arXiv:2512. 18367v2 Announce Type: replace-cross Abstract: Diffusion models are highly expressive image priors for Bayesian inverse problems.
Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.
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.
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 introduces PiX-MC, a time‑parallel posterior sampling framework that combines proximal Langevin dynamics with Picard iteration for Bayesian imaging inverse problems. By leveraging efficient proximal operators for many imaging likelihoods and exploiting parallelism across discretization nodes, PiX-MC supports multi‑GPU implementation and includes multi‑block and annealed variants to enhance scalability. Experiments on various imaging tasks, including a large‑scale sparse‑view CT problem, show that PiX‑MC can reduce runtime by up to 50× while maintaining reconstruction quality.
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).
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: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...