arXiv:2602. 02948v3 Announce Type: replace Abstract: Inverse problems are fundamental to many scientific and engineering disciplines; they arise when one seeks to reconstruct hidden, underlying quantities from noisy measurements.
arXiv:2606. 31290v1 Announce Type: new Abstract: Diffusion models enable probabilistic super-resolution and conditional generation, but pixel-space methods are computationally expensive and learned latent spaces often lack interpretable uncertainty quantification.
arXiv:2607. 01275v1 Announce Type: cross Abstract: Variational Autoencoders (VAEs) commonly assume a standard isotropic Gaussian prior over the latent space, an assumption that often fails to capture the true distribution of latent representations for complex datasets.
arXiv:2608. 10398v1 Announce Type: cross Abstract: Variational autoencoders generate samples from probabilistic latent representations but do not distinguish uncertainty about the latent location from variability around it.
arXiv:2608. 11435v1 Announce Type: new Abstract: Forward and inverse modeling of parametric dynamical systems requires surrogate models that are not only accurate for state prediction, but also informative for parameter calibration.
arXiv:2408. 15344v2 Announce Type: replace Abstract: Many scientific and engineering problems involve observing a common phenomenon through multiple heterogeneous sensors or measurement modalities.
arXiv:2606. 27802v1 Announce Type: new Abstract: Hierarchical predictive coding provides an interpretable framework for perception as error-driven inference in multi-layer generative models, while sparse coding imposes parsimonious latent representations through explicit sparsity constraints.
arXiv:2606. 03553v1 Announce Type: cross Abstract: While principal component analysis (PCA) is a fundamental tool for dimensionality reduction, its dense representations make it ill-suited for high-dimensional data.
arXiv:2508. 05321v4 Announce Type: replace-cross Abstract: Assume you encounter an inverse problem that shall be solved for a large number of data, but no ground-truth data is available.
arXiv:2501. 09876v3 Announce Type: replace-cross Abstract: Generative modeling aims to generate new data samples that resemble a given dataset.
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).
arXiv:2410. 10137v5 Announce Type: replace Abstract: We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent manifolds.
arXiv:2603. 00205v2 Announce Type: replace-cross Abstract: Generative models, particularly Diffusion Models (DM), have shown strong potential for Computed Tomography (CT) reconstruction serving as expressive priors for solving ill-posed inverse problems.