  The cosmic neutrino flux recently discovered by IceCube will be instrumental
in probing the highest-energy astrophysical processes. Nevertheless, the origin
of these neutrinos is still unknown. While it would be more straightforward to
identify a transient, or galactic source class, finding a population of
distant, continuous sources is challenging. We introduce a source-type
classification technique that incorporates all available information from
catalogs of source candidates. We show that IceCube-Gen2 can statistically
establish the origin of cosmic neutrinos even for the most challenging source
populations--starburst galaxies, AGN or galaxy clusters, if neutrino track
directions can be reconstructed with a precision ~$0.3^\circ$. We further show
that source catalog out to ~100 Mpc can be sufficient for the most challenging
source types, allowing for more straightforward source surveys. We also
characterize the role of detector properties, namely angular resolution, size
and veto power in order to understand the effects of IceCube-Gen2's design
specifics.
