Latent Generative Models with Tunable Complexity for Compressed Sensing and other Inverse Problems
This work offers a method to improve the performance of generative models in inverse problems by allowing their complexity to adapt to the specific problem, which is significant for researchers and practitioners working on signal reconstruction and inverse problem solving.
The paper addresses the limitation of fixed-complexity generative models in inverse problems by developing tunable-complexity priors for diffusion models, normalizing flows, and variational autoencoders, leveraging nested dropout. They empirically demonstrate that these tunable priors consistently achieve lower reconstruction errors than fixed-complexity baselines across various tasks like compressed sensing, inpainting, denoising, and phase retrieval.
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.