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Continuous Conditional Diffusion Model (CCDM) is a diffusion-based framework designed to generate high-quality images conditioned on continuous regression labels. Although CCDM has demonstrated clear advantages over prior approaches across…

Computer Vision and Pattern Recognition · Computer Science 2026-02-03 Xin Ding , Yun Chen , Sen Zhang , Kao Zhang , Nenglun Chen , Peibei Cao , Yongwei Wang , Fei Wu

Continuous Conditional Generative Modeling (CCGM) estimates high-dimensional data distributions, such as images, conditioned on scalar continuous variables (aka regression labels). While Continuous Conditional Generative Adversarial…

Computer Vision and Pattern Recognition · Computer Science 2025-08-19 Xin Ding , Yongwei Wang , Kao Zhang , Z. Jane Wang

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

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

Boltzmann machines (BMs) are powerful energy-based generative models, but their heavy training cost has largely confined practical use to Restricted BMs (RBMs) trained with an efficient learning method called contrastive divergence. More…

Machine Learning · Computer Science 2025-12-03 Kentaro Kubo , Hayato Goto

This paper proposes a multi-grid method for learning energy-based generative ConvNet models of images. For each grid, we learn an energy-based probabilistic model where the energy function is defined by a bottom-up convolutional neural…

Machine Learning · Statistics 2020-10-16 Ruiqi Gao , Yang Lu , Junpei Zhou , Song-Chun Zhu , Ying Nian Wu

With the advent of score-matching techniques for model training and Langevin dynamics for sample generation, energy-based models (EBMs) have gained renewed interest as generative models. Recent EBMs usually use neural networks to define…

Machine Learning · Computer Science 2025-05-05 Yukun Li , Li-Ping Liu

Restricted Boltzmann machines (RBMs) and their extensions, called 'deep-belief networks', are powerful neural networks that have found applications in the fields of machine learning and artificial intelligence. The standard way to training…

Machine Learning · Computer Science 2018-10-25 Haik Manukian , Fabio L. Traversa , Massimiliano Di Ventra

Contrastive learning is a method of learning visual representations by training Deep Neural Networks (DNNs) to increase the similarity between representations of positive pairs (transformations of the same image) and reduce the similarity…

Machine Learning · Computer Science 2022-10-26 Beomsu Kim , Jong Chul Ye

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

We present a new method of training energy-based models (EBMs) for anomaly detection that leverages low-dimensional structures within data. The proposed algorithm, Manifold Projection-Diffusion Recovery (MPDR), first perturbs a data point…

Machine Learning · Computer Science 2023-10-31 Sangwoong Yoon , Young-Uk Jin , Yung-Kyun Noh , Frank C. Park

Learning algorithms for energy based Boltzmann architectures that rely on gradient descent are in general computationally prohibitive, typically due to the exponential number of terms involved in computing the partition function. In this…

Machine Learning · Computer Science 2018-07-13 Enrique Romero Merino , Ferran Mazzanti Castrillejo , Jordi Delgado Pin , David Buchaca Prats

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

Energy-based models are a simple yet powerful class of probabilistic models, but their widespread adoption has been limited by the computational burden of training them. We propose a novel loss function called Energy Discrepancy (ED) which…

Machine Learning · Statistics 2023-11-28 Tobias Schröder , Zijing Ou , Jen Ning Lim , Yingzhen Li , Sebastian J. Vollmer , Andrew B. Duncan

We study a new approach to learning energy-based models (EBMs) based on adversarial training (AT). We show that (binary) AT learns a special kind of energy function that models the support of the data distribution, and the learning process…

Machine Learning · Computer Science 2022-12-29 Xuwang Yin , Shiying Li , Gustavo K. Rohde

This paper studies a curious phenomenon in learning energy-based model (EBM) using MCMC. In each learning iteration, we generate synthesized examples by running a non-convergent, non-mixing, and non-persistent short-run MCMC toward the…

Machine Learning · Statistics 2019-11-27 Erik Nijkamp , Mitch Hill , Song-Chun Zhu , Ying Nian Wu

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

Adjoint-based design optimizations are usually computationally expensive and those costs scale with resolution. To address this, researchers have proposed machine learning approaches for inverse design that can predict higher-resolution…

Machine Learning · Computer Science 2024-08-19 Milad Habibi , Mark Fuge

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

This study investigates the effects of Markov chain Monte Carlo (MCMC) sampling in unsupervised Maximum Likelihood (ML) learning. Our attention is restricted to the family of unnormalized probability densities for which the negative log…

Machine Learning · Statistics 2019-12-02 Erik Nijkamp , Mitch Hill , Tian Han , Song-Chun Zhu , Ying Nian Wu