This Letter describes the theoretical structure of the plasma diffusion layer that develops from an initially sharp gas-metal interface. The layer dynamics under isothermal and isobaric conditions is considered so that only mass diffusion (mixing) processes can occur. The layer develops a distinctive structure with asymmetric and highly nonlinear features. On the gas side of the layer the diffusion coefficient goes nearly to zero, causing a sharp "front," or well defined boundary between mix layer and clean gas with similarities to the Marshak thermal waves. Similarity solutions for the nonlinear profiles are found and verified with full ion kinetic code simulations. A criterion for plasma diffusion to significantly affect burn is given.