# Properties of f-divergences and f-GAN training

arXiv: https://arxiv.org/abs/2009.00757 · HTML: https://mlsanity.com/paper/2009.00757/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Sep 2020.

## Built on by (most cited first, 3 of 3)

- [Speaker Generation](https://mlsanity.com/paper/2111.05095/) (2021)
- [Addressing GAN Training Instabilities via Tunable Classification Losses](https://mlsanity.com/paper/2310.18291/) (2023)
- [Connecting Jensen-Shannon and Kullback-Leibler Divergences: A New Bound for Representation Learning](https://mlsanity.com/paper/2510.20644/) (2025)

## Abstract (arXiv)

In this technical report we describe some properties of f-divergences and f-GAN training. We present an elementary derivation of the f-divergence lower bounds which form the basis of f-GAN training. We derive informative but perhaps underappreciated properties of f-divergences and f-GAN training, including a gradient matching property and the fact that all f-divergences agree up to an overall scale factor on the divergence between nearby distributions. We provide detailed expressions for computing various common f-divergences and their variational lower bounds. Finally, based on our reformulation, we slightly generalize f-GAN training in a way that may improve its stability.