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Inverse problems, where the goal is to recover an unknown signal from noisy or incomplete measurements, are central to applications in medical imaging, remote sensing, and computational biology. Diffusion models have recently emerged as…

Diffusion Posterior Sampling(DPS) methodology is a novel framework that permits nonlinear CT reconstruction by integrating a diffusion prior and an analytic physical system model, allowing for one-time training for different applications.…

Unified image restoration is a significantly challenging task in low-level vision. Existing methods either make tailored designs for specific tasks, limiting their generalizability across various types of degradation, or rely on training…

Blind image separation (BIS) refers to the inverse problem of simultaneously estimating and restoring multiple independent source images from a single observation image under conditions of unknown mixing mode and without prior knowledge of…

In this work, we introduce a new deep learning approach based on diffusion posterior sampling (DPS) to perform material decomposition from spectral CT measurements. This approach combines sophisticated prior knowledge from unsupervised…

Standard diffusion models (DMs) rely on the total destruction of data into non-informative white noise, forcing the backward process to denoise from a fully unstructured noise state. While ensuring diversity, this results in a cumbersome…

The inverse imaging task in radio interferometry is a key limiting factor to retrieving Bayesian uncertainties in radio astronomy in a computationally effective manner. We use a score-based prior derived from optical images of galaxies to…

Incoherent k-space undersampling and deep learning-based reconstruction methods have shown great success in accelerating MRI. However, the performance of most previous methods will degrade dramatically under high acceleration factors, e.g.,…

Diffusion Posterior Sampling (DPS) provides a principled Bayesian approach to inverse problems by sampling from $p(x_0 \mid y)$. While posterior sampling is valuable for capturing uncertainty and multi-modality, many classical and practical…

Inverse problems are prevalent across various disciplines in science and engineering. In the field of computer vision, tasks such as inpainting, deblurring, and super-resolution are commonly formulated as inverse problems. Recently,…

Inverse problems are fundamental to science and engineering, where the goal is to infer an underlying signal or state from incomplete or noisy measurements. Recent approaches employ diffusion models as powerful implicit priors for such…

Solving image inverse problems (e.g., super-resolution and inpainting) requires generating a high fidelity image that matches the given input (the low-resolution image or the masked image). By using the input image as guidance, we can…

Denoising diffusion models (DDMs) have recently attracted increasing attention by showing impressive synthesis quality. DDMs are built on a diffusion process that pushes data to the noise distribution and the models learn to denoise. In…

Ptychography is a data-intensive computational imaging technique that achieves high spatial resolution over large fields of view. The technique involves scanning a coherent beam across overlapping regions and recording diffraction patterns.…

We present a Bayesian machine learning architecture that combines a physically motivated parametrization and an analytic error model for the likelihood with a deep generative model providing a powerful data-driven prior for complex signals.…

Diffusion models are the current state-of-the-art for solving inverse problems in imaging. Their impressive generative capability allows them to approximate sampling from a prior distribution, which alongside a known likelihood function…

This paper addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive noise, (2) the problem is ill-posed and regularization is introduced in a Bayesian framework by an a…

Recovering high-dimensional signals from corrupted measurements is a central challenge in inverse problems. Recent advances in generative diffusion models have shown remarkable empirical success in providing strong data-driven priors, but…

Hyperspectral imaging has become a significant source of valuable data for astronomers over the past decades. Current instrumental and observing time constraints allow direct acquisition of multispectral images, with high spatial but low…

We propose a data-efficient, physics-aware generative framework in function space for inverse PDE problems. Existing plug-and-play diffusion posterior samplers represent physics implicitly through joint coefficient-solution modeling,…