  We estimate the diffuse supernova neutrino background (DSNB) using the recent
progenitor-dependent, long-term supernova simulations from the Basel group and
including neutrino oscillations at several post-bounce times. Assuming
multi-angle matter suppression of collective effects during the accretion
phase, we find that oscillation effects are dominated by the matter-driven MSW
resonances, while neutrino-neutrino collective effects contribute at the 5-10%
level. The impact of the neutrino mass hierarchy, of the time-dependent
neutrino spectra and of the diverse progenitor star population is 10% or less,
small compared to the uncertainty of at least 25% of the normalization of the
supernova rate. Therefore, assuming that the sign of the neutrino mass
hierarchy will be determined within the next decade, the future detection of
the DSNB will deliver approximate information on the MSW-oscillated neutrino
spectra. With a reliable model for neutrino emission, its detection will be a
powerful instrument to provide complementary information on the star formation
rate and for learning about stellar physics.
