This reminds me of phase-problem from protein crystallograpy (PX). I'm 15+ years away from that space, so I have no idea what the modern solution space looks like, but it seems like there's a corollary between reverse-AD-over-SDFs (in this work) and the MLE methods for inverse space in PX. It <i>feels like</i> we should be able to take an initial estimate of some SDF over the direct space (2d object) as an ellipsoid, flip to inverse space, do an MLE for phase improvement, and then just do the regular ping-pong on that. The MLE (and successor?) methods are <i>really</i> robust.