Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors

• URL: http://arxiv.org/abs/2405.18782v2
• Date: Thu, 07 Nov 2024 01:31:00 GMT
• Title: Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors
• Authors: Zihui Wu, Yu Sun, Yifan Chen, Bingliang Zhang, Yisong Yue, Katherine L. Bouman,
• Abstract summary: Diffusion models (DMs) have recently shown outstanding capabilities in modeling complex image distributions. We propose a Markov chain Monte Carlo algorithm that performs posterior sampling for general inverse problems. We demonstrate the effectiveness of the proposed method on six inverse problems.
• Score: 29.203951468436145
• License:
• Abstract: Diffusion models (DMs) have recently shown outstanding capabilities in modeling complex image distributions, making them expressive image priors for solving Bayesian inverse problems. However, most existing DM-based methods rely on approximations in the generative process to be generic to different inverse problems, leading to inaccurate sample distributions that deviate from the target posterior defined within the Bayesian framework. To harness the generative power of DMs while avoiding such approximations, we propose a Markov chain Monte Carlo algorithm that performs posterior sampling for general inverse problems by reducing it to sampling the posterior of a Gaussian denoising problem. Crucially, we leverage a general DM formulation as a unified interface that allows for rigorously solving the denoising problem with a range of state-of-the-art DMs. We demonstrate the effectiveness of the proposed method on six inverse problems (three linear and three nonlinear), including a real-world black hole imaging problem. Experimental results indicate that our proposed method offers more accurate reconstructions and posterior estimation compared to existing DM-based imaging inverse methods.

Related papers

• Diffusion Prior-Based Amortized Variational Inference for Noisy Inverse Problems [12.482127049881026]
  We propose a novel approach to solve inverse problems with a diffusion prior from an amortized variational inference perspective. Our amortized inference learns a function that directly maps measurements to the implicit posterior distributions of corresponding clean data, enabling a single-step posterior sampling even for unseen measurements.
  arXiv  Detail & Related papers  (2024-07-23T02:14:18Z)
• Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priors [21.51814794909746]
  In this work, we take a different approach to define a set of intermediate and simpler posterior sampling problems, resulting in a lower approximation error compared to previous methods. We empirically demonstrate the reconstruction capability of our method for general linear inverse problems using synthetic examples and various image restoration tasks.
  arXiv  Detail & Related papers  (2024-03-18T01:47:24Z)
• Ambient Diffusion Posterior Sampling: Solving Inverse Problems with Diffusion Models trained on Corrupted Data [56.81246107125692]
  Ambient Diffusion Posterior Sampling (A-DPS) is a generative model pre-trained on one type of corruption. We show that A-DPS can sometimes outperform models trained on clean data for several image restoration tasks in both speed and performance. We extend the Ambient Diffusion framework to train MRI models with access only to Fourier subsampled multi-coil MRI measurements.
  arXiv  Detail & Related papers  (2024-03-13T17:28:20Z)
• Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models [98.95988351420334]
  We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. We theoretically analyze our algorithm showing provable sample recovery in a linear model setting.
  arXiv  Detail & Related papers  (2023-07-02T17:21:30Z)
• A Variational Perspective on Solving Inverse Problems with Diffusion Models [101.831766524264]
  Inverse tasks can be formulated as inferring a posterior distribution over data. This is however challenging in diffusion models since the nonlinear and iterative nature of the diffusion process renders the posterior intractable. We propose a variational approach that by design seeks to approximate the true posterior distribution.
  arXiv  Detail & Related papers  (2023-05-07T23:00:47Z)
• Variational Laplace Autoencoders [53.08170674326728]
  Variational autoencoders employ an amortized inference model to approximate the posterior of latent variables. We present a novel approach that addresses the limited posterior expressiveness of fully-factorized Gaussian assumption. We also present a general framework named Variational Laplace Autoencoders (VLAEs) for training deep generative models.
  arXiv  Detail & Related papers  (2022-11-30T18:59:27Z)
• JPEG Artifact Correction using Denoising Diffusion Restoration Models [110.1244240726802]
  We build upon Denoising Diffusion Restoration Models (DDRM) and propose a method for solving some non-linear inverse problems. We leverage the pseudo-inverse operator used in DDRM and generalize this concept for other measurement operators.
  arXiv  Detail & Related papers  (2022-09-23T23:47:00Z)
• Denoising Diffusion Restoration Models [110.1244240726802]
  Denoising Diffusion Restoration Models (DDRM) is an efficient, unsupervised posterior sampling method. We demonstrate DDRM's versatility on several image datasets for super-resolution, deblurring, inpainting, and colorization.
  arXiv  Detail & Related papers  (2022-01-27T20:19:07Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.