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Probabilistic forecasting is crucial for real-world spatiotemporal systems, such as climate, energy, and urban environments, where quantifying uncertainty is essential for informed, risk-aware decision-making. While diffusion models have…

Machine Learning · Computer Science 2025-09-30 Zhi Sheng , Yuan Yuan , Yudi Zhang , Jingtao Ding , Yong Li

This work presents an autoregressive generative diffusion model (DiffObs) to predict the global evolution of daily precipitation, trained on a satellite observational product, and assessed with domain-specific diagnostics. The model is…

Computational Physics · Physics 2024-04-11 Jason Stock , Jaideep Pathak , Yair Cohen , Mike Pritchard , Piyush Garg , Dale Durran , Morteza Mardani , Noah Brenowitz

The imputation of missing values in time series has many applications in healthcare and finance. While autoregressive models are natural candidates for time series imputation, score-based diffusion models have recently outperformed existing…

Machine Learning · Computer Science 2021-10-28 Yusuke Tashiro , Jiaming Song , Yang Song , Stefano Ermon

The planning and operation of renewable energy, especially wind power, depend crucially on accurate, timely, and high-resolution weather information. Coarse-grid global numerical weather forecasts are typically downscaled to meet these…

Score-based diffusion models are a powerful class of generative models, widely utilized across diverse domains. Despite significant advancements in large-scale tasks such as text-to-image generation, their application to constrained domains…

Machine Learning · Computer Science 2025-07-15 Saeid Naderiparizi , Xiaoxuan Liang , Setareh Cohan , Berend Zwartsenberg , Frank Wood

To tackle the global climate challenge, it urgently needs to develop a collaborative platform for comprehensive weather forecasting on large-scale meteorological data. Despite urgency, heterogeneous meteorological sensors across countries…

Machine Learning · Computer Science 2023-05-30 Shengchao Chen , Guodong Long , Tao Shen , Jing Jiang

Extreme precipitation causes severe societal and economic damage, and weather control has long been discussed as a potential mitigation strategy. However, to the best of our knowledge, perturbation-based interventions for weather control…

Machine Learning · Computer Science 2026-05-15 Ayumu Ueyama , Kazuhiko Kawamoto , Hiroshi Kera

Score-based methods, such as diffusion models and Bayesian inverse problems, are often interpreted as learning the data distribution in the low-noise limit ($\sigma \to 0$). In this work, we propose an alternative perspective: their success…

Machine Learning · Statistics 2026-03-17 Xiang Li , Zebang Shen , Ya-Ping Hsieh , Niao He

The recent, impressive advances in algorithmic generation of high-fidelity image, audio, and video are largely due to great successes in score-based diffusion models. A key implementing step is score matching, that is, the estimation of the…

Machine Learning · Statistics 2024-09-12 Zehao Dou , Subhodh Kotekal , Zhehao Xu , Harrison H. Zhou

In situ and remotely sensed observations have potential to facilitate data-driven predictive models for oceanography. A suite of machine learning models, including regression, decision tree and deep learning approaches were developed to…

Atmospheric and Oceanic Physics · Physics 2020-06-24 Stefan Wolff , Fearghal O'Donncha , Bei Chen

Deep Learning has recently emerged as a perfect prognosis downscaling technique to compute high-resolution fields from large-scale coarse atmospheric data. Despite their promising results to reproduce the observed local variability, they…

Machine Learning · Computer Science 2023-05-03 Jose González-Abad , Jorge Baño-Medina , Ignacio Heredia Cachá

The success of deep learning techniques over the last decades has opened up a new avenue of research for weather forecasting. Here, we take the novel approach of using a neural network to predict full probability density functions at each…

Machine Learning · Statistics 2022-01-05 Mariana Clare , Omar Jamil , Cyril Morcrette

Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models,…

Weather forecasting is essential for various human activities. Recent data-driven models have outperformed numerical weather prediction by utilizing deep learning in forecasting performance. However, challenges remain in efficiently…

Machine Learning · Computer Science 2024-07-01 Ayumu Ueyama , Kazuhiko Kawamoto , Hiroshi Kera

Sampling based on score diffusions has led to striking empirical results, and has attracted considerable attention from various research communities. It depends on availability of (approximate) Stein score functions for various levels of…

Statistics Theory · Mathematics 2026-01-01 M. J. Wainwright

Score-based diffusion models have emerged as powerful techniques for generating samples from high-dimensional data distributions. These models involve a two-phase process: first, injecting noise to transform the data distribution into a…

Machine Learning · Computer Science 2024-10-21 Runjia Li , Qiwei Di , Quanquan Gu

Diffusion models have indeed shown great promise in solving inverse problems in image processing. In this paper, we propose a novel, problem-agnostic diffusion model called the maximum a posteriori (MAP)-based guided term estimation method…

Image and Video Processing · Electrical Eng. & Systems 2026-03-10 Pingping Tao , Haixia Liu , Jing Su

Modern weather and climate models share a common heritage, and often even components, however they are used in different ways to answer fundamentally different questions. As such, attempts to emulate them using machine learning should…

Atmospheric and Oceanic Physics · Physics 2022-03-21 Duncan Watson-Parris

Diffusion models, initially developed for image synthesis, demonstrate remarkable generative capabilities. Recently, their application has expanded to time series forecasting (TSF), yielding promising results. Existing surveys on time…

Machine Learning · Statistics 2025-09-03 Chen Su , Zhengzhou Cai , Yuanhe Tian , Zhuochao Chang , Zihong Zheng , Yan Song

Subseasonal forecasting of the weather two to six weeks in advance is critical for resource allocation and advance disaster notice but poses many challenges for the forecasting community. At this forecast horizon, physics-based dynamical…

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