  We have conducted 22 GHz 1" JVLA imaging of 70 radio-quiet AGN from the
Swift-BAT survey. We find radio cores in all but three objects. The radio
morphologies of the sample fall into three groups: compact and core-dominated,
extended, and jet-like. We spatially decompose each image into core flux and
extended flux, and compare the extended radio emission to that predicted from
previous Herschel observations using the canonical FIR-radio relation. After
removing the AGN contribution to the FIR and radio flux densities, we find that
the relation holds remarkably well despite the potentially different star
formation physics in the circumnuclear environment. We also compare our core
radio flux densities with predictions of coronal models and scale-invariant jet
models for the origin of radio emission in radio-quiet AGN, and find general
consistency with both models. However, we find that the $L_{\mathrm{R}} /
L_{\mathrm{X}}$ relation does not distinguish between star formation and
non-relativistic AGN-driven outflows as the origin of radio emission in
radio-quiet AGN. Finally, we examine where objects with different radio
morphologies fall in relation to the main sequence of star formation, and
conclude that those AGN that fall below the main sequence, as X-ray selected
AGN have been found to do, have core-dominated or jet-like 22 GHz morphologies.
