arXiv:2512. 08022v2 Announce Type: replace-cross Abstract: We propose a novel diffusion-based posterior sampling method within a plug-and-play framework.
By Jinyuan Chang, Chenguang Duan, Yuling Jiao, Ruoxuan Li, Jerry Zhijian Yang, Cheng Yuan
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).
By Yuanzhe Wang, Alexandre M. Tartakovsky
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...
By Tim Y. J. Wang, O. Deniz Akyildiz
PosteriorBench is a new benchmark that evaluates how well generative inverse solvers recover full posterior distributions rather than just a single reconstruction. It tests four physics-based inverse problems—Darcy flow inversion, Poisson source recovery, carbon capture and storage, and light transport material inference—using high-fidelity reference posteriors generated by rejection sampling and MCMC. The benchmark employs five metrics (posterior-mean error, posterior-standard-deviation error, maximum mean discrepancy, sliced Wasserstein distance, and radially averaged power-spectrum error) to assess pointwise accuracy, uncertainty, distributional alignment, and global frequency fidelity, revealing significant distribution-matching gaps in current solvers and highlighting the importance of neural operators, guidance weights, and generation noise for posterior-variance calibration.
By Jiachen Yao, Zi-Siang Hsu, Xi Deng, Aditi Gupta, Xin Ju, Sally M Benson, Gege Wen, Anima Anandkumar
arXiv:2606.22346v2 Announce Type: replace-cross
Abstract: Principled regression for stochastic processes is a long-standing challenge with deep connections to scientific inverse problems. We introduc...
By Yaozhong Shi, Zachary E. Ross, Yisong Yue
arXiv:2609.15702v1 Announce Type: new
Abstract: Pretrained score-based diffusion models provide strong unconditional priors, yet enforcing measurement or physics consistency in inverse problems is of...
By Zihao Wang