arXiv:2602. 10792v2 Announce Type: replace-cross Abstract: In signal processing, the data collected from sensing devices is often a noisy linear superposition of multiple components, and the estimation of components of interest constitutes a crucial pre-processing step.
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.
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.
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.
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.
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.
arXiv:2502. 07580v4 Announce Type: replace Abstract: We present a novel view of diffusion-like generative modeling from the perspective of iterative Gaussian posterior inference.
One of the primary challenges in Bayesian inference on the parameters of a diffusion model from discrete observations is the unavailability of an analytical expression for the transition density function between consecutive observation times, which is needed to derive the likelihood function. Extending previous studies that solve Fokker-Planck (FP) type partial differential equations with Normalizing Flows, we propose a new Normalizing Flow architecture to learn the transition density function of the diffusion process between two observation times.
arXiv:2512. 08022v2 Announce Type: replace-cross Abstract: We propose a novel diffusion-based posterior sampling method within a plug-and-play framework.
arXiv:2608. 03566v1 Announce Type: cross Abstract: The drift diffusion model (DDM) is a cornerstone of cognitive decision-making research.
The paper explores using denoising diffusion generative models as plug‑and‑play priors for high‑dimensional inference problems. By combining a pre‑trained diffusion prior with a differentiable auxiliary constraint, the authors enable approximate inference through iterative differentiation across multiple noisy versions of the data. This framework opens possibilities for conditional generation, image segmentation, and novel combinatorial optimization algorithms.
arXiv:2606. 04324v1 Announce Type: new Abstract: One of the primary challenges in Bayesian inference on the parameters of a diffusion model from discrete observations is the unavailability of an analytical expression for the transition density function between consecutive observation times, which is needed to derive the likelihood function.