Generative Translation Priors (GTP) is a Bayesian framework that repurposes diffusion-based image-to-image translation models as cross-modality priors for ill‑posed imaging inverse problems. It incorporates target‑domain measurements via likelihood guidance, steering the translation toward the desired posterior distribution. The authors analyze the resulting posterior dynamics, identify an intrinsic bias from likelihood guidance, and propose a ground‑truth‑free metric to estimate this bias, leading to two discretized GTP algorithms that demonstrate high‑fidelity reconstruction in CT and PET imaging using complementary side information.
By Evan Bell, Jiaming Liu, Yifan Chen, Yu Sun
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).
By Tianao Li, Xinhui Qian, Emma Alexander
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.
By Zhaoqiang Liu, Tongyao Pang, Ruibing Wang, Yang Zheng
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.
By Hao Chen, Renzheng Zhang, Scott S. Howard
arXiv:2512. 18367v2 Announce Type: replace-cross Abstract: Diffusion models are highly expressive image priors for Bayesian inverse problems.
By Wenhan Guo, Jinglun Yu, Yaning Wang, Jin U. Kang, Yu Sun
arXiv:2605. 15407v3 Announce Type: replace-cross Abstract: We consider amortized Bayesian inference for nonlinear inverse problems using only samples from the joint distribution of parameters and observations, including problems with unknown functions in a Banach space.
By Ricardo Baptista, Hojjat Kaveh, Andrew M. Stuart
arXiv:2606. 06236v1 Announce Type: new Abstract: Pretrained diffusion models demonstrate impressive potential in solving highly ill-posed 3D computed tomography (CT) inverse problems, while the inference process suffers from significant computational overhead.
By Yujia Wu, Zhaoqiang Liu
The paper introduces a high‑resolution Rectified Flow Matching model trained on 256×256 chest CT images to serve as a generative prior for CT reconstruction. A two‑stage training strategy—initial strong anatomically informed augmentation followed by fine‑tuning—helps mitigate overfitting and improve structural fidelity. When evaluated on various CT inverse problems, Flow Matching‑based reconstruction methods outperform diffusion‑based algorithms in PSNR, SSIM, and perceptual quality while requiring fewer sampling steps.
By Davide Evangelista
arXiv:2607. 00773v1 Announce Type: new Abstract: Discrete diffusion models are widely used for learning and generating discrete distributions.
By Yu Yao, Huanjian Zhou, Andi Han, Wei Huang, Masashi Sugiyama
arXiv:2607. 19333v1 Announce Type: cross Abstract: Diffusion-based methods have achieved remarkable empirical success in solving inverse problems.
By Yuchen Jiao, Na Li, Changxiao Cai, Yuxin Chen, Gen Li
arXiv:2609.39660v1 Announce Type: new
Abstract: Generative models are transforming Bayesian computational imaging, yet the field still lacks physics-aware foundation models. Current practice falls in...
By Alessio Spagnoletti, Charlesquin Kemajou Mbakam, Jonathan Spence, Andr\'es Almansa, Marcelo Pereyra
arXiv:2602. 23214v2 Announce Type: replace-cross Abstract: Plug-and-Play diffusion prior (PnPDP) frameworks have emerged as a powerful paradigm for solving imaging inverse problems by treating pretrained generative models as modular priors.
By Chenhe Du, Xuanyu Tian, Qing Wu, Muyu Liu, Jingyi Yu, Hongjiang Wei, Yuyao Zhang