arXiv Machine Learning

Full-Model Optimality for Tunable Linear Generative Priors in Compressed Sensing

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.

arXiv Machine Learning

4d ago

Tunable Latent Generative Priors for Compressed Sensing and Inverse Problems

The paper introduces tunable latent priors for diffusion models, normalizing flows, and variational autoencoders using nested dropout. These priors allow the latent dimensionality to adapt to each inverse problem, reducing reconstruction errors compared to fixed-complexity models across tasks such as compressed sensing, inpainting, denoising, and phase retrieval. In linear denoising, the authors derive the optimal latent complexity in closed form, linking it to noise level and signal spectrum.

By Sean Gunn, Jorio Cocola, Oliver De Candido, Vaggos Chatziafratis, Paul Hand

diffusion

arXiv AI

Jun 2

Flow-Based Generative Modeling for Optimizing Sampling Policies in Compressed Sensing Applications

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

diffusion computer-vision benchmarks

arXiv Machine Learning

Jul 9

Statistical inverse learning and $\ell^1$-regularization

arXiv:2607. 07468v1 Announce Type: cross Abstract: We study the recovery of sparse functions from finite, noisy, and indirect observations in the framework of statistical inverse learning.

By Abhishake Rastogi, Tatiana A. Bubba, Tapio Helin, Luca Ratti

efficiency

arXiv Machine Learning

Jul 7

MACS: Measurement-Aware Consistency Sampling for Inverse Problems

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

diffusion

arXiv Machine Learning

Jun 16

Exact Posterior Score Estimation for Solving Linear Inverse Problems

arXiv:2606. 17048v1 Announce Type: new Abstract: Diffusion and flow-based models learn powerful data priors by training a denoiser to reverse Gaussian corruption.

By Abbas Mammadov, Ozgur Kara, Kaan Oktay, Iskander Azangulov, Adil Kaan Akan, Hyungjin Chung, James Matthew Rehg, Yee Whye Teh

diffusion fine-tuning

arXiv AI

Jul 22

Provable diffusion-based posterior sampling for linear inverse problems via DDIM

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

diffusion

arXiv AI

Jul 20

Energy-based Transport for Amortized Bayesian Inference

arXiv:2605. 15407v3 Announce Type: replace-cross Abstract: We consider amortized Bayesian inference for nonlinear inverse problems using only samples from the joint distribution of parameters and observations, including problems with unknown functions in a Banach space.

By Ricardo Baptista, Hojjat Kaveh, Andrew M. Stuart

arXiv Machine Learning

Sep 10

The Price of Sparsity: Sufficient Conditions for Sparse Recovery using Sparse and Sparsified Measurements

arXiv:2509.01809v2 Announce Type: replace-cross Abstract: We consider the problem of support recovery for sparse binary signals from noisy linear measurements. For sparse Gaussian measurement matrice...

By Youssef Chaabouni, David Gamarnik

efficiency

arXiv AI

Jun 16

Variance Reduction for Non-Log-Concave Sampling with Applications to Inverse Problems

arXiv:2606. 16257v1 Announce Type: cross Abstract: Sampling from high-dimensional, non-log-concave distributions with unnormalized densities is a fundamental challenge in machine learning, particularly when the exact gradient of the potential is unavailable and must be approximated via stochastic gradients that exhibit high variance under a fixed budget of gradient computations per iteration.

By M. Berk Sahin, Ahmet Ege Tanriverdi, Behzad Sharif, Abolfazl Hashemi

arXiv Machine Learning

Jun 30

A Distributionally Robust Framework for Learned Reconstructions in Inverse Problems

arXiv:2606. 30230v1 Announce Type: cross Abstract: Learned reconstruction operators for inverse problems are typically trained under a fixed noise model, and generalize poorly when the distribution during testing differs from the one assumed during training.

By Floor van Maarschalkerwaart, Subhadip Mukherjee, Christoph Brune, Marcello Carioni

safety

arXiv Machine Learning

Jul 2

Breaking the Weak Recovery Limit in Random Phase Retrieval with Learned Regularizers

arXiv:2509. 15026v2 Announce Type: replace-cross Abstract: We seek to recover an unknown signal from nonlinear amplitude-only measurements, a challenging inverse problem.

By Stanislas Ducotterd, Zhiyuan Hu, Michael Unser, Jonathan Dong

arXiv Machine Learning

Jun 2

Measurement Geometry and Design for Trustworthy Generative Inverse Problems

arXiv:2606. 02309v1 Announce Type: new Abstract: Generative models are increasingly used as priors for inverse problems, but their ability to produce realistic images creates a basic trust problem: a plausible reconstruction may be supported by the measurements, or it may be filled in by the prior along unobserved directions.

By Pengfei Jin, Na Li, Quanzheng Li

safety

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