Pure water direct contact membrane distillation (DCMD) experiments were used to measure the permeability parameter associated with the molecular diffusion in membrane distillation (MD). The fluxes given by a recently reported MD model, which is based on the dusty-gas model of gas transport through porous media, showed good agreement with the experimental results over the entire range of feed temperatures studied. The model was also capable of predicting flux as a function of the difference between bulk feed and permeate temperatures for the limiting case in which only molecular diffusion contributes to flow. The DCMD experiments were performed in this work with a new laboratory-scale module that does not require a support for flat-sheet membranes. The resulting DCMD fluxes were two to three times higher than those reported in the literature for either DCMD or reverse osmosis. The MD model was also used to predict the performance of DCMD desalination, and the results were compared to those of reverse osmosis, in terms of both water production rates and NaCl rejection.