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We present an updated version of the UNITY (Unified Nonlinear Inference for Type-Ia cosmologY) Bayesian SN cosmology framework. The new UNITY 1.5 regresses on the true amount of dust extinction and intrinsic color for each supernova and has a more precise and flexible model for selection effects. This model enables UNITY to blindly recover the selection function of a SN survey, although more precise constraints can be realized with external efficiency information. Along with other updates to the treatment of systematic uncertainties, UNITY enables the most precise and accurate cosmological constraints to date.