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We describe catalog-level simulations of Type Ia supernova (SN~Ia) lightcurves in the Dark Energy Survey Supernova Program (DES-SN), and inlow-redshift samples from the Center for Astrophysics (CfA) and the CarnegieSupernova Project (CSP). These simulations are used to model biases fromselection effects and light curve analysis, and to determine bias correctionsfor SN~Ia distance moduli that are used to measure cosmological parameters. Togenerate realistic light curves, the simulation uses a detailed SN~Ia model,incorporates information from observations (PSF, sky noise, zero point), anduses summary information (e.g., detection efficiency vs. signal to noise ratio)based on 10,000 fake SN light curves whose fluxes were overlaid on images andprocessed with our analysis pipelines. The quality of the simulation isillustrated by predicting distributions observed in the data. Averaging withinredshift bins, we find distance modulus biases up to 0.05~mag over the redshiftranges of the low-z and DES-SN samples. For individual events, particularlythose with extreme red or blue color, distance biases can reach 0.4~mag.Therefore, accurately determining bias corrections is critical for precisionmeasurements of cosmological parameters. Files used to make these correctionsare available at https://des.ncsa.illinois.edu/releases/sn.

First Cosmology Results using Type Ia Supernova from the Dark Energy Survey: Simulations to Correct Supernova Distance Biases