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Star-forming and starburst galaxies are considered as one of the viablecandidate sources of the high-energy cosmic neutrino background detected inIceCube. We revisit contributions of supernova remnants (SNRs) and hypernovaremnants (HNRs) in such galaxies to the diffuse high-energy neutrino andgamma-ray backgrounds, in light of the latest Fermi data above 50GeV. We alsotake into account possible time dependent effects of the cosmic-ray (CR)acceleration during the SNR evolution. CRs accelerated by the SNR shocks canproduce high-energy neutrinos up to $\sim100$ TeV energies, but CRs from HNRscan extend the spectrum up to PeV energies. We show that, only if HNRs aredominant over SNRs, the diffuse neutrino background above 100 TeV can beexplained without contradicting the gamma-ray data. However, the neutrino dataaround 30 TeV remain unexplained, which might suggest a different population ofgamma-ray dark CR sources. Alternatively, we consider possible contributions ofPop-III HNRs up to $z\lesssim10$, and show that they are not constrained by thegamma-ray data, and thus could contribute to the diffuse high-energybackgrounds if their explosion energy reaches ${\mathcal E}_{\rmPOP-III}\sim{\rm a~few}\times10^{53}$erg. More conservatively, our resultssuggest that the explosion energy of POP-III HNRs is ${\mathcal E}_{\rmPOP-III}\lesssim7\times{10}^{53}$erg.

Revisiting the Contributions of Supernova and Hypernova Remnants to the Diffuse High-Energy Backgrounds: Constraints on Very-High-Redshift Injections