Related papers: Product of Gaussian Mixture Diffusion Model for no…

In this work we tackle the problem of estimating the density $ f_X $ of a random variable $ X $ by successive smoothing, such that the smoothed random variable $ Y $ fulfills the diffusion partial differential equation $ (\partial_t -…

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…

We present a concise, self-contained derivation of diffusion-based generative models. Starting from basic properties of Gaussian distributions (densities, quadratic expectations, re-parameterisation, products, and KL divergences), we…

Recent diffusion models have achieved promising performances in audio-denoising tasks. The unique property of the reverse process could recover clean signals. However, the distribution of real-world noises does not comply with a single…

We explain how to use diffusion models to learn inverse renormalization group flows of statistical and quantum field theories. Diffusion models are a class of machine learning models which have been used to generate samples from complex…

Supervised deep learning methods have shown promise in undersampled Magnetic Resonance Imaging (MRI) reconstruction, but their requirement for paired data limits their generalizability to the diverse MRI acquisition parameters. Recently,…

We propose a novel framework for joint magnetic resonance image reconstruction and uncertainty quantification using under-sampled k-space measurements. The problem is formulated as a Bayesian linear inverse problem, where prior…

Diffusion models have become a popular approach for image generation and reconstruction due to their numerous advantages. However, most diffusion-based inverse problem-solving methods only deal with 2D images, and even recently published 3D…

Recovering a signal from its degraded measurements is a long standing challenge in science and engineering. Recently, zero-shot diffusion based methods have been proposed for such inverse problems, offering a posterior sampling based…

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…

Diffusion models have emerged as powerful tools for solving inverse problems, yet prior work has primarily focused on observations with Gaussian measurement noise, restricting their use in real-world scenarios. This limitation persists due…

This paper proposes using a Gaussian mixture model as a prior, for solving two image inverse problems, namely image deblurring and compressive imaging. We capitalize on the fact that variable splitting algorithms, like ADMM, are able to…

Image restoration aims to recover high-quality images from degraded observations. When the degradation process is known, the recovery problem can be formulated as an inverse problem, and in a Bayesian context, the goal is to sample a clean…

Even in low dimensions, sampling from multi-modal distributions is challenging. We provide the first sampling algorithm for a broad class of distributions -- including all Gaussian mixtures -- with a query complexity that is polynomial in…

Ill-posed imaging inverse problems remain challenging due to the ambiguity in mapping degraded observations to clean images. Diffusion-based generative priors have recently shown promise, but typically rely on computationally intensive…

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…

While learned image compression (LIC) focuses on efficient data transmission, generative image compression (GIC) extends this framework by integrating generative modeling to produce photo-realistic reconstructed images. In this paper, we…

We present GSD, a diffusion model approach based on Gaussian Splatting (GS) representation for 3D object reconstruction from a single view. Prior works suffer from inconsistent 3D geometry or mediocre rendering quality due to improper…

Diffusion model is the most advanced method in image generation and has been successfully applied to MRI reconstruction. However, the existing methods do not consider the characteristics of multi-coil acquisition of MRI data. Therefore, we…

The reconstruction of unsteady flow fields from limited measurements is a challenging and crucial task for many engineering applications. Machine learning models are gaining popularity for solving this problem due to their ability to learn…