  We examine in detail the detectability of a signal of diffuse high energy
neutrinos produced in the Milky Way by the interaction of cosmic rays (CRs)
with the interstellar medium (ISM). We show that highly inhomogeneous galactic
CR densities arise naturally from large scale drift effects and the
inhomogeneous distribution of CR sources. In particular, the CR density in the
Galactic Center region (where the ISM density is maximal) could be an order of
magnitude larger than the local CR density. Hence, the expected diffuse flux of
neutrinos from the Galactic Center region becomes enhanced and could be
detected at energies above $\sim 10^4$ GeV in a km$^3$-size neutrino telescope
within 10 years of operation. The galactic anisotropy, which is the main
signature of this flux, allows to discriminate this signal from other possible
extraterrestrial diffuse fluxes of high energy neutrinos.
