Vibrational relaxation:

The arrow on the extreme right (blue) represents the condition wherein the molecule in the virtual state acquired through absorption of incident photon through the molecule within the vibrational excited state of the ground electronic state releases a photon. On releasing the photon the molecule comes down to the vibrational ground state of the ground electronic state. The whole procedure of excitation and relaxation is equivalent to the vibrational relaxation of a molecule as a consequence of the inelastic collision. The energy of the scattered photon is greater than that of the incident photon; this provides rise to anti-Stokes line.

The most likely event in these interactions is the energy absorption and re-emission through the molecules in the ground state. Thus, the Rayleigh lines are the most intense. Additionally, since the virtual state from that the Stokes line originates is more populated than the one for anti-Stokes lines, a Stokes lines are more intense and then the anti-Stokes lines.