Related papers: Function-Space Decoupled Diffusion for Forward and…

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,…

We propose a general framework for conditional sampling in PDE-based inverse problems, targeting the recovery of whole solutions from extremely sparse or noisy measurements. This is accomplished by a function-space diffusion model and…

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 models have emerged as a powerful foundation model for visual generations. With an appropriate sampling process, it can effectively serve as a generative prior for solving general inverse problems. Current posterior sampling-based…

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…

This paper proposes a novel approach to spectral computed tomography (CT) material decomposition that uses the recent advances in generative diffusion models (DMs) for inverse problems. Spectral CT and more particularly photon-counting CT…

Many spectral CT applications require accurate material decomposition. Existing material decomposition algorithms are often susceptible to significant noise magnification or, in the case of one-step model-based approaches, hampered by slow…

We provide a framework for solving inverse problems with diffusion models learned from linearly corrupted data. Firstly, we extend the Ambient Diffusion framework to enable training directly from measurements corrupted in the Fourier…

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…

Flow matching is a recent state-of-the-art framework for generative modeling based on ordinary differential equations (ODEs). While closely related to diffusion models, it provides a more general perspective on generative modeling. Although…

Diffusion Posterior Sampling (DPS) can be used in Computed Tomography (CT) reconstruction by leveraging diffusion-based generative models for unconditional image synthesis while matching the observations (data) of a CT scan. Of particular…

Inverse problems exist in many disciplines of science and engineering. In computer vision, for example, tasks such as inpainting, deblurring, and super resolution can be effectively modeled as inverse problems. Recently, denoising diffusion…

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.…

With the rapid development of diffusion models and flow-based generative models, there has been a surge of interests in solving noisy linear inverse problems, e.g., super-resolution, deblurring, denoising, colorization, etc, with generative…

Accurately capturing the full-range response of structures is crucial in structural health monitoring (SHM) for ensuring safety and operational integrity. However, limited sensor deployment due to cost, accessibility, or scale often hinders…

Deep generative models have emerged as state-of-the-art for solving inverse problems, but applying them to inverse problems for PDEs, like electrical impedance tomography (EIT) remains challenging. Because physical domains are naturally…

Diffusion models have been used in cosmological applications as a generative model for fast simulations and to reconstruct underlying cosmological fields or astrophysical images from noisy data. These two tasks are often treated as…

Diffusion-based posterior samplers use pretrained diffusion priors to sample from measurement- or reward-conditioned posteriors, and are widely used for inverse problems. Yet their theoretical behavior remains poorly understood: even with…

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…

Deconvolution of astronomical images is a key aspect of recovering the intrinsic properties of celestial objects, especially when considering ground-based observations. This paper explores the use of diffusion models (DMs) and the Diffusion…