  In electromagnetic inverse scattering, the goal is to reconstruct object
permittivity using scattered waves. While deep learning has shown promise as an
alternative to iterative solvers, it is primarily used in supervised frameworks
which are sensitive to distribution drift of the scattered fields, common in
practice. Moreover, these methods typically provide a single estimate of the
permittivity pattern, which may be inadequate or misleading due to noise and
the ill-posedness of the problem. In this paper, we propose a data-driven
framework for inverse scattering based on deep generative models. Our approach
learns a low-dimensional manifold as a regularizer for recovering target
permittivities. Unlike supervised methods that necessitate both scattered
fields and target permittivities, our method only requires the target
permittivities for training; it can then be used with any experimental setup.
We also introduce a Bayesian framework for approximating the posterior
distribution of the target permittivity, enabling multiple estimates and
uncertainty quantification. Extensive experiments with synthetic and
experimental data demonstrate that our framework outperforms traditional
iterative solvers, particularly for strong scatterers, while achieving
comparable reconstruction quality to state-of-the-art supervised learning
methods like the U-Net.
