  Starburst galaxies represent one of the most plausible origins of the cosmic
high-energy neutrino flux recently discovered by IceCube. At $\sim$ PeV
energies, the neutrino flux from starburst galaxies is expected to exhibit a
characteristic spectral break due to cosmic-rays escaping the galaxy. We
examine the 'smearing' of this spectral break by a population of starburst
galaxies with varying properties. We incorporate galaxy distribution w.r.t.
star-formation rate and redshift. Our results (i) show characteristic spectral
softening in IceCube's energy band; (ii) resolve the conflicting observations
of soft neutrino spectrum and diffuse gamma-ray flux observed by Fermi-LAT;
(iii) constrain the properties of the magnetic fields in starburst galaxies.
