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A Unified f-divergence Framework Generalizing VAE and GAN
Machine Learning · Submitted 11 May 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Developing deep generative models that flexibly incorporate diverse measures of probability distance is an important area of research. | background 1.00 | 0.04 | 0.03 | asserted 1.00 |
| s1 | 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. | contribution 0.90 | 0.96 | 0.32 | asserted 1.00 |
| s2 | 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. | interpretation 0.86 | 0.75 | 0.17 | asserted 1.00 |
| s3 | 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. | result 0.60 | 0.93 | 0.30 | asserted 1.00 |
| s4 | We leverage it to experimentally explore the effects -- e.g. mode collapse and image sharpness -- of different choices of f-divergence. | contribution 0.60 | 0.94 | 0.08 | asserted 0.97 |
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The paper
Original abstract
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.
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How the literature uses it
1 arXiv paper cite this in 1 sentence
Papers citing it
Cites it as background 1 paper
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In recent years, $f$-mutual information has been studied in many deep learning applications, such as generative models [ref] , representation learning [ref] , image classification [ref] , imitation learning [ref] , etc.
Internally Rewarded Reinforcement Learning · Interpretation from the Information-theoretic Perspective · 0.99
What it cites · 12 sentences without a confident label
Uses the method or tool of 1 paper
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Then parameters can be updated following standard optimizer such as Adam [ref] .
Adam: A Method for Stochastic Optimization · The Unified f-GM Model · 0.97
Uses data or values from 1 paper
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We validate it with experiments on MNIST and Fashion-MNIST [ref] .
Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms · Experiments · 0.97
Compares with 5 papers
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We are not matching marginals only in the $𝒳$ space as the $f$-GAN does, nor we are using different losses for different sections of the model [ref] .
The Information Autoencoding Family: A Lagrangian Perspective on Latent Variable Generative Models · Comparison to Related Works and Discussion · 0.95
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We are not matching marginals only in the $𝒳$ space as the $f$-GAN does, nor we are using different losses for different sections of the model [ref] .
Adversarial Autoencoders · Comparison to Related Works and Discussion · 0.95
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Similar to the BiGAN/ALI models [ref] , we use the Fenchel-Young inequality to approximate the $f$-divergence over the joint distributions, but instead of substituting the whole likelihood ratio by an auxiliary term, we replace $p^*$, the one term we do not have access to, and keep the terms $q_ϕ$ and $p_θ^XZ$ in the expectation.
Adversarially Learned Inference · Comparison to Related Works and Discussion · 0.96
Cites as background 3 papers
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There are two main categories of training procedures for generative models: Variational Auto-Encoders (VAEs) [ref] and Generative Adversarial Networks (GANs) [ref] , each training the generative network $p_θ$ with an auxiliary network.
Auto-Encoding Variational Bayes · Introduction · 1.00
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A more general class of generative models has been developed by merging these two families: these are called encoder-decoder GANs [ref] .
Adversarially Learned Inference · Introduction · 0.81
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A more general class of generative models has been developed by merging these two families: these are called encoder-decoder GANs [ref] .
Adversarial Feature Learning · Introduction · 0.81
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