The success of diffusion probabilistic models in generative tasks, such as text-to-image generation, has motivated the exploration of their application to regression problems commonly encountered in scientific computing and various other domains. In this context, the use of diffusion regression models for ensemble prediction is becoming a practice with increasing popularity. Under such background, we conducted a study to quantitatively evaluate the effectiveness of ensemble methods on solving different regression problems using diffusion models. We consider the ensemble prediction of a diffusion model as a means for zero-shot uncertainty quantification, since the diffusion models in our study are not trained with a loss function containing any uncertainty estimation. Through extensive experiments on 1D and 2D data, we demonstrate that ensemble methods consistently improve model prediction accuracy across various regression tasks. Notably, we observed a larger accuracy gain in auto-regressive prediction compared with point-wise prediction, and that enhancements take place in both the mean-square error and the physics-informed loss. Additionally, we reveal a statistical correlation between ensemble prediction error and ensemble variance, offering insights into balancing computational complexity with prediction accuracy and monitoring prediction confidence in practical applications where the ground truth is unknown. Our study provides a comprehensive view of the utility of diffusion ensembles, serving as a useful reference for practitioners employing diffusion models in regression problem-solving.
Uncertainty Quantification in Probabilistic Machine Learning Models: Theory, Methods, and Insights
Weill Cornell Medicine, Cornell University, New York, NY（韦尔·科恩医学中心，康奈尔大学，纽约，纽约）；Department of Electrical and Computer Engineering, Stony Brook University, Stony Brook, NY（电气与计算机工程系，史泰文斯布鲁克大学，史泰文斯布鲁克，纽约）
Comparison of Deterministic and Probabilistic Machine Learning Algorithms for Precise Dimensional Control and Uncertainty Quantification in Additive Manufacturing
Center for Nanoscale Materials, Argonne National Laboratory（阿贡国家实验室纳米尺度材料中心）；Department of Mechanical and Industrial Engineering, University of Illinois, Chicago（伊利诺伊大学芝加哥分校机械与工业工程系）；Shell International Exploration and Production Inc.（壳牌国际勘探与生产公司）
Analyzing Uncertainty Quantification in Statistical and Deep Learning Models for Probabilistic Electricity Price Forecasting
Institute of Energy Engineering and Energy Economics, Ulm University of Applied Sciences（能源工程与经济学研究所，乌尔姆应用科学大学）；Faculty of Mathematics and Economics, Ulm University（数学与经济学学院，乌尔姆大学）；Faculty of Statistics, TU Dortmund University（统计学院，多特蒙德技术大学）
Probabilistic operator learning: generative modeling and uncertainty quantification for foundation models of differential equations
Division of Applied Mathematics, Brown University（布朗大学应用数学系）；Department of Mathematics, University of California, Riverside（加州大学河滨分校数学系）；Department of Mathematics, University of California, Los Angeles（加州大学洛杉矶分校数学系）；Department of Mathematics and Statistics, University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校数学与统计学系）
Probabilistic electrical power demand forecasting with uncertainty quantification
Nepal College of Information Technology（尼泊尔信息技术学院）；Nepal Telecommunications Authority（尼泊尔电信管理局）；Nepal Electricity Authority（尼泊尔电力局）；University of Bergen（卑尔根大学）；Western Norway University of Applied Sciences（挪威西部应用科学大学）
alpha-Deep Probabilistic Inference (alpha-DPI): efficient uncertainty quantification from exoplanet astrometry to black hole feature extraction
California Institute of Technology（加州理工学院）；Perimeter Institute for Theoretical Physics（圆周理论物理研究所）；University of Waterloo（滑铁卢大学）；Harvard University（哈佛大学）；Center for Astrophysics — Harvard & Smithsonian（哈佛-史密森尼天体物理中心）
Uncertainty quantification for probabilistic machine learning in earth observation using conformal prediction
Stellenbosch University（斯泰伦博斯大学）；The Nature Conservancy（大自然保护协会）；University of Cape Town（开普敦大学）；Norwegian Institute for Nature Research—NINA（挪威自然研究所—NINA）；Jet Propulsion Laboratory（喷气推进实验室）；California Institute of Technology（加州理工学院）；South African Environmental Observation Network（南非环境观测网络）
On the Predictive Skill of Artificial Intelligence-based Weather Models for Extreme Events using Uncertainty Quantification
Applied Machine Learning Group（应用机器学习组）；Fraunhofer Heinrich-Hertz Institute（弗劳恩霍夫海因里希-赫兹研究所）；Signal Theory and Communications Dept.（信号理论与通信系）；Universidad Carlos III de Madrid (UC3M)（马德里卡洛斯三世大学）
Probabilistic Forecasting of Electric Vehicle Charging in a Time-varying Hierarchical Infrastructure
Laboratoire de Mathematiques d’Orsay, Université Paris-Saclay, CNRS, INRIA（奥赛数学实验室，巴黎萨克雷大学，法国国家科学研究中心，法国国家信息与自动化研究所）；Université Paris-Cité（巴黎西岱大学）；Electricité de France R&D（法国电力公司研发部）
A Comprehensive Framework for Uncertainty Quantification of Voxel-wise Supervised Models in IVIM MRI
Department of Acute Brain（急性脑和心血管损伤部门）；Department of Neuroscience（神经科学部门）；Istituto di Ricerche Farmacologiche Mario Negri IRCCS（马里奥·内格里药理研究所）；Milan（米兰）；Italy（意大利）
AODDiff: Probabilistic Reconstruction of Aerosol Optical Depth via Diffusion-based Bayesian Inference
State Key Laboratory of Fire Science（火灾科学国家重点实验室）；University of Science and Technology of China（中国科学技术大学）；Fire Research Division（火灾研究部）；National Institute of Standards and Technology（美国国家标准与技术研究院）
Probabilistic neural operators for functional uncertainty quantification
Ludwig-Maximilians-Universität München（慕尼黑大学）；Munich Center for Machine Learning (MCML)（慕尼黑机器学习中心）；University of Tromsø（特罗姆瑟大学）；DLR-German Aerospace Center（德国航空航天中心）
Improved probabilistic regression using diffusion models
Ludwig-Maximilians-Universität München（慕尼黑莱布尼茨大学）；Munich Center for Machine Learning (MCML)（慕尼黑机器学习中心）；University of Tromsø（特罗姆斯大学）；DLR-German Aerospace Center（德国航空航天中心）
Quantile Regression, Variational Autoencoders, and Diffusion Models for Uncertainty Quantification: A Spatial Analysis of Sub-seasonal Wind Speed Prediction
Beyond Expected Goals: A Probabilistic Framework for Shot Occurrences in Soccer
Department of Statistics & Data Science, University of Pennsylvania（统计与数据科学系，宾夕法尼亚大学）；Department of Computer & Information Science, University of Pennsylvania（计算机与信息科学系，宾夕法尼亚大学）
