arXiv AI
Jul 22
Provable diffusion-based posterior sampling for linear inverse problems via DDIM
arXiv:2607. 19333v1 Announce Type: cross Abstract: Diffusion-based methods have achieved remarkable empirical success in solving inverse problems.
Weak Diffusion Priors Can Still Achieve Strong Inverse-Problem Performance
arXiv:2601. 22443v2 Announce Type: replace Abstract: Can a diffusion model trained on bedrooms recover human faces?
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arXiv Machine Learning
Jun 2
Hallucination-Aware Diffusion Sampling for Inverse Problems via Robust Prior Updates
arXiv:2606. 02331v1 Announce Type: cross Abstract: Diffusion-based inverse problem solvers can produce realistic reconstructions, but realism alone does not ensure that the recovered details are supported by the measurement.
arXiv Machine Learning
Sep 17
A Gradient Flow Approach to Solving Inverse Problems with Latent Diffusion Models
arXiv:2509.19276v2 Announce Type: replace-cross Abstract: Solving ill-posed inverse problems requires powerful and flexible priors. We propose leveraging pretrained latent diffusion models for this t...
arXiv AI
Jun 30
DAPS++: Rethinking Diffusion Inverse Problems with Decoupled Posterior Annealing
arXiv:2511. 17038v4 Announce Type: replace Abstract: From a Bayesian perspective, score-based diffusion solves inverse problems through joint inference, embedding the likelihood with the prior to guide the sampling process.
arXiv Machine Learning
Sep 18
Score-based diffusion models for severely ill-posed problems in diffuse optical tomography
Score-based diffusion models, a recent framework for posterior sampling in Bayesian inverse problems, are applied to diffuse optical tomography (DOT), a highly ill‑posed boundary value problem for recovering tissue absorption and scattering. The authors introduce a mixed score that combines a learned component with a model‑based component, providing a theoretical justification for its local approximation to the true score in the small diffusion‑time regime. Four difference‑imaging approaches are compared—classical model‑based, approximate diffusion, exact posterior sampling (UCoS), and a regularized UCoS—showing that UCoS yields more accurate reconstructions, especially under limited‑view geometry and real experimental data.
arXiv Computer Vision
Sep 2
Diffusion Based Unpaired Data Learning for Inverse Problems
The paper introduces LUD-DIF, a diffusion-based method that solves inverse problems using unpaired data. By deriving the evidence lower bound of the joint distribution and decoupling it into two independent diffusion processes under a weak‑coupling assumption, the authors provide a variational inference framework, a loss function, and an error‑bound analysis. Experiments show that LUD‑DIF performs well across multiple image inverse problems, demonstrating its effectiveness and generalization in unpaired settings.
arXiv Machine Learning
Jul 8
Estimation of instrument and noise parameters for inverse problem based on prior diffusion model
arXiv:2602. 11711v2 Announce Type: replace-cross Abstract: This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems.
arXiv AI
Aug 28
Active Diffusion-Based Inference for Ill-Posed Inverse Problems under Incomplete Priors
The paper introduces an active diffusion-based inverse problem solver that trains a diffusion model to map between parameter and observable spaces. By iteratively detecting and correcting model misspecification through posterior uncertainty, the method can discover and learn the correct parameter region even when initial training bounds exclude the true parameters. The authors demonstrate the solver on a toy inverse problem with infinite solutions and on parameterizing quantum correlation functions for a Quantum Chromodynamics analysis of nucleon structure.
arXiv Machine Learning
4d ago
Principled MAP estimation for inverse problems: bridging the gap between convergence and performance
arXiv:2609.37529v1 Announce Type: cross Abstract: Pretrained denoisers provide a powerful way to incorporate image priors into restoration algorithms. Plug-and-Play and RED approaches exploit fixed-n...
arXiv AI
Sep 4
A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors
The paper introduces a Posterior‑Dynamics Framework that leverages pretrained diffusion models as multiscale priors for linear imaging inverse problems such as deblurring, super‑resolution, and inpainting. By constructing a surrogate likelihood centered on the clean image and incorporating diffusion uncertainty, the authors derive continuous posterior dynamics and a tunable Langevin component for adaptive exploration. They prove theoretical guarantees (endpoint consistency, finite‑horizon tracking, weak accuracy) and present the PD‑IMEX sampler, which achieves high‑quality reconstructions with only 100 score evaluations and controllable fidelity‑diversity trade‑offs.
arXiv AI
Aug 26
Outlier-Robust Diffusion Solvers for Inverse Problems
arXiv:2605.09477v2 Announce Type: replace-cross Abstract: Methods based on diffusion models (DMs) for solving inverse problems (IPs) have recently achieved remarkable performance. However, DM-based m...
arXiv Machine Learning
Jul 7
MACS: Measurement-Aware Consistency Sampling for Inverse Problems
arXiv:2510. 02208v3 Announce Type: replace-cross Abstract: Diffusion models have emerged as powerful generative priors for solving inverse imaging problems.