Conventional Type Ia supernova (SN Ia) cosmology analyses currently use a
simplistic linear regression of magnitude versus color and light curve shape,
which does not model intrinsic SN Ia variations and host galaxy dust as
physically distinct effects, resulting in low color-magnitude slopes. We
construct a probabilistic generative model for the distribution of dusty
extinguished absolute magnitudes and apparent colors as a convolution of the
intrinsic SN Ia color-magnitude distribution and the host galaxy dust
reddening-extinction distribution. If the intrinsic color-magnitude (M_B vs.
B-V) slope beta_int differs from the host galaxy dust law R_B, this convolution
results in a specific curve of mean extinguished absolute magnitude vs.
apparent color. The derivative of this curve smoothly transitions from beta_int
in the blue tail to R_B in the red tail of the apparent color distribution. The
conventional linear fit approximates this effective curve at this transition
near the average apparent color, resulting in an apparent slope beta_app
between beta_int and R_B. We incorporate these effects into a hierarchical
Bayesian statistical model for SN Ia light curve measurements, and analyze a
dataset of SALT2 optical light curve fits of a compilation of 277 nearby SN Ia
at z < 0.10. The conventional linear fit obtains beta_app = 3. Our model finds
a beta_int = 2.2 +/- 0.3 and a distinct dust law of R_B = 3.7 +/- 0.3,
consistent with the average for Milky Way dust, while correcting a systematic
distance bias of ~0.10 mag in the tails of the apparent color distribution.