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In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization…

Probability · Mathematics 2018-03-30 C. Soizea , R. Ghanem , C. Safta , X. Huan , Z. P. Vane , J. Oefelein , G. Lacaz , H. N. Najm , Q. Tang , X. Chen

Diffusion models have demonstrated significant promise in various generative tasks; however, they often struggle to satisfy challenging constraints. Our approach addresses this limitation by rethinking training-free loss-guided diffusion…

Machine Learning · Computer Science 2024-11-19 William Huang , Yifeng Jiang , Tom Van Wouwe , C. Karen Liu

A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent)…

Machine Learning · Computer Science 2025-04-22 Dimitris G. Giovanis , Ellis Crabtree , Roger G. Ghanem , Ioannis G. Kevrekidis

Efficient exploration remains a central challenge in reinforcement learning, serving as a useful pretraining objective for data collection, particularly when an external reward function is unavailable. A principled formulation of the…

Machine Learning · Computer Science 2026-03-16 Jacob Adamczyk , Adam Kamoski , Rahul V. Kulkarni

Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth…

Methodology · Statistics 2017-05-01 Gabriel Loaiza-Ganem , Yuanjun Gao , John P. Cunningham

We study the problem of exploration in Reinforcement Learning and present a novel model-free solution. We adopt an information-theoretical viewpoint and start from the instance-specific lower bound of the number of samples that have to be…

Machine Learning · Computer Science 2024-07-02 Alessio Russo , Alexandre Proutiere

We study the problem of efficient exploration in order to learn an accurate model of an environment, modeled as a Markov decision process (MDP). Efficient exploration in this problem requires the agent to identify the regions in which…

Modern successes of diffusion models in learning complex, high-dimensional data distributions are attributed, in part, to their capability to construct diffusion processes with analytic transition kernels and score functions. The…

Machine Learning · Statistics 2024-03-01 Guan-Horng Liu , Tianrong Chen , Evangelos A. Theodorou , Molei Tao

Exploration in high-dimensional, continuous spaces with sparse rewards is an open problem in reinforcement learning. Artificial curiosity algorithms address this by creating rewards that lead to exploration. Given a reinforcement learning…

Machine Learning · Computer Science 2023-11-08 Alexander Nedergaard , Matthew Cook

Diffusion models have had a profound impact on many application areas, including those where data are intrinsically infinite-dimensional, such as images or time series. The standard approach is first to discretize and then to apply…

Machine Learning · Statistics 2025-06-09 Jakiw Pidstrigach , Youssef Marzouk , Sebastian Reich , Sven Wang

Addressing real-world optimization problems becomes particularly challenging when analytic objective functions or constraints are unavailable. While numerous studies have addressed the issue of unknown objectives, limited research has…

Maximum entropy reinforcement learning (MaxEnt-RL) has become the standard approach to RL due to its beneficial exploration properties. Traditionally, policies are parameterized using Gaussian distributions, which significantly limits their…

Machine Learning · Computer Science 2025-06-11 Onur Celik , Zechu Li , Denis Blessing , Ge Li , Daniel Palenicek , Jan Peters , Georgia Chalvatzaki , Gerhard Neumann

In most data-scientific approaches, the principle of Maximum Entropy (MaxEnt) is used to a posteriori justify some parametric model which has been already chosen based on experience, prior knowledge or computational simplicity. In a…

Methodology · Statistics 2022-06-29 Orestis Loukas , Ho Ryun Chung

In this work, we propose a novel framework for estimating the dimension of the data manifold using a trained diffusion model. A diffusion model approximates the score function i.e. the gradient of the log density of a noise-corrupted…

Machine Learning · Computer Science 2023-05-26 Jan Stanczuk , Georgios Batzolis , Teo Deveney , Carola-Bibiane Schönlieb

Popularized by their strong image generation performance, diffusion and related methods for generative modeling have found widespread success in visual media applications. In particular, diffusion methods have enabled new approaches to data…

Image and Video Processing · Electrical Eng. & Systems 2026-01-28 Yibo Yang , Stephan Mandt

Diffusion models have become central to various image editing tasks, yet they often fail to fully adhere to physical laws, particularly with effects like shadows, reflections, and occlusions. In this work, we address the challenge of…

Computer Vision and Pattern Recognition · Computer Science 2025-04-23 Ankit Dhiman , Manan Shah , R Venkatesh Babu

Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step…

Machine Learning · Computer Science 2024-05-21 Hyungjin Chung , Byeongsu Sim , Dohoon Ryu , Jong Chul Ye

Since its foundations, more than one hundred years ago, the field of structural biology has strived to understand and analyze the properties of molecules and their interactions by studying the structure that they take in 3D space. However,…

Biomolecules · Quantitative Biology 2023-02-27 Gabriele Corso

Flow and diffusion models are typically pre-trained on limited available data (e.g., molecular samples), covering only a fraction of the valid design space (e.g., the full molecular space). As a consequence, they tend to generate samples…

Machine Learning · Computer Science 2026-02-19 Riccardo De Santi , Kimon Protopapas , Ya-Ping Hsieh , Andreas Krause

Exploration is essential for solving complex Reinforcement Learning (RL) tasks. Maximum State-Visitation Entropy (MSVE) formulates the exploration problem as a well-defined policy optimization problem whose solution aims at visiting all…

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