We discuss the luminosity function of SNe Ia under the assumption that recent evidence for dispersion in this standard candle is related to variations in the white dwarf mass function (WDMF) in the host galaxies. We develop a simple parameterization of the WDMF as a function of age of a stellar population and apply this to galaxies of different morphological types. We show that this simplified model is consistent with the observed WDMF of Bergeron et al. (1992) for the solar neighborhood. Our simple models predict that WDMF variations can produce a range of more than 1.8 mag in MB(SN Ia), which is comparable to the observed value using the data of Phillips (1993) and van den Bergh (1996). We also predict a galaxy type dependence of MB(SN Ia) under standard assumptions of the star formation history in these galaxies and show that MB(SN Ia) can evolve with redshift. In principle both evolutionary and galaxy type corrections should be applied to recover the intrinsic range of MB(SN Ia) from the observed values. Our current inadequate knowledge of the star formation history of galaxies coupled with poor physical understanding of the SN Ia mechanism makes the reliable estimation of these corrections both difficult and controversial. The predictions of our models combined with the observed galaxy and redshift correlations may have the power to discriminate between the Chandrasekhar and the sub-Chandrasekhar progenitor scenarios for SNe Ia.