  There are two classes of viable progenitors for normal Type Ia supernovae
(SNe Ia): systems in which a white dwarf explodes at the Chandrasekhar mass
($M_{ch}$), and systems in which a white dwarf explodes below the Chandrasekhar
mass (sub-$M_{ch}$). It is not clear which of these channels is dominant;
observations and light curve modeling have provided evidence for both. Here we
use an extensive grid of 4500 time-dependent, multiwavelength radiation
transport simulations to show that the sub-$M_{ch}$ model can reproduce the
entirety of the width-luminosity relation (WLR), while the $M_{ch}$ model can
only produce the brighter events $(0.8 < \Delta M_{15}(B) < 1.55)$, implying
that fast-declining SNe Ia come from sub-$M_{ch}$ explosions. We do not assume
a particular theoretical paradigm for the progenitor or explosion mechanism,
but instead construct parameterized models that vary the mass, kinetic energy,
and compositional structure of the ejecta, thereby realizing a broad range of
possible outcomes of white dwarf explosions. We provide fitting functions based
on our large grid of detailed simulations that map observable properties of SNe
Ia such as peak brightness and light curve width to physical parameters such as
$^{56}\mathrm{Ni}$ and total ejected mass. These can be used to estimate the
physical properties of observed SNe Ia.
