# Guiding Energy-based Models via Contrastive Latent Variables

arXiv: https://arxiv.org/abs/2303.03023 · HTML: https://mlsanity.com/paper/2303.03023/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 61 of its 79 references that are in the map.
- First posted on arXiv 6 Mar 2023.

## Builds on (most cited first, 30 of 61)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [What Makes for Good Views for Contrastive Learning?](https://mlsanity.com/paper/2005.10243/) (2020)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [Generative Adversarial Text to Image Synthesis](https://mlsanity.com/paper/1605.05396/) (2016)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Conditional Image Synthesis With Auxiliary Classifier GANs](https://mlsanity.com/paper/1610.09585/) (2016)

## Built on by (most cited first, 18 of 18)

- [Energy Matching: Unifying Flow Matching and Energy-Based Models for Generative Modeling](https://mlsanity.com/paper/2504.10612/) (2025)
- [Learning Energy-Based Models by Cooperative Diffusion Recovery Likelihood](https://mlsanity.com/paper/2309.05153/) (2023)
- [Energy-Based Models for Anomaly Detection: A Manifold Diffusion Recovery Approach](https://mlsanity.com/paper/2310.18677/) (2023)
- [EGC: Image Generation and Classification via a Diffusion Energy-Based Model](https://mlsanity.com/paper/2304.02012/) (2023)
- [Efficient Training of Energy-Based Models Using Jarzynski Equality](https://mlsanity.com/paper/2305.19414/) (2023)
- [Projection Regret: Reducing Background Bias for Novelty Detection via Diffusion Models](https://mlsanity.com/paper/2312.02615/) (2023)
- [Improving Adversarial Energy-Based Model via Diffusion Process](https://mlsanity.com/paper/2403.01666/) (2024)
- [BoltzNCE: Learning Likelihoods for Boltzmann Generation with Stochastic Interpolants and Noise Contrastive Estimation](https://mlsanity.com/paper/2507.00846/) (2025)
- [Maximum Entropy Inverse Reinforcement Learning of Diffusion Models with Energy-Based Models](https://mlsanity.com/paper/2407.00626/) (2024)
- [Energy-Calibrated VAE with Test Time Free Lunch](https://mlsanity.com/paper/2311.04071/) (2023)
- [Learning Energy-Based Generative Models via Potential Flow: A Variational Principle Approach to Probability Density Homotopy Matching](https://mlsanity.com/paper/2504.16262/) (2025)
- [Generalized Contrastive Divergence: Joint Training of Energy-Based Model and Diffusion Model through Inverse Reinforcement Learning](https://mlsanity.com/paper/2312.03397/) (2023)
- [Variational Potential Flow: A Novel Probabilistic Framework for Energy-Based Generative Modelling](https://mlsanity.com/paper/2407.15238/) (2024)
- [Exploring bidirectional bounds for minimax-training of Energy-based models](https://mlsanity.com/paper/2506.04609/) (2025)
- [Annealed Langevin Posterior Sampling (ALPS): A Rapid Algorithm for Image Restoration with Multiscale Energy Models](https://mlsanity.com/paper/2601.02594/) (2026)
- [Distance Marching for Generative Modeling](https://mlsanity.com/paper/2602.02928/) (2026)
- [CGRL: Causal-Guided Representation Learning for Node-Level Out-of-Distribution Generalization](https://mlsanity.com/paper/2603.24304/) (2026)
- [PotentialEP: Backprop-Free Training of CIFAR-Scale Generative Models via Equilibrium Propagation](https://mlsanity.com/paper/2610.14409/) (2026)

## Abstract (arXiv)

An energy-based model (EBM) is a popular generative framework that offers both explicit density and architectural flexibility, but training them is difficult since it is often unstable and time-consuming. In recent years, various training techniques have been developed, e.g., better divergence measures or stabilization in MCMC sampling, but there often exists a large gap between EBMs and other generative frameworks like GANs in terms of generation quality. In this paper, we propose a novel and effective framework for improving EBMs via contrastive representation learning (CRL). To be specific, we consider representations learned by contrastive methods as the true underlying latent variable. This contrastive latent variable could guide EBMs to understand the data structure better, so it can improve and accelerate EBM training significantly. To enable the joint training of EBM and CRL, we also design a new class of latent-variable EBMs for learning the joint density of data and the contrastive latent variable. Our experimental results demonstrate that our scheme achieves lower FID scores, compared to prior-art EBM methods (e.g., additionally using variational autoencoders or diffusion techniques), even with significantly faster and more memory-efficient training. We also show conditional and compositional generation abilities of our latent-variable EBMs as their additional benefits, even without explicit conditional training. The code is available at https://github.com/hankook/CLEL.