Related papers: Gradient-Free Score-Based Sampling Methods with En…
Diffusion models have demonstrated state-of-the-art performance across vision, language, and scientific domains. Despite their empirical success, prior theoretical analyses of the sample complexity suffer from poor scaling with input data…
Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…
In the study of natural and artificial complex systems, responses that are not completely determined by the considered decision variables are commonly modelled probabilistically, resulting in response distributions varying across decision…
A generative diffusion model is used to produce probabilistic ensembles of precipitation intensity maps at the 1-hour 5-km resolution. The generation is conditioned on infrared and microwave radiometric measurements from the GOES and DMSP…
The classical Langevin Monte Carlo method looks for samples from a target distribution by descending the samples along the gradient of the target distribution. The method enjoys a fast convergence rate. However, the numerical cost is…
Distribution-free uncertainty estimation for ensemble methods is increasingly desirable due to the widening deployment of multi-modal black-box predictive models. Conformal prediction is one approach that avoids such distributional…
This paper explores the interplay between statistics and generative artificial intelligence. Generative statistics, an integral part of the latter, aims to construct models that can generate efficiently and meaningfully new data across the…
We investigate the application of ensemble transform approaches to Bayesian inference of logistic regression problems. Our approach relies on appropriate extensions of the popular ensemble Kalman filter and the feedback particle filter to…
Score-based generative models (SGMs) have recently emerged as a promising class of generative models. However, a fundamental limitation is that their sampling process is slow due to a need for many (e.g., 2000) iterations of sequential…
This study investigates the dynamics of Score-based Generative Models (SGMs) by treating the score estimation error as a stochastic source driving the Fokker-Planck equation. Departing from particle-centric SDE analyses, we employ an SPDE…
Diffusion models are widely used in applications ranging from image generation to inverse problems. However, training diffusion models typically requires clean ground-truth images, which are unavailable in many applications. We introduce…
As a highly expressive generative model, diffusion models have demonstrated exceptional success across various domains, including image generation, natural language processing, and combinatorial optimization. However, as data distributions…
Ensembles of machine learning models yield improved system performance as well as robust and interpretable uncertainty estimates; however, their inference costs may often be prohibitively high. \emph{Ensemble Distribution Distillation} is…
Variable selection for high-dimensional, highly correlated data has long been a challenging problem, often yielding unstable and unreliable models. We propose a resample-aggregate framework that exploits diffusion models' ability to…
We present a family of \textit{Gaussian Mixture Approximation} (GMA) samplers for sampling unnormalised target densities, encompassing \textit{weights-only GMA} (W-GMA), \textit{Laplace Mixture Approximation} (LMA),…
This paper proposes a novel diffusion-based posterior sampling method within a plug-and-play (PnP) framework. Our approach constructs a probability transport from an easy-to-sample terminal distribution to the target posterior, using a…
Score-based generative modelling (SGM) has proven to be a very effective method for modelling densities on finite-dimensional spaces. In this work we propose to extend this methodology to learn generative models over functional spaces. To…
Score-based generative models have emerged as a powerful approach for sampling high-dimensional probability distributions. Despite their effectiveness, their theoretical underpinnings remain relatively underdeveloped. In this work, we study…
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…
Generative models that satisfy hard constraints are critical in many scientific and engineering applications, where physical laws or system requirements must be strictly respected. Many existing constrained generative models, especially…