While "off the grid" for a long weekend, I spent time writing documents for Coryn Bailer-Jones (MPIA) and Dennis Zaritsky (Arizona). The former was about using spatial priors for inference of the three-dimensional dust density constrained by Gaia data. If you use a Gaussian Process spatial prior, you can perform the inference in extinction space (not dust space) and transfer extinction predictions to new points given extinction data without ever explicitly instantiating the dust density field. This is not a genius idea; it flows from the fact that any linear projection of a Gaussian pdf is itself a Gaussian pdf. The whole thing might not be computationally tractable, but at least it is philosophically possible. One issue with using a Gaussian Process here is that it puts support onto negative dust densities. I don't think that is a problem, but if it is a problem, the fixes are not cheap.
The latter document—for Zaritsky—is about finding the H-alpha photons that are coming from the outskirts of low-redshift galaxies by doing cross-correlations between SDSS spectroscopy and nearby galaxy centers. This project is designed to test or constrain some of the ideas in a talk at NYU by Juna Kollmeier a few months ago.