# Learning Latent Energy-Based Models via Interacting Particle Langevin Dynamics

arXiv: https://arxiv.org/abs/2510.12311 · HTML: https://mlsanity.com/paper/2510.12311/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 61 of its 91 references that are in the map.
- First posted on arXiv 14 Oct 2025.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (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)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [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)
- [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)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://mlsanity.com/paper/1912.03263/) (2019)
- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [Residual Flows for Invertible Generative Modeling](https://mlsanity.com/paper/1906.02735/) (2019)
- [Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysis](https://mlsanity.com/paper/1702.03849/) (2017)
- [Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC](https://mlsanity.com/paper/2302.11552/) (2023)
- [Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1507.05021/) (2015)
- [Diagnosing and Enhancing VAE Models](https://mlsanity.com/paper/1903.05789/) (2019)
- [Learning Non-Convergent Non-Persistent Short-Run MCMC Toward Energy-Based Model](https://mlsanity.com/paper/1904.09770/) (2019)
- [From Variational to Deterministic Autoencoders](https://mlsanity.com/paper/1903.12436/) (2019)
- [Improved Contrastive Divergence Training of Energy Based Models](https://mlsanity.com/paper/2012.01316/) (2020)
- [Learning Energy-Based Models by Diffusion Recovery Likelihood](https://mlsanity.com/paper/2012.08125/) (2020)
- [User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient](https://mlsanity.com/paper/1710.00095/) (2017)
- [Deep Structured Energy Based Models for Anomaly Detection](https://mlsanity.com/paper/1605.07717/) (2016)
- [On the Anatomy of MCMC-Based Maximum Likelihood Learning of Energy-Based Models](https://mlsanity.com/paper/1903.12370/) (2019)
- [Learning Latent Space Energy-Based Prior Model](https://mlsanity.com/paper/2006.08205/) (2020)
- [VAEBM: A Symbiosis between Variational Autoencoders and Energy-based Models](https://mlsanity.com/paper/2010.00654/) (2020)
- [Residual Energy-Based Models for Text Generation](https://mlsanity.com/paper/2004.11714/) (2020)
- [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)
- [No MCMC for me: Amortized sampling for fast and stable training of energy-based models](https://mlsanity.com/paper/2010.04230/) (2020)

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

- [Efficient Stochastic Optimisation via Sequential Monte Carlo](https://mlsanity.com/paper/2601.22003/) (2026)
- [Momentum SVGD-EM for Accelerated Maximum Marginal Likelihood Estimation](https://mlsanity.com/paper/2603.08676/) (2026)
- [Learning Multimodal Energy-Based Model with Multimodal Variational Auto-Encoder via MCMC Revision](https://mlsanity.com/paper/2605.00644/) (2026)
- [Particle-based Generalised Stochastic Optimisation](https://mlsanity.com/paper/2608.02844/) (2026)
- [Structure-Adaptive Tree Field Integrators](https://mlsanity.com/paper/2609.34025/) (2026)

## Abstract (arXiv)

We develop interacting particle algorithms for learning latent variable models with energy-based priors. To do so, we leverage recent developments in particle-based methods for solving maximum marginal likelihood estimation (MMLE) problems. Specifically, we provide a continuous-time framework for learning latent energy-based models, by defining stochastic differential equations (SDEs) that provably solve the MMLE problem. We obtain a practical algorithm as a discretisation of these SDEs and provide theoretical guarantees for the convergence of the proposed algorithm. Finally, we empirically validate the effectiveness of our method on synthetic and image datasets and demonstrate that using a particle based approach offers significant improvement in computational efficiency.