  As we observe a rapidly growing number of astrophysical transients, we learn
more about the diverse host galaxy environments in which they occur. Host
galaxy information can be used to purify samples of cosmological Type Ia
supernovae, uncover the progenitor systems of individual classes, and
facilitate low-latency follow-up of rare and peculiar explosions. In this work,
we develop a novel data-driven methodology to simulate the time-domain sky that
includes detailed modeling of the probability density function for multiple
transient classes conditioned on host galaxy magnitudes, colours, star
formation rates, and masses. We have designed these simulations to optimize
photometric classification and analysis in upcoming large synoptic surveys. We
integrate host galaxy information into the SNANA simulation framework to
construct the Simulated Catalogue of Optical Transients and Correlated Hosts
(SCOTCH), a publicly-available catalogue of 5 million idealized transient light
curves in LSST passbands and their host galaxy properties over the redshift
range $0<z<3$. This catalogue includes supernovae, tidal disruption events,
kilonovae, and active galactic nuclei. Each light curve consists of true
top-of-the-galaxy magnitudes sampled with high ($\lesssim$2 day) cadence. In
conjunction with SCOTCH, we also release an associated set of tutorials and the
transient-specific libraries to enable simulations of arbitrary space- and
ground-based surveys. Our methodology is being used to test critical science
infrastructure in advance of surveys by the Vera C. Rubin Observatory and the
Nancy G. Roman Space Telescope.

Instrumentation and Methods for Astrophysics;Cosmology and Nongalactic Astrophysics;Astrophysics of Galaxies;High Energy Astrophysical Phenomena