Delight infers photometric redshifts in deep galaxy and quasar surveys. It uses a data-driven model of latent spectral energy distributions (SEDs) and a physical model of photometric fluxes as a function of redshift, thus leveraging the advantages of both machine- learning and template-fitting methods by building template SEDs directly from the training data. Delight obtains accurate redshift point estimates and probability distributions and can also be used to predict missing photometric fluxes or to simulate populations of galaxies with realistic fluxes and redshifts.