A general theorem is derived for the diffusion of grains and the formation of dust concentrations in molecular clouds. The clouds are of arbitrary configuration and are supported by thermal pressure gradients, turbulence motions, and magnetic fields. The time scale for drainage of dust into pools of enhanced concentration is typically approx.10/sup 8/ years and is less than the estimated ages of giant molecular clouds according to recent evidence. Relevant time scales and length scales, and the effect of magnetic fields, are discussed. Brief comments are made on some possible consequences of dust sedimentation, such as the formation of Bok globules and low-mass stars, and the sequestration of heavy elements in cometary condensations.