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Ordinary differential equation (ODE)-based diffusion models enable deterministic image synthesis, establishing a reversible mapping suitable for generative steganography. While prevailing methods strictly adhere to a standard normal prior,…

Diffusion models have demonstrated remarkable efficacy in generating high-quality samples. Existing diffusion-based image restoration algorithms exploit pre-trained diffusion models to leverage data priors, yet they still preserve elements…

In the paper, we develop an ensemble-based implicit sampling method for Bayesian inverse problems. For Bayesian inference, the iterative ensemble smoother (IES) and implicit sampling are integrated to obtain importance ensemble samples,…

Panchromatic (PAN) and multi-spectral (MS) image fusion, named Pan-sharpening, refers to super-resolve the low-resolution (LR) multi-spectral (MS) images in the spatial domain to generate the expected high-resolution (HR) MS images,…

Diffusion models are widely used in applications ranging from image generation to inverse problems. However, training diffusion models typically requires clean ground-truth images, which are unavailable in many applications. We introduce…

Almost all existing methods for image restoration are based on optimizing the mean squared error (MSE), even though it is known that the best estimate in terms of MSE may yield a highly atypical image due to the fact that there are many…

Inverse design problems are common in engineering and materials science. The forward direction, i.e., computing output quantities from design parameters, typically requires running a numerical simulation, such as a FEM, as an intermediate…

Posterior sampling has been shown to be a powerful Bayesian approach for solving imaging inverse problems. The recent plug-and-play unadjusted Langevin algorithm (PnP-ULA) has emerged as a promising method for Monte Carlo sampling and…

Energy-based models (EBMs) are powerful probabilistic models, but suffer from intractable sampling and density evaluation due to the partition function. As a result, inference in EBMs relies on approximate sampling algorithms, leading to a…

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…

Diffusion models are powerful tools for sampling from high-dimensional distributions by progressively transforming pure noise into structured data through a denoising process. When equipped with a guidance mechanism, these models can also…

In the realm of medical imaging, inverse problems aim to infer high-quality images from incomplete, noisy measurements, with the objective of minimizing expenses and risks to patients in clinical settings. The Diffusion Models have recently…

We propose a modular framework for hybrid image restoration that integrates transformer and state-space model (SSM) blocks with a focus on improving runtime efficiency on edge hardware. While transformers provide strong global modeling…

Snapshot back-ended reduced basis methods for dynamical systems commonly rely on the singular value decomposition of a matrix whose columns are high-fidelity solution vectors. An alternative basis generation framework is developed here. The…

One popular approach for blind deconvolution is to formulate a maximum a posteriori (MAP) problem with sparsity priors on the gradients of the latent image, and then alternatingly estimate the blur kernel and the latent image. While several…

Magnetic Resonance Imaging (MRI) is a kind of medical imaging technology used for diagnostic imaging of diseases, but its image quality may be suffered by the long acquisition time. The compressive sensing (CS) based strategy may decrease…

Deep learning methods for accelerated MRI achieve state-of-the-art results but largely ignore additional speedups possible with noncartesian sampling trajectories. To address this gap, we created a generative diffusion model-based…

Many Bayesian statistical inference problems come down to computing a maximum a-posteriori (MAP) assignment of latent variables. Yet, standard methods for estimating the MAP assignment do not have a finite time guarantee that the algorithm…

For image inpainting, the existing Denoising Diffusion Probabilistic Model (DDPM) based method i.e. RePaint can produce high-quality images for any inpainting form. It utilizes a pre-trained DDPM as a prior and generates inpainting results…

Undoing the image formation process and therefore decomposing appearance into its intrinsic properties is a challenging task due to the under-constraint nature of this inverse problem. While significant progress has been made on inferring…