# Generative Adversarial Networks as Variational Training of Energy Based Models

arXiv: https://arxiv.org/abs/1611.01799 · HTML: https://mlsanity.com/paper/1611.01799/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Nov 2016.

## Built on by (most cited first, 10 of 10)

- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [A review of Generative Adversarial Networks for Electronic Health Records: applications, evaluation measures and data sources](https://mlsanity.com/paper/2203.07018/) (2022)
- [Bounds all around: training energy-based models with bidirectional bounds](https://mlsanity.com/paper/2111.00929/) (2021)
- [Non-Imaging Medical Data Synthesis for Trustworthy AI: A Comprehensive Survey](https://mlsanity.com/paper/2209.09239/) (2022)
- [Time-series Generation by Contrastive Imitation](https://mlsanity.com/paper/2311.01388/) (2023)
- [Moment Matching Denoising Gibbs Sampling](https://mlsanity.com/paper/2305.11650/) (2023)
- [Improving Adversarial Energy-Based Model via Diffusion Process](https://mlsanity.com/paper/2403.01666/) (2024)
- [Learning Proposals for Practical Energy-Based Regression](https://mlsanity.com/paper/2110.11948/) (2021)
- [OT-Net: A Reusable Neural Optimal Transport Solver](https://mlsanity.com/paper/2306.08233/) (2023)
- [Exploring bidirectional bounds for minimax-training of Energy-based models](https://mlsanity.com/paper/2506.04609/) (2025)

## Abstract (arXiv)

In this paper, we study deep generative models for effective unsupervised learning. We propose VGAN, which works by minimizing a variational lower bound of the negative log likelihood (NLL) of an energy based model (EBM), where the model density p(x) is approximated by a variational distribution q(x) that is easy to sample from. The training of VGAN takes a two step procedure: given p(x), q(x) is updated to maximize the lower bound; p(x) is then updated one step with samples drawn from q(x) to decrease the lower bound. VGAN is inspired by the generative adversarial networks (GANs), where p(x) corresponds to the discriminator and q(x) corresponds to the generator, but with several notable differences. We hence name our model variational GANs (VGANs). VGAN provides a practical solution to training deep EBMs in high dimensional space, by eliminating the need of MCMC sampling. From this view, we are also able to identify causes to the difficulty of training GANs and propose viable solutions. footnoteExperimental code is available at https://github.com/Shuangfei/vgan