The diffuse flux of supernova neutrinos provides an immediate opportunity to detect stellar core-collapse neutrinos. This signal is spatially isotropic and temporally constant, arising from the combined fluxes of neutrinos emitted from all distant stellar core collapses. It has not been detected yet, but the Super-Kamiokande detector, now upgraded with gadolinium, should detect a few neutrino events every year, providing a new probe of core-collapse neutrinos and the cosmic core-collapse rate. In this talk, I will review predictions of this signal. Inputs from both the theoretical and observational communicates are crucial, and I will cover recent insights gained from both simulations of core collapse and surveys of supernovae. I will close with promising probes in both the discovery and precision phases.