# Flow Contrastive Estimation of Energy-Based Models

arXiv: https://arxiv.org/abs/1912.00589 · HTML: https://mlsanity.com/paper/1912.00589/

## Key facts

- Cited by 75 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Dec 2019.

## Built on by (most cited first, 30 of 75)

- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [Learning to Compose Visual Relations](https://mlsanity.com/paper/2111.09297/) (2021)
- [Unsupervised Learning of Compositional Energy Concepts](https://mlsanity.com/paper/2111.03042/) (2021)
- [A Tale of Two Flows: Cooperative Learning of Langevin Flow and Normalizing Flow Toward Energy-Based Model](https://mlsanity.com/paper/2205.06924/) (2022)
- [JEM++: Improved Techniques for Training JEM](https://mlsanity.com/paper/2109.09032/) (2021)
- [Energy-guided Entropic Neural Optimal Transport](https://mlsanity.com/paper/2304.06094/) (2023)
- [Learning Energy-Based Models by Cooperative Diffusion Recovery Likelihood](https://mlsanity.com/paper/2309.05153/) (2023)
- [Adaptive Multi-stage Density Ratio Estimation for Learning Latent Space Energy-based Model](https://mlsanity.com/paper/2209.08739/) (2022)
- [Guiding Energy-based Models via Contrastive Latent Variables](https://mlsanity.com/paper/2303.03023/) (2023)
- [Energy-Based Models for Anomaly Detection: A Manifold Diffusion Recovery Approach](https://mlsanity.com/paper/2310.18677/) (2023)
- [On Out-of-distribution Detection with Energy-based Models](https://mlsanity.com/paper/2107.08785/) (2021)
- [Deep Generative Modeling for Protein Design](https://mlsanity.com/paper/2109.13754/) (2021)
- [EGC: Image Generation and Classification via a Diffusion Energy-Based Model](https://mlsanity.com/paper/2304.02012/) (2023)
- [Analyzing and Improving the Optimization Landscape of Noise-Contrastive Estimation](https://mlsanity.com/paper/2110.11271/) (2021)
- [Efficient Training of Energy-Based Models Using Jarzynski Equality](https://mlsanity.com/paper/2305.19414/) (2023)
- [Energy-Based Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2202.04933/) (2022)
- [Learning Energy-Based Prior Model with Diffusion-Amortized MCMC](https://mlsanity.com/paper/2310.03218/) (2023)
- [Provable benefits of annealing for estimating normalizing constants: Importance Sampling, Noise-Contrastive Estimation, and beyond](https://mlsanity.com/paper/2310.03902/) (2023)
- [Density Ratio Estimation with Conditional Probability Paths](https://mlsanity.com/paper/2502.02300/) (2025)
- [The Optimal Noise in Noise-Contrastive Learning Is Not What You Think](https://mlsanity.com/paper/2203.01110/) (2022)
- [Learning Probabilistic Models from Generator Latent Spaces with Hat EBM](https://mlsanity.com/paper/2210.16486/) (2022)
- [Revisiting Energy Based Models as Policies: Ranking Noise Contrastive Estimation and Interpolating Energy Models](https://mlsanity.com/paper/2309.05803/) (2023)
- [Training Energy-Based Models with Diffusion Contrastive Divergences](https://mlsanity.com/paper/2307.01668/) (2023)
- ["Noisier" Noise Contrastive Eestimation is (Almost) Maximum Likelihood](https://mlsanity.com/paper/2405.16730/) (2024)
- [Identifiable Energy-based Representations: An Application to Estimating Heterogeneous Causal Effects](https://mlsanity.com/paper/2108.03039/) (2021)
- [Pseudo-Spherical Contrastive Divergence](https://mlsanity.com/paper/2111.00780/) (2021)
- [Contrastive Learning of Coarse-Grained Force Fields](https://mlsanity.com/paper/2205.10861/) (2022)
- [A Tale of Two Latent Flows: Learning Latent Space Normalizing Flow with Short-run Langevin Flow for Approximate Inference](https://mlsanity.com/paper/2301.09300/) (2023)

## Abstract (arXiv)

This paper studies a training method to jointly estimate an energy-based model and a flow-based model, in which the two models are iteratively updated based on a shared adversarial value function. This joint training method has the following traits. (1) The update of the energy-based model is based on noise contrastive estimation, with the flow model serving as a strong noise distribution. (2) The update of the flow model approximately minimizes the Jensen-Shannon divergence between the flow model and the data distribution. (3) Unlike generative adversarial networks (GAN) which estimates an implicit probability distribution defined by a generator model, our method estimates two explicit probabilistic distributions on the data. Using the proposed method we demonstrate a significant improvement on the synthesis quality of the flow model, and show the effectiveness of unsupervised feature learning by the learned energy-based model. Furthermore, the proposed training method can be easily adapted to semi-supervised learning. We achieve competitive results to the state-of-the-art semi-supervised learning methods.