The continuum spectral flux distribution of the Seyfert galaxy NGC 1068 is analyzed by detailed models of radiative transfer in an optically thick cloud of dust grains. For wavelengths short of 30 microns, models invoking a spherical dust cloud with visual optical depth near 10 in the nucleus of the galaxy can reproduce the observed spectrum in a way consistent with information derived from spectral lines. The far-infrared emission cannot be explained easily by dust in the nucleus, but it is hypothesized that this radiation is emitted by dust associated with the observed molecular clouds, and that these clouds lie outside the nucleus. This far-infrared emission, therefore, should be extended to the same degree as the molecular-cloud distribution. High angular resolution mapping will be necessary to confirm this hypothesis.