  We derive empirical models for galaxy mass assembly histories, and convolve
these with theoretical delay time distribution (DTD) models for Type Ia
supernovae (SNe Ia) to derive the distribution of progenitor ages for all SNe
Ia occurring at a given epoch of cosmic time. In actively star-forming
galaxies, the progression of the star formation rate is shallower than a
$t^{-1}$ SN Ia DTD, so mean SN Ia ages peak at the DTD peak in all star-forming
galaxies at all epochs of cosmic history. In passive galaxies which have ceased
star formation through some quenching process, the SN Ia age distribution peaks
at the quenching epoch, which in passive galaxies evolves in redshift to track
the past epoch of major star formation. Our models reproduce the SN Ia rate
evolution in redshift, the relationship between SN Ia stretch and host mass,
and the distribution of SN Ia host masses in a manner qualitatively consistent
with observations. Our model naturally predicts that low-mass galaxies tend to
be actively star-forming while massive galaxies are generally passive,
consistent with observations of galaxy "downsizing". Consequently, the mean
ages of SNe Ia undergo a sharp transition from young ages at low host mass to
old ages at high host mass, qualitatively similar to the transition of mean SN
Ia Hubble residuals with host mass. The age discrepancy evolves with redshift
in a manner currently not accounted for in SN Ia cosmology analyses. We thus
suggest that SNe Ia selected only from actively star-forming galaxies will
yield the most cosmologically uniform sample, due to the homogeneity of young
SN Ia progenitor ages at all cosmological epochs.
