MAP-based Problem-Agnostic diffusion model for Inverse Problems

• URL: http://arxiv.org/abs/2501.15128v1
• Date: Sat, 25 Jan 2025 08:30:15 GMT
• Title: MAP-based Problem-Agnostic diffusion model for Inverse Problems
• Authors: Pingping Tao, Haixia Liu, Jing Su, Xiaochen Yang, Hongchen Tan,
• Abstract summary: We propose a novel, problem-agnostic diffusion model called the maximum a posteriori (MAP)-based guided term estimation method for inverse problems. We design the MAP-based guided term estimation method, while the unconditional score function is approximated by an existing score network.
• Score: 8.161067848524976
• License:
• Abstract: Diffusion models have indeed shown great promise in solving inverse problems in image processing. In this paper, we propose a novel, problem-agnostic diffusion model called the maximum a posteriori (MAP)-based guided term estimation method for inverse problems. We divide the conditional score function into two terms according to Bayes' rule: the unconditional score function and the guided term. We design the MAP-based guided term estimation method, while the unconditional score function is approximated by an existing score network. To estimate the guided term, we base on the assumption that the space of clean natural images is inherently smooth, and introduce a MAP estimate of the $t$-th latent variable. We then substitute this estimation into the expression of the inverse problem and obtain the approximation of the guided term. We evaluate our method extensively on super-resolution, inpainting, and denoising tasks, and demonstrate comparable performance to DDRM, DMPS, DPS and $\Pi$GDM.

Related papers

• Geophysical inverse problems with measurement-guided diffusion models [0.4532517021515834]
  I consider two sampling algorithms recently proposed under the name of Diffusion Posterior Sampling (DPS) and Pseudo-inverse Guided Diffusion Model (PGDM) In DPS, the guidance term is obtained by applying the adjoint of the modeling operator to the residual obtained from a one-step denoising estimate of the solution. On the other hand, PGDM utilizes a pseudo-inverse operator that originates from the fact that the one-step denoised solution is not assumed to be deterministic.
  arXiv  Detail & Related papers  (2025-01-08T23:33:50Z)
• Total Uncertainty Quantification in Inverse PDE Solutions Obtained with Reduced-Order Deep Learning Surrogate Models [50.90868087591973]
  We propose an approximate Bayesian method for quantifying the total uncertainty in inverse PDE solutions obtained with machine learning surrogate models. We test the proposed framework by comparing it with the iterative ensemble smoother and deep ensembling methods for a non-linear diffusion equation.
  arXiv  Detail & Related papers  (2024-08-20T19:06:02Z)
• Inverse Problems with Diffusion Models: A MAP Estimation Perspective [5.002087490888723]
  In Computer, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. We propose a MAP estimation framework to model the reverse conditional generation process of a continuous time diffusion model. We use our proposed framework to develop effective algorithms for image restoration.
  arXiv  Detail & Related papers  (2024-07-27T15:41:13Z)
• Bayesian Conditioned Diffusion Models for Inverse Problems [11.67269909384503]
  Diffusion models excel in many image reconstruction tasks that involve inverse problems based on a forward measurement operator. We propose a novel Bayesian conditioning technique for diffusion models, BCDM, based on score-functions associated with the conditional distribution of desired images. We show state-of-the-art performance in image dealiasing, deblurring, super-resolution, and inpainting with the proposed technique.
  arXiv  Detail & Related papers  (2024-06-14T07:13:03Z)
• BlindDiff: Empowering Degradation Modelling in Diffusion Models for Blind Image Super-Resolution [52.47005445345593]
  BlindDiff is a DM-based blind SR method to tackle the blind degradation settings in SISR. BlindDiff seamlessly integrates the MAP-based optimization into DMs. Experiments on both synthetic and real-world datasets show that BlindDiff achieves the state-of-the-art performance.
  arXiv  Detail & Related papers  (2024-03-15T11:21:34Z)
• Posterior Sampling Based on Gradient Flows of the MMD with Negative Distance Kernel [2.199065293049186]
  conditional flows of the maximum mean discrepancy (MMD) with the negative distance kernel for posterior sampling and conditional generative modeling. We approximate the joint distribution of the ground truth and the observations using discrete Wasserstein gradient flows.
  arXiv  Detail & Related papers  (2023-10-04T11:40:02Z)
• Fast Diffusion EM: a diffusion model for blind inverse problems with application to deconvolution [0.0]
  Current methods assume the degradation to be known and provide impressive results in terms of restoration and diversity. In this work, we leverage the efficiency of those models to jointly estimate the restored image and unknown parameters of the kernel model. Our method alternates between approximating the expected log-likelihood of the problem using samples drawn from a diffusion model and a step to estimate unknown model parameters.
  arXiv  Detail & Related papers  (2023-09-01T06:47:13Z)
• 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)
• Improving Diffusion Models for Inverse Problems using Manifold Constraints [55.91148172752894]
  We show that current solvers throw the sample path off the data manifold, and hence the error accumulates. To address this, we propose an additional correction term inspired by the manifold constraint. We show that our method is superior to the previous methods both theoretically and empirically.
  arXiv  Detail & Related papers  (2022-06-02T09:06:10Z)
• Posterior temperature optimized Bayesian models for inverse problems in medical imaging [59.82184400837329]
  We present an unsupervised Bayesian approach to inverse problems in medical imaging using mean-field variational inference with a fully tempered posterior. We show that an optimized posterior temperature leads to improved accuracy and uncertainty estimation. Our source code is publicly available at calibrated.com/Cardio-AI/mfvi-dip-mia.
  arXiv  Detail & Related papers  (2022-02-02T12:16:33Z)
• Parallel Stochastic Mirror Descent for MDPs [72.75921150912556]
  We consider the problem of learning the optimal policy for infinite-horizon Markov decision processes (MDPs) Some variant of Mirror Descent is proposed for convex programming problems with Lipschitz-continuous functionals. We analyze this algorithm in a general case and obtain an estimate of the convergence rate that does not accumulate errors during the operation of the method.
  arXiv  Detail & Related papers  (2021-02-27T19:28:39Z)

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.