In this paper we investigate the problem of isothermal pressure driven gas flow through a channel using a continuum equations set with a mass diffusion correction to the mass-density equation. The additional term is invoked as a way of releasing the local-equilibrium assumption in the presence of strong local gradients. Then the dissipative mass flux is proportional to local density/pressure gradient which is constant in a cross section and results in a correction to the velocity profile. Subsequently, better mass-flow rate predictions are obtained than those obtained using Maxwell-type first order slip boundary conditions. Results indicate that the mass diffusion correction captures the "Knudsen paradox" and change in curvature of the streamwise pressure profile without the need for setting higher order slip boundary conditions. © 2011 American Institute of Physics.