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We study the theoretical behavior of denoising score matching--the learning task associated to diffusion models--when the data distribution is supported on a low-dimensional manifold and the score is parameterized using a random feature…

Machine Learning · Computer Science 2026-04-14 Anand Jerry George , Nicolas Macris

The notion of concept drift refers to the phenomenon that the data generating distribution changes over time; as a consequence machine learning models may become inaccurate and need adjustment. In this paper we consider the problem of…

Machine Learning · Computer Science 2022-05-16 Fabian Hinder , André Artelt , Valerie Vaquet , Barbara Hammer

Diffusion models generate high-dimensional data with remarkable quality, yet how their training efficiently learns the score function, bypassing the curse of dimensionality when data is supported on low-dimensional manifolds, remains…

Machine Learning · Computer Science 2026-05-21 Wei Huang , Andi Han , Mingyuan Bai , Huanjian Zhou , Qixin Zhang , Taiji Suzuki , Kenji Fukumizu

Weather forecasting remains a crucial yet challenging domain, where recently developed models based on deep learning (DL) have approached the performance of traditional numerical weather prediction (NWP) models. However, these DL models,…

Atmospheric and Oceanic Physics · Physics 2024-02-13 Zhanxiang Hua , Yutong He , Chengqian Ma , Alexandra Anderson-Frey

Discrete-time diffusion-based generative models and score matching methods have shown promising results in modeling high-dimensional image data. Recently, Song et al. (2021) show that diffusion processes that transform data into noise can…

Machine Learning · Computer Science 2021-10-01 Chin-Wei Huang , Jae Hyun Lim , Aaron Courville

Simulation of conditioned diffusion processes is an essential tool in inference for stochastic processes, data imputation, generative modelling, and geometric statistics. Whilst simulating diffusion bridge processes is already difficult on…

Probability · Mathematics 2024-04-24 Erlend Grong , Karen Habermann , Stefan Sommer

Diffusion models are loosely modelled based on non-equilibrium thermodynamics, where \textit{diffusion} refers to particles flowing from high-concentration regions towards low-concentration regions. In statistics, the meaning is quite…

Machine Learning · Computer Science 2023-12-19 Inga Strümke , Helge Langseth

Drift in machine learning refers to the phenomenon where the statistical properties of data or context, in which the model operates, change over time leading to a decrease in its performance. Therefore, maintaining a constant monitoring…

Computation and Language · Computer Science 2023-09-08 Saeed Khaki , Akhouri Abhinav Aditya , Zohar Karnin , Lan Ma , Olivia Pan , Samarth Marudheri Chandrashekar

Targeting to understand the underlying explainable factors behind observations and modeling the conditional generation process on these factors, we connect disentangled representation learning to Diffusion Probabilistic Models (DPMs) to…

Computer Vision and Pattern Recognition · Computer Science 2023-10-31 Tao Yang , Yuwang Wang , Yan Lv , Nanning Zheng

Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make…

Machine Learning · Computer Science 2023-06-14 Marc Finzi , Anudhyan Boral , Andrew Gordon Wilson , Fei Sha , Leonardo Zepeda-Núñez

Conditional diffusion models serve as the foundation of modern image synthesis and find extensive application in fields like computational biology and reinforcement learning. In these applications, conditional diffusion models incorporate…

Machine Learning · Computer Science 2024-03-19 Hengyu Fu , Zhuoran Yang , Mengdi Wang , Minshuo Chen

Although numerical weather forecasting methods have dominated the field, recent advances in deep learning methods, such as diffusion models, have shown promise in ensemble weather forecasting. However, such models are typically…

Machine Learning · Computer Science 2025-09-16 Kevin Valencia , Ziyang Liu , Justin Cui

Denoising Diffusion Probabilistic Models (DDPM) are powerful state-of-the-art methods used to generate synthetic data from high-dimensional data distributions and are widely used for image, audio, and video generation as well as many more…

Machine Learning · Statistics 2025-04-25 Iskander Azangulov , George Deligiannidis , Judith Rousseau

The smoothing distribution is the conditional distribution of the diffusion process in the space of trajectories given noisy observations made continuously in time. It is generally difficult to sample from this distribution. We use the…

Probability · Mathematics 2025-03-07 Oskar Eklund , Annika Lang , Moritz Schauer

Beam alignment is a key challenge in directional mmWave and THz systems, where narrow beams require accurate yet low-overhead training. Existing learning-based approaches typically predict a single beam and do not quantify uncertainty,…

Signal Processing · Electrical Eng. & Systems 2026-04-14 Esraa Fahmy Othman , Lina Bariah , Merouane Debbah

High-dimensional data are often assumed to lie on lower-dimensional manifolds. We study how to construct diffusion processes on this data manifold using only point cloud samples and without access to charts, projections, or other geometric…

Machine Learning · Computer Science 2026-05-21 Victor Kawasaki-Borruat , Clara Grotehans , Pierre Vandergheynst , Adam Gosztolai

Diffusion models are commonly interpreted as learning the score function, i.e., the gradient of the log-density of noisy data. However, this assumption implies that the target of learning is a conservative vector field, which is not…

Machine Learning · Computer Science 2025-09-03 An B. Vuong , Michael T. McCann , Javier E. Santos , Yen Ting Lin

Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…

Statistics Theory · Mathematics 2024-08-26 Andrea Montanari , Yuchen Wu

Drift theory is an intuitive tool for reasoning about random processes: It allows turning expected stepwise changes into expected first-hitting times. While drift theory is used extensively by the community studying randomized search…

Probability · Mathematics 2023-07-07 Andreas Göbel , Timo Kötzing , Martin S. Krejca

Score-based diffusion models, which generate new data by learning to reverse a diffusion process that perturbs data from the target distribution into noise, have achieved remarkable success across various generative tasks. Despite their…

Machine Learning · Computer Science 2025-01-23 Gen Li , Yuling Yan