Dust reprocesses the intrinsic radiation of active galactic nuclei (AGNs) to emerge at longer wavelengths. The observed mid-infrared (MIR) luminosity depends fundamentally on the luminosity of the central engine, but in detail it also depends on the geometric distribution of the surrounding dust. To quantify this relationship, we observe nearby normal AGNs in the MIR to achieve spatial resolution better than 100 pc, and we use absorption-corrected X-ray luminosity as a proxy for the intrinsic AGN emission. We find no significant difference between optically classified Seyfert 1 and 2 galaxies. Spectroscopic differences, both at optical and IR wavelengths, indicate that the immediate surroundings of AGNs is not spherically symmetric, as in standard unified AGN models. A quantitative analysis of clumpy torus radiative transfer models shows that a clumpy local environment can account for this dependence on viewing geometry while producing MIR continuum emission that remains nearly isotropic, as we observe, although the material is not optically thin at these wavelengths. We find some luminosity dependence on the X-ray/MIR correlation in the smallest scale measurements, which may indicate enhanced dust emission associated with star formation, even on these sub-100 pc scales.