Solving Diffusion Inverse Problems with Restart Posterior Sampling

• URL: http://arxiv.org/abs/2511.20705v1
• Date: Mon, 24 Nov 2025 20:42:33 GMT
• Title: Solving Diffusion Inverse Problems with Restart Posterior Sampling
• Authors: Bilal Ahmed, Joseph G. Makin,
• Abstract summary: Inverse problems are fundamental to science and engineering, where the goal is to infer an underlying signal or state from noisy measurements.<n>Recent approaches employ diffusion models as powerful implicit priors for such problems, owing to their ability to capture complex data distributions.<n>We propose Restart for Posterior Sampling (RePS), a general and efficient framework for solving both linear and non-linear inverse problems.
• Score: 2.9527010146189556
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Inverse problems are fundamental to science and engineering, where the goal is to infer an underlying signal or state from incomplete or noisy measurements. Recent approaches employ diffusion models as powerful implicit priors for such problems, owing to their ability to capture complex data distributions. However, existing diffusion-based methods for inverse problems often rely on strong approximations of the posterior distribution, require computationally expensive gradient backpropagation through the score network, or are restricted to linear measurement models. In this work, we propose Restart for Posterior Sampling (RePS), a general and efficient framework for solving both linear and non-linear inverse problems using pre-trained diffusion models. RePS builds on the idea of restart-based sampling, previously shown to improve sample quality in unconditional diffusion, and extends it to posterior inference. Our method employs a conditioned ODE applicable to any differentiable measurement model and introduces a simplified restart strategy that contracts accumulated approximation errors during sampling. Unlike some of the prior approaches, RePS avoids backpropagation through the score network, substantially reducing computational cost. We demonstrate that RePS achieves faster convergence and superior reconstruction quality compared to existing diffusion-based baselines across a range of inverse problems, including both linear and non-linear settings.

Related papers

• Solving ill-conditioned polynomial equations using score-based priors with application to multi-target detection [4.009569125126148]
  We propose a new framework that integrates score-based diffusion priors with moment-based estimators to regularize inverse problems.<n>As a concrete application, we study the multi-target detection (MTD) model in the high-noise regime.<n>We demonstrate two main results: (i) diffusion priors substantially improve recovery from third-order moments, and (ii) they make the super-resolution MTD problem, otherwise ill-posed, feasible.
  arXiv  Detail & Related papers  (2025-09-14T19:21:32Z)
• Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach [19.860268382547357]
  Current DM-based posterior sampling methods rely on approximations to the generative process.<n>We propose an ensemble-based algorithm that performs posterior sampling without the use of approximations.<n>Our algorithm is motivated by existing works that combine DM-based methods with the sequential Monte Carlo method.
  arXiv  Detail & Related papers  (2025-06-04T14:09:25Z)
• EquiReg: Equivariance Regularized Diffusion for Inverse Problems [67.01847869495558]
  We propose EquiReg diffusion, a framework for regularizing posterior sampling in diffusion-based inverse problem solvers.<n>When applied to a variety of solvers, EquiReg outperforms state-of-the-art diffusion models in both linear and nonlinear image restoration tasks.
  arXiv  Detail & Related papers  (2025-05-29T01:25:43Z)
• Diffusion State-Guided Projected Gradient for Inverse Problems [82.24625224110099]
  We propose Diffusion State-Guided Projected Gradient (DiffStateGrad) for inverse problems.<n>DiffStateGrad projects the measurement gradient onto a subspace that is a low-rank approximation of an intermediate state of the diffusion process.<n>We highlight that DiffStateGrad improves the robustness of diffusion models in terms of the choice of measurement guidance step size and noise.
  arXiv  Detail & Related papers  (2024-10-04T14:26:54Z)
• Amortized Posterior Sampling with Diffusion Prior Distillation [55.03585818289934]
  Amortized Posterior Sampling is a novel variational inference approach for efficient posterior sampling in inverse problems.<n>Our method trains a conditional flow model to minimize the divergence between the variational distribution and the posterior distribution implicitly defined by the diffusion model.<n>Unlike existing methods, our approach is unsupervised, requires no paired training data, and is applicable to both Euclidean and non-Euclidean domains.
  arXiv  Detail & Related papers  (2024-07-25T09:53:12Z)
• 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)
• Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance [52.093434664236014]
  Recent diffusion models provide a promising zero-shot solution to noisy linear inverse problems without retraining for specific inverse problems. Inspired by this finding, we propose to improve recent methods by using more principled covariance determined by maximum likelihood estimation.
  arXiv  Detail & Related papers  (2024-02-03T13:35:39Z)
• 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)
• Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems [64.29491112653905]
  We propose a novel and efficient diffusion sampling strategy that synergistically combines the diffusion sampling and Krylov subspace methods. Specifically, we prove that if tangent space at a denoised sample by Tweedie's formula forms a Krylov subspace, then the CG with the denoised data ensures the data consistency update to remain in the tangent space. Our proposed method achieves more than 80 times faster inference time than the previous state-of-the-art method.
  arXiv  Detail & Related papers  (2023-03-10T07:42:49Z)
• Diffusion Posterior Sampling for General Noisy Inverse Problems [50.873313752797124]
  We extend diffusion solvers to handle noisy (non)linear inverse problems via approximation of the posterior sampling. Our method demonstrates that diffusion models can incorporate various measurement noise statistics.
  arXiv  Detail & Related papers  (2022-09-29T11:12:27Z)

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.