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Recovering high-dimensional statistical structure from limited measurements is a fundamental challenge in hyperspectral imaging, where capturing full-resolution data is often infeasible due to sensor, bandwidth, or acquisition constraints.…

Diffusion models provide powerful generative priors for solving inverse problems by sampling from a posterior distribution conditioned on corrupted measurements. Existing methods primarily follow two paradigms: direct methods, which…

Diffusion models have been used as priors for solving inverse problems. However, existing approaches typically overlook side information that could significantly improve reconstruction quality, especially in severely ill-posed settings. In…

This work considers a nonlinear inverse source problem in a coupled diffusion equation from the terminal observation. Theoretically, under some conditions on problem data, we build the uniqueness theorem for this inverse problem and show…

Existing diffusion-based methods for inverse problems sample from the posterior using score functions and accept the generated random samples as solutions. In applications that posterior mean is preferred, we have to generate multiple…

Given a noisy linear measurement $y = Ax + \xi$ of a distribution $p(x)$, and a good approximation to the prior $p(x)$, when can we sample from the posterior $p(x \mid y)$? Posterior sampling provides an accurate and fair framework for…

Existing approaches to diffusion-based inverse problem solvers frame the signal recovery task as a probabilistic sampling episode, where the solution is drawn from the desired posterior distribution. This framework suffers from several…

We present Wideband Back-Projection Diffusion, an end-to-end probabilistic framework for approximating the posterior distribution induced by the inverse scattering map from wideband scattering data. This framework produces highly accurate…

Diffusion models, which convert noise into new data instances by learning to reverse a diffusion process, have become a cornerstone in contemporary generative modeling. In this work, we develop non-asymptotic convergence theory for a…

We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our…

We present a likelihood-free probabilistic inversion method based on normalizing flows for high-dimensional inverse problems. The proposed method is composed of two complementary networks: a summary network for data compression and an…

Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift…

In this paper, we apply a recently developed nonparametric modeling approach, the "diffusion forecast", to predict the time-evolution of Fourier modes of turbulent dynamical systems. While the diffusion forecasting method assumes the…

Recently, research on denoising diffusion models has expanded its application to the field of image restoration. Traditional diffusion-based image restoration methods utilize degraded images as conditional input to effectively guide the…

Inverse problems arise in a multitude of applications, where the goal is to recover a clean signal from noisy and possibly (non)linear observations. The difficulty of a reconstruction problem depends on multiple factors, such as the ground…

This book presents the core principles that have guided the development of diffusion models, tracing their origins and showing how diverse formulations arise from shared mathematical ideas. Diffusion modeling starts by defining a forward…

Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…

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…

Recent advancements in text-guided diffusion models have unlocked powerful image manipulation capabilities. However, applying these methods to real images necessitates the inversion of the images into the domain of the pretrained diffusion…

Diffusion models have emerged as powerful priors for image editing tasks such as inpainting and local modification, where the objective is to generate realistic content that remains consistent with observed regions. In particular, zero-shot…