We present synthetic far-and near-ultraviolet (FUV and NUV) maps of M31, both with and without dust reddening. These maps were constructed from spatially resolved star formation histories (SFHs) derived from optical Hubble Space Telescope imaging of resolved stars, taken as part of the Panchromatic Hubble Andromeda Treasury program. We use stellar population synthesis modeling to generate synthetic UV maps with a spatial resolution of ∼100 pc (∼24 arcsec), projected. When reddening is included, these maps reproduce all of the main morphological features in the GALEX imaging, including rings and large star-forming complexes. The predicted UV flux also agrees well with the observed flux, with median ratios between the modeled and observed flux of in the FUV and NUV, respectively. This agreement is particularly impressive given that we used only optical photometry to construct these UV maps. Having verified the synthetic reddened maps, we use the dust-free maps to examine properties of obscured flux and star formation. We compare our dust-free and reddened maps of FUV flux with the observed GALEX FUV flux and FUV + 24 μm flux to examine the fraction of obscured flux. We find that the maps of synthetic flux require that ∼90% of the FUV flux in M31 is obscured by dust, while the GALEX -based methods suggest that ∼70% of the FUV flux is absorbed by dust. This 30% increase in the estimate of the obscured flux is driven by significant differences between the dust-free synthetic FUV flux and that derived when correcting the observed FUV flux for dust absorption with 24 μm emission observations. The difference is further illustrated when we compare the SFRs derived from the FUV + 24 μm flux with the 100 Myr average SFR from the CMD-based SFHs. We find that the 24 μm corrected FUV flux underestimates the SFR by a factor of 2.3-2.5, depending on the chosen calibration. This discrepancy could be reduced by allowing for variability in the weight applied to the 24 μm data, as has been recently suggested in the literature.