arXiv:2606. 03212v1 Announce Type: new Abstract: Low-rank tensor decomposition (TD) is usually effective on clean, fully observed data, but it often degrades under severe missingness or noise.
By Zerui Tao, Qibin Zhao
The paper introduces a learning-based approach to replace the MCMC step in split-Gibbs diffusion posterior sampling. By reformulating both Gibbs updates as Gaussian denoising problems, the method uses ODE diffusion for the prior step with a pretrained denoiser and a lightweight deep-unfolded network for the likelihood step. Experiments on nonlinear phase retrieval show that this alternative reduces likelihood-update cost while maintaining effectiveness compared to MCMC-based split Gibbs.
By Yi Zhang, Rui Guo, Mengchu Xu, Zhaofeng Liu, Yonina C. Eldar
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: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
The paper proposes a classification-oriented adaptive sensing method that uses posterior sampling from diffusion models. It leverages the closed-form posterior covariance of a class-conditional Gaussian mixture model to separate within-class and between-class uncertainty, estimating these terms from diffusion posterior samples via calibrated soft classifier outputs. Experiments on MNIST and CIFAR-10 demonstrate that this approach can achieve better classification accuracy for a given measurement cost compared to reconstruction-oriented methods, while also quantifying the associated reconstruction quality.
By Andriy Enttsel, Maxime Rousselot, Vincent Corlay
arXiv:2602. 11059v2 Announce Type: replace-cross Abstract: This paper addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive error, (2) the problem is ill-posed and regularization relies on a Bayesian strategy, (3)~the prior is modeled by a diffusion process adjusted on an available large set of examples.
By Jean-Fran\c{c}ois Giovannelli