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Energy-Based Models (EBMs), also known as non-normalized probabilistic models, specify probability density or mass functions up to an unknown normalizing constant. Unlike most other probabilistic models, EBMs do not place a restriction on…

Machine Learning · Computer Science 2021-02-19 Yang Song , Diederik P. Kingma

Energy-based models (EBMs) exhibit a variety of desirable properties in predictive tasks, such as generality, simplicity and compositionality. However, training EBMs on high-dimensional datasets remains unstable and expensive. In this…

Computer Vision and Pattern Recognition · Computer Science 2023-03-09 Xiulong Yang , Shihao Ji

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

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

Multi-attribute classification generalizes classification, presenting new challenges for making accurate predictions and quantifying uncertainty. We build upon recent work and show that architectures for multi-attribute prediction can be…

Computer Vision and Pattern Recognition · Computer Science 2021-08-10 Jacob Kelly , Richard Zemel , Will Grathwohl

Energy-Based Models (EBMs) provide a flexible framework for generative modeling, but their training remains theoretically challenging due to the need to approximate normalization constants and efficiently sample from complex, multi-modal…

Machine Learning · Computer Science 2025-06-10 Davide Carbone

Energy-based models (EBMs) are a flexible class of deep generative models and are well-suited to capture complex dependencies in multimodal data. However, learning multimodal EBM by maximum likelihood requires Markov Chain Monte Carlo…

Machine Learning · Computer Science 2026-05-04 Jiali Cui , Zhiqiang Lao , Heather Yu

We show that the bias of the approximate maximum-likelihood estimation (MLE) objective of a persistent chain energy-based model (EBM) is precisely equal to the thermodynamic excess work of an overdamped Langevin dynamical system. We then…

Statistical Mechanics · Physics 2025-10-06 Jeff Hnybida , Simon Verret

Purpose: Although recent deep energy-based generative models (EBMs) have shown encouraging results in many image generation tasks, how to take advantage of the self-adversarial cogitation in deep EBMs to boost the performance of Magnetic…

Image and Video Processing · Electrical Eng. & Systems 2021-09-10 Yu Guan , Zongjiang Tu , Shanshan Wang , Qiegen Liu , Yuhao Wang , Dong Liang

This paper proposes a joint training method to learn both the variational auto-encoder (VAE) and the latent energy-based model (EBM). The joint training of VAE and latent EBM are based on an objective function that consists of three…

Computer Vision and Pattern Recognition · Computer Science 2020-06-12 Tian Han , Erik Nijkamp , Linqi Zhou , Bo Pang , Song-Chun Zhu , Ying Nian Wu

Energy-based latent variable models (EBLVMs) are more expressive than conventional energy-based models. However, its potential on visual tasks are limited by its training process based on maximum likelihood estimate that requires sampling…

Computer Vision and Pattern Recognition · Computer Science 2022-03-29 Ge Kan , Jinhu Lü , Tian Wang , Baochang Zhang , Aichun Zhu , Lei Huang , Guodong Guo , Hichem Snoussi

In this chapter we provide a thorough overview of the use of energy-based models (EBMs) in the context of inverse imaging problems. EBMs are probability distributions modeled via Gibbs densities $p(x) \propto \exp{-E(x)}$ with an…

Image and Video Processing · Electrical Eng. & Systems 2025-09-17 Andreas Habring , Martin Holler , Thomas Pock , Martin Zach

Energy-based models (EBMs) provide a powerful and flexible way of learning a joint probability distribution over data by constructing an energy surface. This energy surface enables insight extraction and conditional sampling. We apply EBMs…

Plasma Physics · Physics 2026-05-12 Phil Travis , Troy Carter

We offer a study that connects robust discriminative classifiers trained with adversarial training (AT) with generative modeling in the form of Energy-based Models (EBM). We do so by decomposing the loss of a discriminative classifier and…

Machine Learning · Computer Science 2023-06-06 Senad Beadini , Iacopo Masi

Decision-focused learning (DFL) was recently proposed for stochastic optimization problems that involve unknown parameters. By integrating predictive modeling with an implicitly differentiable optimization layer, DFL has shown superior…

Machine Learning · Computer Science 2022-11-28 Lingkai Kong , Jiaming Cui , Yuchen Zhuang , Rui Feng , B. Aditya Prakash , Chao Zhang

Large language models (LLMs) trained via KL-regularized reinforcement learning demonstrate strong instruction following, self-correction, and reasoning abilities. Yet their theoretical underpinnings remain limited. We exploit the…

Machine Learning · Computer Science 2025-12-23 Zhiquan Tan , Yinrong Hong

Energy-based models (EBMs) are a powerful class of probabilistic generative models due to their flexibility and interpretability. However, relationships between potential flows and explicit EBMs remain underexplored, while contrastive…

We present Generalized Contrastive Divergence (GCD), a novel objective function for training an energy-based model (EBM) and a sampler simultaneously. GCD generalizes Contrastive Divergence (Hinton, 2002), a celebrated algorithm for…

Machine Learning · Computer Science 2023-12-07 Sangwoong Yoon , Dohyun Kwon , Himchan Hwang , Yung-Kyun Noh , Frank C. Park

Simultaneously achieving robust classification and high-fidelity generative modeling within a single framework presents a significant challenge. Hybrid approaches, such as Joint Energy-Based Models (JEM), interpret classifiers as EBMs but…

Machine Learning · Computer Science 2026-03-19 Xuwang Yin , Claire Zhang , Julie Steele , Nir Shavit , Tony T. Wang

This paper studies the fundamental problem of learning multi-layer generator models. The multi-layer generator model builds multiple layers of latent variables as a prior model on top of the generator, which benefits learning complex data…

Computer Vision and Pattern Recognition · Computer Science 2023-10-13 Jiali Cui , Ying Nian Wu , Tian Han