Parsec-scale VLBA imaging of five Seyfert galaxies with flat-spectrum radio nuclei was conducted to determine whether the flat spectrum represents thermal emission from the accretion disk/obscuring torus or nonthermal, synchrotron self-absorbed emission. Four of the five show emission consistent with synchrotron self-absorption, with intrinsic sizes ∼0.05-0.2 pc (or 104 gravitational radii for a 108 M⊙ black hole for the smallest). In contrast, NGC 4388, which was detected with MERLIN but not the VLBA, shows thermal emission with similar properties to that detected in NGC 1068. It is notable that the two Seyfert galaxies with detected thermal nuclear radio emission both have large X-ray absorbing columns, suggesting that columns in excess of ∼1024 cm−2 are needed for such disks to be detectable.