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This research introduces tunable latent priors for generative models like diffusion and VAEs, addressing the trade-off between representation error and overfitting in inverse problems. By leveraging nested dropout, the method dynamically adjusts complexity based on noise levels and signal spectra to achieve superior reconstruction performance across tasks such as compressed sensing and denoising. The work provides both empirical evidence and closed-form theoretical bounds for optimal model complexity, advancing the utility of generative priors in practical applications.
Tunable Latent Generative Priors for Compressed Sensing and Inverse Problems
arXiv:2603.07357v3 Announce Type: replace Abstract: Latent generative models have emerged as powerful priors for solving inverse problems. These models typically represent a class of natural signals at a single, fixed complexity, governed by the latent dimensionality. This can be limiting: depending on the problem, a latent dimensionality that is too small may result in high representation error, while one that is too large may overfit to noise. We develop tunable latent 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 derive the optimal complexity in closed form, showing how it depends on the noise level and the signal spectrum. This work demonstrates the potential of tunable latent generative priors and motivates both the development of supporting theory and their application across a wide range of inverse problems.
Abstract:Latent generative models have emerged as powerful priors for solving inverse problems. These models typically represent a class of natural signals at a single, fixed complexity, governed by the latent dimensionality. This can be limiting: depending on the problem, a latent dimensionality that is too small may result in high representation error, while one that is too large may overfit to noise. We develop tunable latent 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 derive the optimal complexity in closed form, showing how it depends on the noise level and the signal spectrum. This work demonstrates the potential of tunable latent generative priors and motivates both the development of supporting theory and their application across a wide range of inverse problems.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2603.07357 [cs.LG]
(or arXiv:2603.07357v3 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2603.07357 Focus to learn more arXiv-issued DOI via DataCite
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