We provide insight into the origin of the far-IR to mm emission from the Galaxy by presenting a decomposition of the emission where we separate the contributions from dust in the atomic gas and dust associated with quiescent molecular gas, as a function of Galacto-centric distance. We find that the sub-mm dust emissivity per hydrogen change by a factor 3 between the diffuse ISM and molecular clouds, first observed on localized clouds in the Solar Neighborhood, applies on large scale to the Molecular Ring. The decomposition leaves an emission excess in the sub-mm with a very cold effective temperature, concentrated in the plane but with a brightness independent of Galactic longitude. This emission might be associated with interstellar matter in the outer Galaxy not traced by H I nor CO emission.