# Hitchhiker's guide on the relation of Energy-Based Models with other generative models, sampling and statistical physics: a comprehensive review

arXiv: https://arxiv.org/abs/2406.13661 · HTML: https://mlsanity.com/paper/2406.13661/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 131 references that are in the map.
- First posted on arXiv 19 Jun 2024.

## Builds on (most cited first, 30 of 48)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [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)
- [Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC](https://mlsanity.com/paper/2302.11552/) (2023)
- [A Theory of Generative ConvNet](https://mlsanity.com/paper/1602.03264/) (2016)
- [Dynamical Variational Autoencoders: A Comprehensive Review](https://mlsanity.com/paper/2008.12595/) (2020)
- [Lagging Inference Networks and Posterior Collapse in Variational Autoencoders](https://mlsanity.com/paper/1901.05534/) (2019)
- [Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problem](https://mlsanity.com/paper/1802.08089/) (2018)
- [Score-Based Generative Models Detect Manifolds](https://mlsanity.com/paper/2206.01018/) (2022)
- [Deep Structured Energy Based Models for Anomaly Detection](https://mlsanity.com/paper/1605.07717/) (2016)
- [GraphEBM: Molecular Graph Generation with Energy-Based Models](https://mlsanity.com/paper/2102.00546/) (2021)
- [Flow Contrastive Estimation of Energy-Based Models](https://mlsanity.com/paper/1912.00589/) (2019)
- [Generalized Energy Based Models](https://mlsanity.com/paper/2003.05033/) (2020)
- [Your GAN is Secretly an Energy-based Model and You Should use Discriminator Driven Latent Sampling](https://mlsanity.com/paper/2003.06060/) (2020)

## Built on by (most cited first, 5 of 5)

- [Distributional Energy-Based Models for Uncertainty-Aware Structured LLM Reasoning](https://mlsanity.com/paper/2605.18871/) (2026)
- [Jarzynski Reweighting and Sampling Dynamics for Training Energy-Based Models: Theoretical Analysis of Different Transition Kernels](https://mlsanity.com/paper/2506.07843/) (2025)
- [Tutorial on Reasoning for IR & IR for Reasoning](https://mlsanity.com/paper/2602.03640/) (2026)
- [Reasoning as Energy Minimization over Structured Latent Trajectories](https://mlsanity.com/paper/2603.28248/) (2026)
- [Cross-Block Conditioning in Deep Boltzmann Machines for Statistical Data Fusion](https://mlsanity.com/paper/2609.14934/) (2026)

## Abstract (arXiv)

Energy-Based Models have emerged as a powerful framework in the realm of generative modeling, offering a unique perspective that aligns closely with principles of statistical mechanics. This review aims to provide physicists with a comprehensive understanding of EBMs, delineating their connection to other generative models such as Generative Adversarial Networks, Variational Autoencoders, and Normalizing Flows. We explore the sampling techniques crucial for EBMs, including Markov Chain Monte Carlo (MCMC) methods, and draw parallels between EBM concepts and statistical mechanics, highlighting the significance of energy functions and partition functions. Furthermore, we delve into recent training methodologies for EBMs, covering recent advancements and their implications for enhanced model performance and efficiency. This review is designed to clarify the often complex interconnections between these models, which can be challenging due to the diverse communities working on the topic.