# Non-saturating GAN training as divergence minimization

arXiv: https://arxiv.org/abs/2010.08029 · HTML: https://mlsanity.com/paper/2010.08029/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2020.

## Built on by (most cited first, 9 of 9)

- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [EMDM: Efficient Motion Diffusion Model for Fast and High-Quality Motion Generation](https://mlsanity.com/paper/2312.02256/) (2023)
- [One-step Diffusion Models with f-Divergence Distribution Matching](https://mlsanity.com/paper/2502.15681/) (2025)
- [Zero-shot Medical Image Translation via Frequency-Guided Diffusion Models](https://mlsanity.com/paper/2304.02742/) (2023)
- [Adversarial Schr"odinger Bridge Matching](https://mlsanity.com/paper/2405.14449/) (2024)
- [Soft-Di[M]O: Improving One-Step Discrete Image Generation with Soft Embeddings](https://mlsanity.com/paper/2509.22925/) (2025)
- [Entropy Controllable Direct Preference Optimization](https://mlsanity.com/paper/2411.07595/) (2024)
- [CHAIN: Enhancing Generalization in Data-Efficient GANs via lipsCHitz continuity constrAIned Normalization](https://mlsanity.com/paper/2404.00521/) (2024)

## Abstract (arXiv)

Non-saturating generative adversarial network (GAN) training is widely used and has continued to obtain groundbreaking results. However so far this approach has lacked strong theoretical justification, in contrast to alternatives such as f-GANs and Wasserstein GANs which are motivated in terms of approximate divergence minimization. In this paper we show that non-saturating GAN training does in fact approximately minimize a particular f-divergence. We develop general theoretical tools to compare and classify f-divergences and use these to show that the new f-divergence is qualitatively similar to reverse KL. These results help to explain the high sample quality but poor diversity often observed empirically when using this scheme.