We present a substantial extension of the mm-wave continuum photometry catalog for Taurus circumstellar dust disks. Combining new Submillimeter Array data with measurements in the literature, we construct a mm-wave luminosity distribution for Class II disks that is statistically complete for stellar hosts with spectral types earlier than M8.5 and has a (3-sigma) depth of ~3 mJy. The resulting census eliminates a longstanding bias against disks with late-type hosts, and thereby reveals a strong correlation between L_mm and the host spectral type. We confirm that this corresponds to a statistically robust relationship between the masses of dust disks and the stars that host them. A Bayesian regression technique is used to characterize these relationships: the results indicate a typical 1.3 mm flux density of 25 mJy for solar mass hosts and a power-law scaling L_mm propto M_star^1.5-2.0. We suggest that a reasonable treatment of dust temperature in the conversion from L_mm to M_disk favors an inherently linear M_disk propto M_star scaling, with a typical disk-to-star mass ratio of $sim$0.2--0.6%. The RMS dispersion around this regression is 0.7 dex, suggesting that the combined effects of diverse evolutionary states, dust opacities, and temperatures in these disks imprint a FWHM range of a factor of 40 on the inferred M_disk (or L_mm) at any given host mass. We argue that this relationship between M_disk and M_star likely represents the origin of the inferred correlation between giant planet frequency and host star mass in the exoplanet population, and provides some basic support for the core accretion model for planet formation. Moreover, we caution that selection bias must be considered in comparative studies of disk evolution, and illustrate that fact with statistical comparisons of L_mm between Taurus and other clusters (abridged).
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