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: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:2601. 22443v2 Announce Type: replace Abstract: Can a diffusion model trained on bedrooms recover human faces?
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.
The paper presents a machine‑learning framework for reconstructing absorption and scattering coefficients in bilayered biological media from single‑distance, time‑resolved reflectance data. By training on a synthetic dataset generated with exact Monte Carlo simulations, the method outperforms traditional diffusion‑equation‑based inverse solvers in both speed and accuracy. It also estimates the dimensionality of the parameter space without prior knowledge of the number of layers, and suggests that future work could further improve accuracy using multi‑distance data.
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).
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: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:2510. 02208v3 Announce Type: replace-cross Abstract: Diffusion models have emerged as powerful generative priors for solving inverse imaging problems.
arXiv:2606. 17048v1 Announce Type: new Abstract: Diffusion and flow-based models learn powerful data priors by training a denoiser to reverse Gaussian corruption.
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:2512. 18367v2 Announce Type: replace-cross Abstract: Diffusion models are highly expressive image priors for Bayesian inverse problems.