Latent Generative Models with Tunable Complexity for Compressed Sensing and other Inverse Problems

TL;DR

This paper introduces tunable-complexity generative priors using nested dropout for inverse problems, enabling adaptable signal representation that improves reconstruction accuracy across various tasks.

Contribution

It develops a novel approach to adjust the complexity of generative models for inverse problems, with empirical and theoretical validation of its effectiveness.

Findings

Tunable priors outperform fixed-complexity models in reconstruction tasks.

Theoretical analysis links optimal tuning to noise level and model structure.

Empirical results across multiple inverse problems demonstrate improved accuracy.

Abstract

Generative models have emerged as powerful priors for solving inverse problems. These models typically represent a class of natural signals using a single fixed complexity or dimensionality. This can be limiting: depending on the problem, a fixed complexity may result in high representation error if too small, or overfitting to noise if too large. We develop tunable-complexity priors for diffusion models, normalizing flows, and variational autoencoders, leveraging nested dropout. Across tasks including compressed sensing, inpainting, denoising, and phase retrieval, we show empirically that tunable priors consistently achieve lower reconstruction errors than fixed-complexity baselines. In the linear denoising setting, we provide a theoretical analysis that explicitly characterizes how the optimal tuning parameter depends on noise and model structure. This work demonstrates the potential of tunable-complexity generative priors and motivates both the development of supporting theory and their application across a wide range of inverse problems.