Related papers: Denoising Diffusion Restoration Tackles Forward an…

Denoising diffusion models are a novel class of generative algorithms that achieve state-of-the-art performance across a range of domains, including image generation and text-to-image tasks. Building on this success, diffusion models have…

Computational fluid dynamics (CFD) is a powerful tool for modeling turbulent flow and is commonly used for urban microclimate simulations. However, traditional CFD methods are computationally intensive, requiring substantial hardware…

The Deep Operator Networks~(DeepONet) is a fundamentally different class of neural networks that we train to approximate nonlinear operators, including the solution operator of parametric partial differential equations (PDE). DeepONets have…

Diffusion bridge models establish probabilistic paths between arbitrary paired distributions and exhibit great potential for universal image restoration. Most existing methods merely treat them as simple variants of stochastic interpolants,…

Denoising diffusion models represent a recent emerging topic in computer vision, demonstrating remarkable results in the area of generative modeling. A diffusion model is a deep generative model that is based on two stages, a forward…

Inverse problems (IPs) involve reconstructing signals from noisy observations. Recently, diffusion models (DMs) have emerged as a powerful framework for solving IPs, achieving remarkable reconstruction performance. However, existing…

Solving high-dimensional parabolic partial differential equations (PDEs) with deep learning methods is often computationally and memory intensive, primarily due to the need for automatic differentiation (AD) to compute large Hessian…

Diffusion models learn to restore noisy data, which is corrupted with different levels of noise, by optimizing the weighted sum of the corresponding loss terms, i.e., denoising score matching loss. In this paper, we show that restoring data…

In the present paper we consider the problem of Laplace deconvolution with noisy discrete observations. The study is motivated by Dynamic Contrast Enhanced imaging using a bolus of contrast agent, a procedure which allows considerable…

While deep neural networks (NN) significantly advance image compressed sensing (CS) by improving reconstruction quality, the necessity of training current CS NNs from scratch constrains their effectiveness and hampers rapid deployment.…

In this paper, we evaluate the effectiveness of deep operator networks (DeepONets) in solving both forward and inverse problems of partial differential equations (PDEs) on unknown manifolds. By unknown manifolds, we identify the manifold by…

Diffusion Probabilistic Models (DPMs) have been recently utilized to deal with various blind image restoration (IR) tasks, where they have demonstrated outstanding performance in terms of perceptual quality. However, the task-specific…

In this paper, we develop an asymptotic expansion-regularization (AER) method for inverse source problems in two-dimensional nonlinear and nonstationary singularly perturbed partial differential equations (PDEs). The key idea of this…

While diffusion models have shown great success in image generation, their noise-inverting generative process does not explicitly consider the structure of images, such as their inherent multi-scale nature. Inspired by diffusion models and…

Ground-roll attenuation is a challenging seismic processing task in land seismic survey. The ground-roll coherent noise with low frequency and high amplitude seriously contaminate the valuable reflection events, corrupting the quality of…

Diffusion Probabilistic Models (DPMs) have recently shown remarkable performance in image generation tasks, which are capable of generating highly realistic images. When adopting DPMs for image restoration tasks, the crucial aspect lies in…

This paper studies the original discrete-time denoising diffusion probabilistic model (DDPM) from a probabilistic point of view. We present three main theoretical results. First, we show that the time-dependent score function associated…

Recent advancements in diffusion models have demonstrated significant success in unsupervised anomaly segmentation. For anomaly segmentation, these models are first trained on normal data; then, an anomalous image is noised to an…

Diffusion Probabilistic Models (DPMs) have emerged as the de facto approach for high-fidelity image synthesis, operating diffusion processes on continuous VAE latent, which significantly differ from the text generation methods employed by…

In medical imaging, the diffusion models have shown great potential for synthetic image generation tasks. However, these approaches often lack the interpretable connections between the generated and real images and can create anatomically…