The Gaia mission is providing precise astrometry for an unprecedented number of white dwarfs (WDs), encoding information on stellar evolution, Type Ia supernovae progenitor scenarios, and the star formation and dynamical history of the Milky Way. With such a large data set, it is possible to infer properties of the WD population using only astrometric and photometric informations. We demonstrate a framework to accomplish this using a mock data set with Sloan Digital Sky Survey ugriz photometry and Gaia astrometric information. Our technique utilizes a Bayesian hierarchical model for inferring properties of a WD population while also taking into account all observational errors of individual objects, as well as selection and incompleteness effects. We demonstrate that photometry alone can constrain the WD population’s distributions of temperature, surface gravity, and atmospheric composition, and that astrometric information significantly improves determination of the WD surface gravity distribution. We also discuss the possibility of identifying unresolved binary WDs using only photometric and astrometric informations.