A diffuse flux of neutrinos emitted from all the past core collapses of massive stars, the diffuse supernova neutrino background (DSNB), still remains undiscovered; however, new generation detectors for the next decades expect to detect DSNB for the first time. This is expected to bring the stage of core collapse studies to the next level and therefore elaborate preparations are required to make statements on physics with observed results. In this study, the fact that the neutrino spectrum changes for different fates of stellar core collapse is focused and the frequencies of successful and failed supernovae are deduced to be as a function of redshift by connecting two evolutions of the galaxy and Universe. The calculated DSNB $\bar{\nu}_e$ flux shows unique spectral features compared to previous theoretical models at high and low neutrino energies. The new model is then tested regarding its detectability and physics model discrimination potential at water Cherenkov detectors.