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