Keywords: Deep generative models, inverse problems, Gaussianization
Abstract: Deep generative models such as GANs, normalizing flows, and diffusion models are powerful regularizers for inverse problems. They exhibit great potential for helping reduce ill-posedness and attain high-quality results. However, the latent tensors of such deep generative models can fall out of the desired high-dimensional standard Gaussian distribution during inversion, particularly in the presence of data noise and inaccurate forward models, leading to low-fidelity solutions. To address this issue, we propose to reparameterize and Gaussianize the latent tensors using novel differentiable data-dependent layers wherein custom operators are defined by solving optimization problems. These proposed layers constrain inverse problems to obtain high-fidelity in-distribution solutions. We validate our technique on three inversion tasks: compressive-sensing MRI, image deblurring, and eikonal tomography (a nonlinear PDE-constrained inverse problem) using two representative deep generative models: StyleGAN2 and Glow. Our approach achieves state-of-the-art performance in terms of accuracy and consistency.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics
Submission Guidelines: Yes
Please Choose The Closest Area That Your Submission Falls Into: Generative models