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Diffusion models are gaining widespread use in cutting-edge image, video, and audio generation. Score-based diffusion models stand out among these methods, necessitating the estimation of score function of the input data distribution. In…

This survey delves into the application of diffusion models in time-series forecasting. Diffusion models are demonstrating state-of-the-art results in various fields of generative AI. The paper includes comprehensive background information…

In this paper, we derive diffusion equation models in the spectral domain for the evolution of training errors of two-layer multi-scale deep neural networks (MscaleDNN) \cite{caixu2019,liu2020multi}, designed to reduce the spectral bias of…

Diffusion models have emerged as the new state-of-the-art generative model with high quality samples, with intriguing properties such as mode coverage and high flexibility. They have also been shown to be effective inverse problem solvers,…

Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…

Gravitational lensing data is frequently collected at low resolution due to instrumental limitations and observing conditions. Machine learning-based super-resolution techniques offer a method to enhance the resolution of these images,…

Many inverse problems are ill-posed and need to be complemented by prior information that restricts the class of admissible models. Bayesian approaches encode this information as prior distributions that impose generic properties on the…

Kilometer-scale weather data is crucial for real-world applications but remains computationally intensive to produce using traditional weather simulations. An emerging solution is to use deep learning models, which offer a faster…

Diffusion models have emerged as a powerful new family of deep generative models with record-breaking performance in many applications, including image synthesis, video generation, and molecule design. In this survey, we provide an overview…

Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models,…

Diffusion models have recently emerged as powerful frameworks for generating high-quality images. While recent studies have explored their application to time series forecasting, these approaches face significant challenges in cross-modal…

Diffusion models (DM) have achieved remarkable promise in image super-resolution (SR). However, most of them are tailored to solving non-blind inverse problems with fixed known degradation settings, limiting their adaptability to real-world…

We use Deep Operator Networks (DeepONets) to perform super-resolution reconstruction of the solutions of two types of partial differential equations and compare the model predictions with the results obtained using conventional…

Atmospheric Turbulence (AT) correction is a challenging restoration task as it consists of two distortions: geometric distortion and spatially variant blur. Diffusion models have shown impressive accomplishments in photo-realistic image…

Recent diffusion models have exhibited great potential in generative modeling tasks. Part of their success can be attributed to the ability of training stable on huge sets of paired synthetic data. However, adapting these models to…

Earth System Models (ESMs) are essential for understanding the interaction between human activities and the Earth's climate. However, the computational demands of ESMs often limit the number of simulations that can be run, hindering the…

Image super-resolution is a fundamentally ill-posed problem because multiple valid high-resolution images exist for one low-resolution image. Super-resolution methods based on diffusion probabilistic models can deal with the ill-posed…

Diffusion models, as a kind of powerful generative model, have given impressive results on image super-resolution (SR) tasks. However, due to the randomness introduced in the reverse process of diffusion models, the performances of…

Reconstructing 3D objects from extremely sparse views is a long-standing and challenging problem. While recent techniques employ image diffusion models for generating plausible images at novel viewpoints or for distilling pre-trained…

Diffusion models have recently gained prominence as powerful deep generative models, demonstrating unmatched performance across various domains. However, their potential in multi-sensor fusion remains largely unexplored. In this work, we…