mlsanity.com/paper/2204.07172/) (2022)
- [Regular Time-series Generation using SGM](https://mlsanity.com/paper/2301.08518/) (2023)
- [UniGuardian: A Unified Defense for Detecting Prompt Injection, Backdoor Attacks and Adversarial Attacks in Large Language Models](https://mlsanity.com/paper/2502.13141/) (2025)
- [Wasserstein Gradient Flows for Moreau Envelopes of f-Divergences in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2402.04613/) (2024)
- [Manifold Learning Benefits GANs](https://mlsanity.com/paper/2112.12618/) (2021)
- [SAN: Inducing Metrizability of GAN with Discriminative Normalized Linear Layer](https://mlsanity.com/paper/2301.12811/) (2023)
- [Re-using Adversarial Mask Discriminators for Test-time Training under Distribution Shifts](https://mlsanity.com/paper/2108.11926/) (2021)
- [Continuous and Distribution-free Probabilistic Wind Power Forecasting: A Conditional Normalizing Flow Approach](https://mlsanity.com/paper/2206.02433/) (2022)
- [Gromov-Wasserstein Autoencoders](https://mlsanity.com/paper/2209.07007/) (2022)
- [Unknown Domain Inconsistency Minimization for Domain Generalization](https://mlsanity.com/paper/2403.07329/) (2024)
- [Stop Throwing Away Discriminators! Re-using Adversaries for Test-Time Training](https://mlsanity.com/paper/2108.12280/) (2021)
- [Invariant Representations with Stochastically Quantized Neural Networks](https://mlsanity.com/paper/2208.02656/) (2022)
- [TSGM: Regular and Irregular Time-series Generation using Score-based Generative Models](https://mlsanity.com/paper/2511.21335/) (2025)
- [Generalization of GANs and overparameterized models under Lipschitz continuity](https://mlsanity.com/paper/2104.02388/) (2021)
- [CHAIN: Enhancing Generalization in Data-Efficient GANs via lipsCHitz continuity constrAIned Normalization](https://mlsanity.com/paper/2404.00521/) (2024)
- [Sit Back and Relax: Learning to Drive Incrementally in All Weather Conditions](https://mlsanity.com/paper/2305.18953/) (2023)
- [Novel Hybrid Integrated Pix2Pix and WGAN Model with Gradient Penalty for Binary Images Denoising](https://mlsanity.com/paper/2407.11865/) (2024)
- [Unified Perspective on Probability Divergence via Maximum Likelihood Density Ratio Estimation: Bridging KL-Divergence and Integral Probability Metrics](https://mlsanity.com/paper/2201.13127/) (2022)
- [Convergences for Minimax Optimization Problems over Infinite-Dimensional Spaces Towards Stability in Adversarial Training](https://mlsanity.com/paper/2312.00991/) (2023)
- [Nested Annealed Training Scheme for Generative Adversarial Networks](https://mlsanity.com/paper/2501.11318/) (2025)
- [SONA: Learning Conditional, Unconditional, and Mismatching-Aware Discriminator](https://mlsanity.com/paper/2510.04576/) (2025)
- [Effective Series Decomposition and Components Learning for Time Series Generation](https://mlsanity.com/paper/2511.00747/) (2025)
- [Representation-driven Endoscopic Visual Embedding Alignment for Latent Generation](https://mlsanity.com/paper/2608.07176/) (2026)

## Abstract (arXiv)

Generative adversarial networks, or GANs, commonly display unstable behavior during training. In this work, we develop a principled theoretical framework for understanding the stability of various types of GANs. In particular, we derive conditions that guarantee eventual stationarity of the generator when it is trained with gradient descent, conditions that must be satisfied by the divergence that is minimized by the GAN and the generator's architecture. We find that existing GAN variants satisfy some, but not all, of these conditions. Using tools from convex analysis, optimal transport, and reproducing kernels, we construct a GAN that fulfills these conditions simultaneously. In the process, we explain and clarify the need for various existing GAN stabilization techniques, including Lipschitz constraints, gradient penalties, and smooth activation functions.