# Calibrating Energy-based Generative Adversarial Networks

arXiv: https://arxiv.org/abs/1702.01691 · HTML: https://mlsanity.com/paper/1702.01691/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Feb 2017.

## Built on by (most cited first, 13 of 13)

- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [Energy-guided Entropic Neural Optimal Transport](https://mlsanity.com/paper/2304.06094/) (2023)
- [S2AC: Energy-Based Reinforcement Learning with Stein Soft Actor Critic](https://mlsanity.com/paper/2405.00987/) (2024)
- [Learning Probabilistic Models from Generator Latent Spaces with Hat EBM](https://mlsanity.com/paper/2210.16486/) (2022)
- [Bounds all around: training energy-based models with bidirectional bounds](https://mlsanity.com/paper/2111.00929/) (2021)
- [Time-series Generation by Contrastive Imitation](https://mlsanity.com/paper/2311.01388/) (2023)
- [Learning Energy-based Model via Dual-MCMC Teaching](https://mlsanity.com/paper/2312.02469/) (2023)
- [Learning Representation from Neural Fisher Kernel with Low-rank Approximation](https://mlsanity.com/paper/2202.01944/) (2022)
- [Maximum Entropy Inverse Reinforcement Learning of Diffusion Models with Energy-Based Models](https://mlsanity.com/paper/2407.00626/) (2024)
- [Adversarial Likelihood Estimation With One-Way Flows](https://mlsanity.com/paper/2307.09882/) (2023)
- [Learning Energy-Based Approximate Inference Networks for Structured Applications in NLP](https://mlsanity.com/paper/2108.12522/) (2021)
- [Joint-stochastic-approximation Random Fields with Application to Semi-supervised Learning](https://mlsanity.com/paper/2505.20330/) (2025)
- [Exploring bidirectional bounds for minimax-training of Energy-based models](https://mlsanity.com/paper/2506.04609/) (2025)

## Abstract (arXiv)

In this paper, we propose to equip Generative Adversarial Networks with the ability to produce direct energy estimates for samples.Specifically, we propose a flexible adversarial training framework, and prove this framework not only ensures the generator converges to the true data distribution, but also enables the discriminator to retain the density information at the global optimal. We derive the analytic form of the induced solution, and analyze the properties. In order to make the proposed framework trainable in practice, we introduce two effective approximation techniques. Empirically, the experiment results closely match our theoretical analysis, verifying the discriminator is able to recover the energy of data distribution.