The paper introduces Prior-Consistent DAPS (PC‑DAPS), a variant of Decoupled Annealing Posterior Sampling designed to handle ambiguous nonlinear inverse problems where multiple measurement‑consistent solutions exist. PC‑DAPS maintains several candidate solutions in a single sampling run and prunes or replaces weaker candidates based on prior consistency as annealing noise decreases, without requiring ground‑truth access. This approach reduces prior‑inconsistent samples and improves sample quality for nonlinear inverse problems while preserving quality and diversity for linear ones.
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:2607. 19333v1 Announce Type: cross Abstract: Diffusion-based methods have achieved remarkable empirical success in solving inverse problems.
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.
Score‑based diffusion models excel at inverse problems but suffer from slow inference and task‑specific hyperparameter tuning. This paper introduces principled reparameterizations that create invariances, enabling the reuse of the same hyperparameters across different tasks. Building on the RED‑diff framework, the authors present OptDiff, a streamlined pipeline that integrates convex optimization to accelerate inference, achieving notable speedups and higher image quality in reconstruction, deblurring, and super‑resolution experiments.
The paper introduces Consecutive Posterior Fusion Denoising Diffusion Null‑Space Models (CPF‑DDNM), an inference‑time method that fuses successive measurement‑aware estimates to better recover unobservable image structures in severely ill‑posed imaging inverse problems. CPF‑DDNM builds on DDNM’s range/null‑space decomposition, preserving measurement‑determined components while refining prior‑driven null‑space estimates. Experiments on sparse‑view CT, low‑dose CT, and medical image super‑resolution demonstrate consistent improvements over DDNM and competitive performance against other diffusion‑based inverse solvers.
arXiv:2510. 02208v3 Announce Type: replace-cross Abstract: Diffusion models have emerged as powerful generative priors for solving inverse imaging problems.
arXiv:2609.14596v1 Announce Type: new Abstract: Training-free diffusion inverse solvers typically choose between local measurement guidance and costly clean-space posterior updates. Independent poste...
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...
FlowSGS introduces a flow-based posterior sampling method that combines Split Gibbs Sampling (SGS) with Langevin dynamics for the likelihood step and Stochastic Interpolants (SI) for the prior step. By integrating a pretrained flow model into the prior step via SI's reverse-time SDE and a novel timestep correction, FlowSGS reduces the number of network evaluations compared to plug‑and‑play diffusion samplers. Experiments demonstrate state‑of‑the‑art performance on various inverse problems, including the first flow‑based solution to a nonlinear inverse problem (Fourier phase retrieval).
FlowSGS introduces a flow-based posterior sampling method that combines Split Gibbs Sampling with annealed coupling and Stochastic Interpolants to improve flow priors for inverse imaging. The approach includes a novel timestep correction and accelerated warm-up using one-step flow models, resulting in faster and more accurate performance across various imaging tasks. It also demonstrates the first application of flow-based samplers to a nonlinear inverse problem, namely Fourier phase retrieval, and extends one-step flow models to principled Bayesian inverse imaging.
arXiv:2610.04624v2 Announce Type: replace Abstract: Recovering Partial Differential Equation (PDE) coefficient fields from extremely sparse observations is a severely ill-posed inverse problem for wh...
arXiv:2606. 26592v1 Announce Type: cross Abstract: We propose latent-space diffusion posterior sampling (L-DPS), an approximate Bayesian framework for high-dimensional inverse problems governed by partial differential equations (PDEs).