Structure of the main generative hierarchical Bayesian models used in the inference. The initial, abstract, and Gaussian-distributed degrees of freedom, ξ, are mostly left out for the sake of clarity. The dashed component indicates a set of instances of the Gaussian correlated field model introduced by Arras et al. (2021, Sect. 3.4). Left: Template-free model M1 with diffuse and point-like fluxes I^diff and I^polπt. Right: Template-informed model M2 with the additional template-informed diffuse flux component I ^dust. I^nd is identical in construction to I ^dlff, but has different prior parameter values. is defined identically in both models.