The Fokker-Planck (FP) approach to describe vibrational kinetics numerically is validated in this work. This approach is shown to be around 1000 times faster than the usual state-to-state (STS) method to calculate a vibrational distribution function (VDF) in stationary conditions. Weakly ionized, nonequilibrium CO2 plasma is the test case for this demonstration, in view of its importance for the production of carbon-neutral fuels. VDFs obtained through the resolution of an FP equation and through the usual STS approach are compared in the same conditions, considering the same kinetic data. The demonstration is shown for chemical networks of increasing generality in vibrational kinetics of polyatomic molecules, including V-V exchanges, V-T relaxation, intermode V-V′ reactions, and excitation through e-V collisions. The FP method is shown to be accurate to describe the vibrational kinetics of the CO2 asymmetric stretching mode, while being much faster than the STS approach. In this way, the quantitative validity of the FP approach in vibrational kinetics is assessed, making it a fully viable alternative to STS solvers, that can be used with other processes, molecules, and physical conditions.