Diffuse $\gamma$-ray emission is a viable tool to probe cosmic rays and their propagation in the Milky Way. In the MeV to GeV energy range the Galactic diffuse emission has been explored in great detail by Fermi-LAT. At very high energies (VHE), $\gamma$-ray sources dominate the TeV sky. Any VHE large-scale diffuse emission is thus likely to consist to a large fraction of $\gamma$-ray sources that are unresolved due to limited instrument sensitivity and the resulting inability to resolve the Milky Way to its full depth. The H.E.S.S. experiment has performed a first measurement of Galactic diffuse $\gamma$-ray emission at TeV energies outside of known $\gamma$-ray source regions. Interpretation of such a signal requires disentangling of the contributions of "truly diffuse'' emission stemming from cosmic-ray propagation and the emission associated with unresolved sources. This can only be achieved by invoking model assumptions for both contributions. While sophisticated codes for cosmic-ray propagation already exist, unresolved-source emission has long been neglected due to its little impact at MeV to GeV energies.
In this contribution first steps towards an estimation of the emission of unresolved $\gamma$-ray sources at TeV energies are presented. A VHE $\gamma$-ray source population is simulated, which follows the spiral structure of the Milky Way. The simulations are constrained by the sum of the detected Galactic VHE $\gamma$-ray sources in the range of completeness and the accumulated $\gamma$-ray emission of this population is compared to the measurement of diffuse TeV emission.