Type Ia supernovae (SN Ia) are faraway exploding stars used as ``standardizable candles'' to determine cosmological distances, measure the accelerating expansion of the Universe, and constrain the properties of dark energy. Inferring peak luminosities of SN Ia from distance-independent observables, such as the shapes and colors of their light curves (time series), underpins the evidence for cosmic acceleration. SN Ia with broader, slower declining optical light curves are more luminous ("broader-brighter") and those with redder colors are dimmer. But the "redder-dimmer" color-luminosity relation widely used in cosmological SN Ia analyses confounds its two separate physical origins. An intrinsic correlation arises from the physics of exploding white dwarfs, while interstellar dust in the host galaxy also makes SN Ia appear redder and dimmer (extinguished). However, conventional 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 unusually low color-magnitude slopes. I have constructed a probabilistic generative model for the dusty distribution of extinguished absolute magnitudes and apparent colors as the convolution of an intrinsic SN Ia color-magnitude distribution and a host galaxy dust reddening-extinction distribution. If the intrinsic color-magnitude slope differs from the host galaxy dust law, this convolution results in a specific curve of mean extinguished absolute magnitude vs. apparent color. I incorporated these effects into a hierarchical Bayesian statistical model for SN Ia light curve measurements, and analyze an optical light curve dataset comprising 277 nearby SN Ia at z < 0.10. The conventional linear fit obtains an effective color-magnitude slope of 3. My model finds an intrinsic slope of 2.2±0.3 and a distinct dust law of R_B = 3.7±0.3, consistent with the average properties of Milky Way dust, while correcting a systematic distance bias of ~0.10 mag in the tails of the apparent color distribution.