Physical processes involving dust grains are studied during the collapse of a dense interstellar cloud. The formation of a central protostar can, via radiation pressure for massive stars or by the generation of protostellar winds for less massive stars, provide a means of supporting the infalling material against accretion onto the protostar. A thin shell is formed, bounded at its inner surface by melting of the grains and compressed by the ram pressure of the infalling material. We show that for sufficiently large protostellar luminosities, produced by stars in excess of approx.5 M/sub sun/, the grain shell will move outward and become convectively unstable. Evaporation, shattering, nucleation, and accretion processes all play a role in determining the emergent grain distribution. For protostars of lower mass, disk formation may be important, and a protostellar wind can expel the smaller particles into the interstellar medium. The emergent grain size spectrum is found to be bimodal, with a predominance of small particles.This scenario yields a tentative explanation for the origin of the bulk of the mass in interstellar grains, because it provides a means of increasing the number of grains for a given total mass. Although the initial refractory cores may be producedmore » during mass loss from evolved stars, by recycling grains through successive protostellar phases where accretion, evaporation, nucleation, and shattering play a role, we are able to account quantitatively for the tatal mass in grains, the relatively large number of small particles required to explain the observed far-ultraviolet extinction, and in a more qualitative manner for the apparent spatial variability in the far-ultraviolet extinction law. (AIP)« less