The VAPEX analytical model is extended to cover situations when diffusion coefficients are dependent on concentration due to the extreme viscosity reduction with solvent dissolution into bitumen. The new analytical model covers such situations along with the cases in which the diffusion coefficient and viscosity relate to each other under the Stokes-Einstein law. In the process, a new concept of the 'average flow fraction of bitumen' in the flowing mixtures is introduced. The modelled result on overall functionality of the drainage rate of bitumen has confirmed the square-root relationships to most of the key reservoir parameters as the previous theories indicate. However, its dependence to the inverse of kinematic viscosity at the interface is closer to linear rather than square-root correlation with the concentration-dependent diffusion coefficient. The theoretical relationships are confirmed by the correlations of the unified bitumen rates to kinematic viscosity at the interface using the existing VAPEX and SAGD experimental data in the literature. This finding indicates that VAPEX process in heavy oils with lower native viscosity can be more effective than originally recognized.