A new approach to calculate the vibrational distribution function of molecules in a medium providing energy for vibrational excitation is proposed and demonstrated. The approach is an improvement of solution methods based on the drift-diffusion Fokker-Planck (FP) equation for a double differentiable function representing the vibrational populations on a continuum internal energy scale. A self-consistent numerical solution avoids approximations used in previous analytical solutions. The dissociation flux, a key parameter in the FP equation, is fixed using the kinetics of molecular dissociation from near-continuum levels, so that the vibrational kinetics becomes a functional problem. The approach is demonstrated for the kinetics of asymmetric stretching of CO2, showing that it represents an alternative, potentially much more efficient in computational terms, to the presently usual state-to-state approach which is based on the kinetics of the populations of individual levels, and gives complementary insight into the dissociation process.