Molecular mixing in cold snow and firn is ordinarily controlled by vapor diffusion. Diffusion through or along the ice matrix is slow, whereas diffusion from the air to within separate grains is comparatively rapid. Thus mixing occurs in the vapor phase, and exchange with the local ice involves all the water molecules. A quantification of these concepts is applied to the diffusion of oxygen-isotopic depth profiles in southern Greenland and at Dome C, Antarctica. It successfully describes the smoothing of measured profiles. The smoothing rate is strongly dependent on temperature and density of the firn.