# A Unified f-divergence Framework Generalizing VAE and GAN

arXiv: https://arxiv.org/abs/2205.05214 · HTML: https://mlsanity.com/paper/2205.05214/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 27 references that are in the map.
- First posted on arXiv 11 May 2022.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Wasserstein GAN](https://mlsanity.com/paper/1701.07875/) (2017)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Autoencoding beyond pixels using a learned similarity metric](https://mlsanity.com/paper/1512.09300/) (2015)
- [Adversarial Feature Learning](https://mlsanity.com/paper/1605.09782/) (2016)
- [Adversarially Learned Inference](https://mlsanity.com/paper/1606.00704/) (2016)
- [Unrolled Generative Adversarial Networks](https://mlsanity.com/paper/1611.02163/) (2016)
- [VEEGAN: Reducing Mode Collapse in GANs using Implicit Variational Learning](https://mlsanity.com/paper/1705.07761/) (2017)
- [Adversarial Variational Bayes: Unifying Variational Autoencoders and Generative Adversarial Networks](https://mlsanity.com/paper/1701.04722/) (2017)
- [PacGAN: The power of two samples in generative adversarial networks](https://mlsanity.com/paper/1712.04086/) (2017)
- [Generative Adversarial Nets from a Density Ratio Estimation Perspective](https://mlsanity.com/paper/1610.02920/) (2016)
- [Adversarial Symmetric Variational Autoencoder](https://mlsanity.com/paper/1711.04915/) (2017)

## Built on by (most cited first, 1 of 1)

- [Internally Rewarded Reinforcement Learning](https://mlsanity.com/paper/2302.00270/) (2023)

## Abstract (arXiv)

Developing deep generative models that flexibly incorporate diverse measures of probability distance is an important area of research. Here we develop an unified mathematical framework of f-divergence generative model, f-GM, that incorporates both VAE and f-GAN, and enables tractable learning with general f-divergences. f-GM allows the experimenter to flexibly design the f-divergence function without changing the structure of the networks or the learning procedure. f-GM jointly models three components: a generator, a inference network and a density estimator. Therefore it simultaneously enables sampling, posterior inference of the latent variable as well as evaluation of the likelihood of an arbitrary datum. f-GM belongs to the class of encoder-decoder GANs: our density estimator can be interpreted as playing the role of a discriminator between samples in the joint space of latent code and observed space. We prove that f-GM naturally simplifies to the standard VAE and to f-GAN as special cases, and illustrates the connections between different encoder-decoder GAN architectures. f-GM is compatible with general network architecture and optimizer. We leverage it to experimentally explore the effects -- e.g. mode collapse and image sharpness -- of different choices of f-divergence.