# Particle Dynamics for Latent-Variable Energy-Based Models

arXiv: https://arxiv.org/abs/2510.15447 · HTML: https://mlsanity.com/paper/2510.15447/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 38 references that are in the map.
- First posted on arXiv 17 Oct 2025.

## Builds on (most cited first, 14 of 14)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://mlsanity.com/paper/1912.03263/) (2019)
- [Inference Suboptimality in Variational Autoencoders](https://mlsanity.com/paper/1801.03558/) (2018)
- [No MCMC for me: Amortized sampling for fast and stable training of energy-based models](https://mlsanity.com/paper/2010.04230/) (2020)
- [Semi-Implicit Variational Inference](https://mlsanity.com/paper/1805.11183/) (2018)
- [Statistical optimal transport](https://mlsanity.com/paper/2407.18163/) (2024)
- [Particle algorithms for maximum likelihood training of latent variable models](https://mlsanity.com/paper/2204.12965/) (2022)
- [Particle Semi-Implicit Variational Inference](https://mlsanity.com/paper/2407.00649/) (2024)
- [Particle Dynamics for Learning EBMs](https://mlsanity.com/paper/2111.13772/) (2021)

## Built on by (most cited first, 1 of 1)

- [Structure-Adaptive Tree Field Integrators](https://mlsanity.com/paper/2609.34025/) (2026)

## Abstract (arXiv)

Latent-variable energy-based models (LVEBMs) assign a single normalized energy to joint pairs of observed data and latent variables, offering expressive generative modeling while capturing hidden structure. We recast maximum-likelihood training as a saddle problem over distributions on the latent and joint manifolds and view the inner updates as coupled Wasserstein gradient flows. The resulting algorithm alternates overdamped Langevin updates for a joint negative pool and for conditional latent particles with stochastic parameter ascent, requiring no discriminator or auxiliary networks. We prove existence and convergence under standard smoothness and dissipativity assumptions, with decay rates in KL divergence and Wasserstein-2 distance. The saddle-point view further yields an ELBO strictly tighter than bounds obtained with restricted amortized posteriors. Our method is evaluated on numerical approximations of physical systems and performs competitively against comparable approaches.