Related papers: A Mixture-Based Framework for Guiding Diffusion Mo…

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…

Recent advancements in solving Bayesian inverse problems have spotlighted denoising diffusion models (DDMs) as effective priors. Although these have great potential, DDM priors yield complex posterior distributions that are challenging to…

Diffusion models have recently shown considerable potential in solving Bayesian inverse problems when used as priors. However, sampling from the resulting denoising posterior distributions remains a challenge as it involves intractable…

In recent years, denoising problems have become intertwined with the development of deep generative models. In particular, diffusion models are trained like denoisers, and the distribution they model coincide with denoising priors in the…

We focus on Bayesian inverse problems with Gaussian likelihood, linear forward model, and priors that can be formulated as a Gaussian mixture. Such a mixture is expressed as an integral of Gaussian density functions weighted by a mixing…

While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However,…

While diffusion priors generate high-quality posterior samples across many inverse problems, they are often trained on limited training sets or purely simulated data, thus inheriting the errors and biases of these underlying sources.…

Diffusion models have been recently studied as powerful generative inverse problem solvers, owing to their high quality reconstructions and the ease of combining existing iterative solvers. However, most works focus on solving simple linear…

Pre-trained diffusion models have been successfully used as priors in a variety of linear inverse problems, where the goal is to reconstruct a signal from noisy linear measurements. However, existing approaches require knowledge of the…

Diffusion models can generate a variety of high-quality images by modeling complex data distributions. Trained diffusion models can also be very effective image priors for solving inverse problems. Most of the existing diffusion-based…

Diffusion models (DMs) have proven to be effective in modeling high-dimensional distributions, leading to their widespread adoption for representing complex priors in Bayesian inverse problems (BIPs). However, current DM-based posterior…

Full Bayesian posteriors are rarely analytically tractable, which is why real-world Bayesian inference heavily relies on approximate techniques. Approximations generally differ from the true posterior and require diagnostic tools to assess…

Using diffusion priors to solve inverse problems in imaging have significantly matured over the years. In this chapter, we review the various different approaches that were proposed over the years. We categorize the approaches into the more…

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…

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…

Diffusion models enable the synthesis of highly accurate samples from complex distributions and have become foundational in generative modeling. Recently, they have demonstrated significant potential for solving Bayesian inverse problems by…

In recent years, the ascendance of diffusion modeling as a state-of-the-art generative modeling approach has spurred significant interest in their use as priors in Bayesian inverse problems. However, it is unclear how to optimally integrate…

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…

We propose a statistical benchmark for diffusion posterior sampling (DPS) algorithms for Bayesian linear inverse problems. The benchmark synthesizes signals from sparse L\'evy-process priors whose posteriors admit efficient Gibbs methods.…

Diffusion models have become increasingly popular for generative modeling due to their ability to generate high-quality samples. This has unlocked exciting new possibilities for solving inverse problems, especially in image restoration and…