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Diffusion models have become a leading framework in generative modeling, yet their theoretical understanding -- especially for high-dimensional data concentrated on low-dimensional structures -- remains incomplete. This paper investigates…

Earth System Models (ESMs) are essential tools for understanding the impact of human actions on Earth's climate. One key application of these models is studying extreme weather events, such as heat waves or dry spells, which have…

The recent wave of large-scale text-to-image diffusion models has dramatically increased our text-based image generation abilities. These models can generate realistic images for a staggering variety of prompts and exhibit impressive…

Conditional diffusion models have exhibited superior performance in high-fidelity text-guided visual generation and editing. Nevertheless, prevailing text-guided visual diffusion models primarily focus on incorporating text-visual…

This study aims to improve the spatial representation of uncertainties when regressing surface wind speeds from large-scale atmospheric predictors for sub-seasonal forecasting. Sub-seasonal forecasting often relies on large-scale…

As a class of generative artificial intelligence frameworks inspired by statistical physics, diffusion models have shown extraordinary performance in synthesizing complicated data distributions through a denoising process gradually guided…

We present a dynamic model in which the weights are conditioned on an input sample x and are learned to match those that would be obtained by finetuning a base model on x and its label y. This mapping between an input sample and network…

Generative diffusion models synthesize new samples by reversing a diffusive process that converts a given data set to generic noise. This is accomplished by training a neural network to match the gradient of the log of the probability…

Diffusion models have emerged as powerful generative priors for high-dimensional inverse problems, yet learning them when only corrupted or noisy observations are available remains challenging. In this work, we propose a new method for…

We propose a deep generative approach to sampling from a conditional distribution based on a unified formulation of conditional distribution and generalized nonparametric regression function using the noise-outsourcing lemma. The proposed…

Guided diffusion is a technique for conditioning the output of a diffusion model at sampling time without retraining the network for each specific task. One drawback of diffusion models, however, is their slow sampling process. Recent…

As Diffusion Models have shown promising performance, a lot of efforts have been made to improve the controllability of Diffusion Models. However, how to train Diffusion Models to have the disentangled latent spaces and how to naturally…

Diffusion models have emerged as powerful tools for high-quality image generation and editing, but guiding these models to produce specific outputs remains a challenge. Conventional approaches rely on conditioning mechanisms, such as text…

Diffusion models have demonstrated strong performance in time series forecasting, yet often suffer from semantic misalignment between generated trajectories and conditioning covariates, especially under complex or multimodal conditions. To…

Diffusion models are a class of generative models that serve to establish a stochastic transport map between an empirically observed, yet unknown, target distribution and a known prior. Despite their remarkable success in real-world…

Diffusion models have recently emerged as powerful tools for missing data imputation by modeling the joint distribution of observed and unobserved variables. However, existing methods, typically based on stochastic denoising diffusion…

Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…

We propose a framework to perform Bayesian inference using conditional score-based diffusion models to solve a class of inverse problems in mechanics involving the inference of a specimen's spatially varying material properties from noisy…

Diffusion models have emerged as powerful generative models in the text-to-image domain. This paper studies their application as observation-to-action models for imitating human behaviour in sequential environments. Human behaviour is…

In this work, we propose FastDPM, a unified framework for fast sampling in diffusion probabilistic models. FastDPM generalizes previous methods and gives rise to new algorithms with improved sample quality. We systematically investigate the…