Related papers: Injecting Measurement Information Yields a Fast an…

We introduced and analyzed robust recovery-based a posteriori error estimators for various lower order finite element approximations to interface problems in [9, 10], where the recoveries of the flux and/or gradient are implicit (i.e.,…

Diffusion models have found valuable applications in anomaly detection by capturing the nominal data distribution and identifying anomalies via reconstruction. Despite their merits, they struggle to localize anomalies of varying scales,…

Diffusion models have emerged as powerful learned priors for solving inverse problems. However, current iterative solving approaches which alternate between diffusion sampling and data consistency steps typically require hundreds or…

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…

Denoising Diffusion Probabilistic Models (DDPMs) have achieved impressive performance on various generation tasks. By modeling the reverse process of gradually diffusing the data distribution into a Gaussian distribution, generating a…

This work investigates both direct and inverse problems of the variable-exponent sub-diffusion model, which attracts increasing attentions in both practical applications and theoretical aspects. Based on the perturbation method, which…

Ill-posed inverse problems are fundamental in many domains, ranging from astrophysics to medical imaging. Emerging diffusion models provide a powerful prior for solving these problems. Existing maximum-a-posteriori (MAP) or posterior…

Inverse medium scattering solvers generally reconstruct a single solution without an associated measure of uncertainty. This is true both for the classical iterative solvers and for the emerging deep learning methods. But ill-posedness and…

We consider the problem of recovering a latent signal $X$ from its noisy observation $Y$. The unknown law $\mathbb{P}^X$ of $X$, and in particular its support $\mathscr{M}$, are accessible only through a large sample of i.i.d.\…

Modelling partial differential equations (PDEs) is of crucial importance in science and engineering, and it includes tasks ranging from forecasting to inverse problems, such as data assimilation. However, most previous numerical and machine…

Diffusion models are extensively used for modeling image priors for inverse problems. We introduce \emph{Diff-Unfolding}, a principled framework for learning posterior score functions of \emph{conditional diffusion models} by explicitly…

The past few years have witnessed substantial advances in image generation powered by diffusion models. However, it was shown that diffusion models are susceptible to training data memorization, raising significant concerns regarding…

Diffusion models, which convert noise into new data instances by learning to reverse a Markov diffusion process, have become a cornerstone in contemporary generative modeling. While their practical power has now been widely recognized, the…

Recently it has been shown that using diffusion models for inverse problems can lead to remarkable results. However, these approaches require a closed-form expression of the degradation model and can not support complex degradations. To…

This paper proposes a new unsupervised audio-visual speech enhancement (AVSE) approach that combines a diffusion-based audio-visual speech generative model with a non-negative matrix factorization (NMF) noise model. First, the diffusion…

Diffusion models represent the state-of-the-art for solving inverse problems such as image restoration tasks. Diffusion-based inverse solvers incorporate a likelihood term to guide prior sampling, generating data consistent with the…

Diffusion models have shown strong performances in solving inverse problems through posterior sampling while they suffer from errors during earlier steps. To mitigate this issue, several Decoupled Posterior Sampling methods have been…

Mutual information (MI) is one of the most general ways to measure relationships between random variables, but estimating this quantity for complex systems is challenging. Denoising diffusion models have recently set a new bar for density…

Diffusion models learn to denoise data and the trained denoiser is then used to generate new samples from the data distribution. In this paper, we revisit the diffusion sampling process and identify a fundamental cause of sample quality…

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…