The paper investigates compressed sensing using a family of tunable linear generative priors linked through their singular value decompositions. It proves that in noiseless Gaussian compressed sensing, the full-dimensional linear prior yields the lowest expected reconstruction error across the entire family, meaning lower-complexity priors do not improve performance in this idealized setting. This contrasts with denoising, where lower complexity priors can reduce error due to bias‑variance tradeoffs, suggesting that the experimental gains seen with neural network priors stem from their nonlinearities.
By Zhaoming Li, Paul Hand
arXiv:2606. 00078v1 Announce Type: cross Abstract: Numerous modern applications in signal processing and medical imaging necessitate acquiring high-dimensional signals under tight resource constraints.
By Roman Pavelkin, Luis A. Zavala-Mondragon, Christiaan G. A. Viviers, Fons van der Sommen
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.
By Jack Michael Solomon, Rishi Leburu, Matthias Chung
arXiv:2606. 14139v1 Announce Type: new Abstract: Full waveform inversion (FWI) recovers subsurface velocity from seismic recordings by solving a severely ill-posed, nonconvex PDE-constrained optimization.
By Chen Min, Zheng Ma
HarmoCore introduces a generative prior in a compact, continuous latent space for reconstructing oscillatory wave fields from extremely sparse sensor data. It models joint real–imaginary channels using Functional Tucker cores over shared spatial bases, learns a frequency‑conditioned diffusion prior, and performs diffusion posterior sampling directly in core space. Experiments on 2D and 3D Helmholtz problems demonstrate significant performance gains with only 1%–2% sensor coverage while remaining scalable to three dimensions.
By Lihao Chen, Xinyu Zhang, Panqi Chen, Lei Cheng, Ting Zhang, Jianlong Li, Shikai Fang
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: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.
By Qijun Chen, Shaofan Li
arXiv:2510. 02208v3 Announce Type: replace-cross Abstract: Diffusion models have emerged as powerful generative priors for solving inverse imaging problems.
By Amirreza Tanevardi, Pooria Abbas Rad Moghadam, Seyed Mohammad Eshtehardian, Sajjad Amini, Babak Khalaj
arXiv:2509. 05441v4 Announce Type: replace-cross Abstract: Latent generative models compress images into learned embeddings prior to synthesis, and the generation quality critically depends on how faithfully these embeddings preserve visual detail.
By Tejaswini Medi, Hsien-Yi Wang, Arianna Rampini, Margret Keuper
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: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
arXiv:2501. 09876v3 Announce Type: replace-cross Abstract: Generative modeling aims to generate new data samples that resemble a given dataset.
By Wonjun Lee, Riley C. W. O'Neill, Dongmian Zou, Jeff Calder, Gilad Lerman