  We present \textit{Wideband back-projection diffusion}, an end-to-end
probabilistic framework for approximating the posterior distribution induced by
the inverse scattering map from wideband scattering data. This framework
leverages conditional diffusion models coupled with the underlying physics of
wave-propagation and symmetries in the problem, to produce highly accurate
reconstructions. The framework introduces a factorization of the score function
into a physics-based latent representation inspired by the filtered
back-propagation formula and a conditional score function conditioned on this
latent representation. These two steps are also constrained to obey symmetries
in the formulation while being amenable to compression by imposing the rank
structure found in the filtered back-projection formula. As a result,
empirically, our framework is able to provide sharp reconstructions
effortlessly, even recovering sub-Nyquist features in the multiple-scattering
regime. It has low-sample and computational complexity, its number of
parameters scales sub-linearly with the target resolution, and it has stable
training dynamics.
