  The cumulative (anti)neutrino production from all core-collapse supernovae
within our cosmic horizon gives rise to the diffuse supernova neutrino
background (DSNB), which is on the verge of detectability. The observed flux
depends on supernova physics, but also on the cosmic history of supernova
explosions; currently, the cosmic supernova rate introduces a substantial
(+/-40%) uncertainty, largely through its absolute normalization. However, a
new class of wide-field, repeated-scan (synoptic) optical sky surveys is coming
online, and will map the sky in the time domain with unprecedented depth,
completeness, and dynamic range. We show that these surveys will obtain the
cosmic supernova rate by direct counting, in an unbiased way and with high
statistics, and thus will allow for precise predictions of the DSNB. Upcoming
sky surveys will substantially reduce the uncertainties in the DSNB source
history to an anticipated +/-5% that is dominated by systematics, so that the
observed high-energy flux thus will test supernova neutrino physics. The
portion of the universe (z < 1) accessible to upcoming sky surveys includes the
progenitors of a large fraction (~ 87%) of the expected 10-26 MeV DSNB event
rate. We show that precision determination of the (optically detected) cosmic
supernova history will also make the DSNB into a strong probe of an extra flux
of neutrinos from optically invisible supernovae, which may be unseen either
due to unexpected large dust obscuration in host galaxies, or because some
core-collapse events proceed directly to black hole formation and fail to give
an optical outburst.
