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Energy-based models (EBMs) have become increasingly popular within computer vision in recent years. While they are commonly employed for generative image modeling, recent work has applied EBMs also for regression tasks, achieving…

Computer Vision and Pattern Recognition · Computer Science 2020-08-17 Fredrik K. Gustafsson , Martin Danelljan , Radu Timofte , Thomas B. Schön

Energy-based models (EBMs) are generative models that are usually trained via maximum likelihood estimation. This approach becomes challenging in generic situations where the trained energy is non-convex, due to the need to sample the Gibbs…

Machine Learning · Computer Science 2022-02-16 Carles Domingo-Enrich , Alberto Bietti , Marylou Gabrié , Joan Bruna , Eric Vanden-Eijnden

The inadequate mixing of conventional Markov Chain Monte Carlo (MCMC) methods for multi-modal distributions presents a significant challenge in practical applications such as Bayesian inference and molecular dynamics. Addressing this, we…

Machine Learning · Statistics 2024-05-30 Wenlin Chen , Mingtian Zhang , Brooks Paige , José Miguel Hernández-Lobato , David Barber

Energy-based models (EBMs) have experienced a resurgence within machine learning in recent years, including as a promising alternative for probabilistic regression. However, energy-based regression requires a proposal distribution to be…

Machine Learning · Computer Science 2023-11-08 Fredrik K. Gustafsson , Martin Danelljan , Thomas B. Schön

Training energy-based models (EBMs) with noise-contrastive estimation (NCE) is theoretically feasible but practically challenging. Effective learning requires the noise distribution to be approximately similar to the target distribution,…

Machine Learning · Computer Science 2022-11-07 Nathaniel Xu

Generative models have shown strong generation ability while efficient likelihood estimation is less explored. Energy-based models~(EBMs) define a flexible energy function to parameterize unnormalized densities efficiently but are notorious…

Machine Learning · Computer Science 2024-06-11 Cong Geng , Tian Han , Peng-Tao Jiang , Hao Zhang , Jinwei Chen , Søren Hauberg , Bo Li

Score-based generative models have recently achieved remarkable success. While they are usually parameterized by the score, an alternative way is to use a series of time-dependent energy-based models (EBMs), where the score is obtained from…

Machine Learning · Statistics 2026-05-22 RuiKang OuYang , Louis Grenioux , José Miguel Hernández-Lobato

Energy-Based Models (EBMs) allow for extremely flexible specifications of probability distributions. However, they do not provide a mechanism for obtaining exact samples from these distributions. Monte Carlo techniques can aid us in…

Machine Learning · Computer Science 2021-12-13 Bryan Eikema , Germán Kruszewski , Hady Elsahar , Marc Dymetman

An energy efficient use of large scale sensor networks necessitates activating a subset of possible sensors for estimation at a fusion center. The problem is inherently combinatorial; to this end, a set of iterative, randomized algorithms…

Information Theory · Computer Science 2017-09-13 Arpan Chattopadhyay , Urbashi Mitra

Dynamic structural equation modeling (DSEM) is widely used for analyzing intensive longitudinal data (ILD). Although many ILD have categorical (Bernoulli or binomially distributed) responses, currently available Metropolis-within-Gibbs…

Computation · Statistics 2026-04-01 Øystein Sørensen , Ethan M. McCormick

Sampling from unnormalized densities using diffusion models has emerged as a powerful paradigm. However, while recent approaches that use least-squares `matching' objectives have improved scalability, they often necessitate significant…

Machine Learning · Computer Science 2026-03-03 Denis Blessing , Lorenz Richter , Julius Berner , Egor Malitskiy , Gerhard Neumann

We present a novel method for training score-based generative models which uses nonlinear noising dynamics to improve learning of structured distributions. Generalizing to a nonlinear drift allows for additional structure to be incorporated…

Machine Learning · Statistics 2025-07-10 Jeremiah Birrell , Markos A. Katsoulakis , Luc Rey-Bellet , Benjamin J. Zhang , Wei Zhu

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

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

Training energy-based models (EBMs) on discrete spaces is challenging because sampling over such spaces can be difficult. We propose to train discrete EBMs with energy discrepancy (ED), a novel type of contrastive loss functional which only…

Machine Learning · Statistics 2023-07-18 Tobias Schröder , Zijing Ou , Yingzhen Li , Andrew B. Duncan

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

Denoising diffusions are state-of-the-art generative models exhibiting remarkable empirical performance. They work by diffusing the data distribution into a Gaussian distribution and then learning to reverse this noising process to obtain…

Machine Learning · Statistics 2024-02-20 Joe Benton , Yuyang Shi , Valentin De Bortoli , George Deligiannidis , Arnaud Doucet

In the last decades, energy-based models (EBMs) have become an important class of probabilistic models in which a component of the likelihood is intractable and therefore cannot be evaluated explicitly. Consequently, parameter estimation in…

Computational Engineering, Finance, and Science · Computer Science 2026-04-10 Luca Martino

Score-based generative models have demonstrated significant practical success in data-generating tasks. The models establish a diffusion process that perturbs the ground truth data to Gaussian noise and then learn the reverse process to…

Machine Learning · Computer Science 2024-05-24 Ziqing Wen , Xiaoge Deng , Ping Luo , Tao Sun , Dongsheng Li

We introduce the Generalized Energy Based Model (GEBM) for generative modelling. These models combine two trained components: a base distribution (generally an implicit model), which can learn the support of data with low intrinsic…

Machine Learning · Statistics 2021-12-22 Michael Arbel , Liang Zhou , Arthur Gretton