Particle Dynamics for Latent-Variable Energy-Based Models

Shiqin Tang, Shuxin Zhuang, Runsheng Yu, Rong Feng, Shujian Yu, Hongzong Li, Mingyang Zhao, Gaofeng Meng
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:6631-6644, 2026.

Abstract

Latent-variable energy-based models (LV-EBMs) 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-tang26a, title = {Particle Dynamics for Latent-Variable Energy-Based Models}, author = {Tang, Shiqin and Zhuang, Shuxin and Yu, Runsheng and Feng, Rong and Yu, Shujian and Li, Hongzong and Zhao, Mingyang and Meng, Gaofeng}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {6631--6644}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/tang26a/tang26a.pdf}, url = {https://proceedings.mlr.press/v337/tang26a.html}, abstract = {Latent-variable energy-based models (LV-EBMs) 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.} }
Endnote
%0 Conference Paper %T Particle Dynamics for Latent-Variable Energy-Based Models %A Shiqin Tang %A Shuxin Zhuang %A Runsheng Yu %A Rong Feng %A Shujian Yu %A Hongzong Li %A Mingyang Zhao %A Gaofeng Meng %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-tang26a %I PMLR %P 6631--6644 %U https://proceedings.mlr.press/v337/tang26a.html %V 337 %X Latent-variable energy-based models (LV-EBMs) 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.
APA
Tang, S., Zhuang, S., Yu, R., Feng, R., Yu, S., Li, H., Zhao, M. & Meng, G.. (2026). Particle Dynamics for Latent-Variable Energy-Based Models. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:6631-6644 Available from https://proceedings.mlr.press/v337/tang26a.html.

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