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Deep generative models such as GANs, normalizing flows, and diffusion modelsare powerful regularizers for inverse problems. They exhibit great potentialfor helping reduce ill-posedness and attain high-quality results. However, thelatent tensors of such deep generative models can fall out of the desiredhigh-dimensional standard Gaussian distribution during inversion, particularlyin the presence of data noise and inaccurate forward models, leading tolow-fidelity solutions. To address this issue, we propose to reparameterize andGaussianize the latent tensors using novel differentiable data-dependent layerswherein custom operators are defined by solving optimization problems. Theseproposed layers constrain inverse problems to obtain high-fidelityin-distribution solutions. We validate our technique on three inversion tasks:compressive-sensing MRI, image deblurring, and eikonal tomography (a nonlinearPDE-constrained inverse problem) using two representative deep generativemodels: StyleGAN2 and Glow. Our approach achieves state-of-the-art performancein terms of accuracy and consistency.

Differentiable Gaussianization Layers for Inverse Problems Regularized by Deep Generative Models