Data to 7 Oct 2026

Which Training Methods for GANs do actually Converge?

arXiv 1801.04406 ↗First posted 13 Jan 2018cs.LG cs.AI cs.GTcited by 672

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Cited by 75 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Recent work has shown local convergence of GAN training for absolutely continuous data and generator distributions. In this paper, we show that the requirement of absolute continuity is necessary: we describe a simple yet prototypical counterexample showing that in the more realistic case of distributions that are not absolutely continuous, unregularized GAN training is not always convergent. Furthermore, we discuss regularization strategies that were recently proposed to stabilize GAN training. Our analysis shows that GAN training with instance noise or zero-centered gradient penalties converges. On the other hand, we show that Wasserstein-GANs and WGAN-GP with a finite number of discriminator updates per generator update do not always converge to the equilibrium point. We discuss these results, leading us to a new explanation for the stability problems of GAN training. Based on our analysis, we extend our convergence results to more general GANs and prove local convergence for simplified gradient penalties even if the generator and data distribution lie on lower dimensional manifolds. We find these penalties to work well in practice and use them to learn high-resolution generative image models for a variety of datasets with little hyperparameter tuning.

Key facts. Cited by 672 papers in the map (data through 7 Oct 2026). First posted on arXiv 13 Jan 2018.

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Citing papers per year: 2018: 1; 2019: 0; 2020: 3; 2021: 163; 2022: 153; 2023: 140; 2024: 87; 2025: 66; 2026: 59.

672 papers.

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2021Tackling the Generative Learning Trilemma with Denoising Diffusion GANscited by 515
2023Scaling up GANs for Text-to-Image Synthesiscited by 492
2022StyleGAN-XL: Scaling StyleGAN to Large Diverse Datasetscited by 489

38 more

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