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Deep energy-based models (EBMs) are very flexible in distribution parametrization but computationally challenging because of the intractable partition function. They are typically trained via maximum likelihood, using contrastive divergence…

Machine Learning · Computer Science 2020-07-22 Lantao Yu , Yang Song , Jiaming Song , Stefano Ermon

Molecules in equilibrium follow a Boltzmann distribution, making the underlying energy landscape a physically grounded modeling objective. However, such landscapes are difficult to learn from data and, once learned, hard to sample from.…

Machine Learning · Computer Science 2026-05-19 Christoph Griesbacher , Lea Bogensperger , Andreas Habring , Thomas Pock

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…

Machine Learning · Computer Science 2025-05-22 Davide Carbone

Training energy-based models (EBMs) on high-dimensional data can be both challenging and time-consuming, and there exists a noticeable gap in sample quality between EBMs and other generative frameworks like GANs and diffusion models. To…

Machine Learning · Statistics 2024-11-12 Yaxuan Zhu , Jianwen Xie , Yingnian Wu , Ruiqi Gao

While energy-based models (EBMs) exhibit a number of desirable properties, training and sampling on high-dimensional datasets remains challenging. Inspired by recent progress on diffusion probabilistic models, we present a diffusion…

Machine Learning · Computer Science 2021-03-30 Ruiqi Gao , Yang Song , Ben Poole , Ying Nian Wu , Diederik P. Kingma

As a classical generative modeling approach, energy-based models have the natural advantage of flexibility in the form of the energy function. Recently, energy-based models have achieved great success in modeling high-dimensional data in…

Machine Learning · Computer Science 2024-01-19 Taoli Cheng , Aaron Courville

Energy-Based Models (EBMs) present a flexible and appealing way to represent uncertainty. Despite recent advances, training EBMs on high-dimensional data remains a challenging problem as the state-of-the-art approaches are costly, unstable,…

Machine Learning · Computer Science 2021-06-08 Will Grathwohl , Jacob Kelly , Milad Hashemi , Mohammad Norouzi , Kevin Swersky , David Duvenaud

Flow matching has recently emerged as a promising alternative to diffusion-based generative models, offering faster sampling and simpler training by learning continuous flows governed by ordinary differential equations. Despite growing…

Machine Learning · Computer Science 2025-12-02 Mudit Gaur , Prashant Trivedi , Shuchin Aeron , Amrit Singh Bedi , George K. Atia , Vaneet Aggarwal

We propose Energy-based generator matching (EGM), a modality-agnostic approach to train generative models from energy functions in the absence of data. Extending the recently proposed generator matching, EGM enables training of arbitrary…

Machine Learning · Computer Science 2025-11-20 Dongyeop Woo , Minsu Kim , Minkyu Kim , Kiyoung Seong , Sungsoo Ahn

We propose Pullback Flow Matching (PFM), a novel framework for generative modeling on data manifolds. Unlike existing methods that assume or learn restrictive closed-form manifold mappings for training Riemannian Flow Matching (RFM) models,…

Machine Learning · Computer Science 2025-07-10 Friso de Kruiff , Erik Bekkers , Ozan Öktem , Carola-Bibiane Schönlieb , Willem Diepeveen

This work studies the learning problem of the energy-based prior model and the multi-layer generator model. The multi-layer generator model, which contains multiple layers of latent variables organized in a top-down hierarchical structure,…

Machine Learning · Computer Science 2024-05-29 Jiali Cui , Tian Han

Multimodal generative models are crucial for various applications. We propose an approach that combines an expressive energy-based model (EBM) prior with Markov Chain Monte Carlo (MCMC) inference in the latent space for multimodal…

Machine Learning · Computer Science 2024-08-21 Shiyu Yuan , Carlo Lipizzi , Tian Han

Maximum likelihood (ML) learning for energy-based models (EBMs) is challenging, partly due to non-convergence of Markov chain Monte Carlo.Several variations of ML learning have been proposed, but existing methods all fail to achieve both…

Machine Learning · Statistics 2023-04-24 Xinwei Zhang , Zhiqiang Tan , Zhijian Ou

The task of conditional generation is one of the most important applications of generative models, and numerous methods have been developed to date based on the celebrated flow-based models. However, many flow-based models in use today are…

Machine Learning · Computer Science 2024-07-08 Noboru Isobe , Masanori Koyama , Jinzhe Zhang , Kohei Hayashi , Kenji Fukumizu

Energy-based learning is a powerful learning paradigm that encapsulates various discriminative and generative approaches. An energy-based model (EBM) is typically formed of inner-model(s) that learn a combination of the different features…

Machine Learning · Computer Science 2023-06-05 Firas Laakom , Jenni Raitoharju , Alexandros Iosifidis , Moncef Gabbouj

In this paper, we establish a connection between the parameterization of flow-based and energy-based generative models, and present a new flow-based modeling approach called energy-based normalizing flow (EBFlow). We demonstrate that by…

Machine Learning · Computer Science 2023-10-31 Chen-Hao Chao , Wei-Fang Sun , Yen-Chang Hsu , Zsolt Kira , Chun-Yi Lee

Generative Bayesian Filtering (GBF) provides a powerful and flexible framework for performing posterior inference in complex nonlinear and non-Gaussian state-space models. Our approach extends Generative Bayesian Computation (GBC) to…

Methodology · Statistics 2025-11-07 Edoardo Marcelli , Sean O'Hagan , Veronika Rockova

Generative machine learning has emerged as a powerful tool for design representation and exploration. However, its application is often constrained by the need for large datasets of existing designs and the lack of interpretability about…

Machine Learning · Computer Science 2025-08-13 Eric Seng , Hugh O'Connor , Adam Boyce , Josh J. Bailey , Anton van Beek

Residential Load Profile (RLP) generation and prediction are critical for the operation and planning of distribution networks, especially as diverse low-carbon technologies (e.g., photovoltaic and electric vehicles) are increasingly…

Machine Learning · Computer Science 2025-10-28 Weijie Xia , Chenguang Wang , Peter Palensky , Pedro P. Vergara

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…

Machine Learning · Computer Science 2025-10-20 Shiqin Tang , Shuxin Zhuang , Rong Feng , Runsheng Yu , Hongzong Li , Youzhi Zhang