  In this paper, we present high-energy neutrino spectra from 21 Galactic
supernova remnants (SNRs), derived from gamma-ray measurements in the GeV-TeV
range. We find that only the strongest sources, i.e. G40.5-0.5 in the north and
Vela Junior in the south could be detected as single point sources by IceCube
or KM3NeT, respectively. For the first time, it is also possible to derive a
diffuse signal by applying the observed correlation between gamma-ray emission
and radio signal. Radio data from 234 supernova remnants listed in Green's
catalog are used to show that the total diffuse neutrino flux is approximately
a factor of 2.5 higher compared to the sources that are resolved so far. We
show that the signal at above 10 TeV energies can actually become comparable to
the diffuse neutrino flux component from interactions in the interstellar
medium. Recently, the IceCube collaboration announced the detection of a first
diffuse signal of astrophysical high-energy neutrinos. Directional information
cannot unambiguously reveal the nature of the sources at this point due to low
statistics. A number of events come from close to the Galactic center and one
of the main questions is whether at least a part of the signal can be of
Galactic nature. In this paper, we show that the diffuse flux from
well-resolved SNRs is at least a factor of 20 below the observed flux.
