The methods producing cold molecules from cold atoms tend to leave molecular ensembles with substantial residual internal energy. For instance, Cs 2 molecules initially formed via photoassociation of cold Cs atoms are in several vibrational levels, v, of the electronic ground state. Here we apply a broadband femtosecond laser that redistributes the vibrational population in the ground state via a few electronic excitation -spontaneous emission cycles. The laser pulses are shaped to remove the excitation frequency band of the v = 0 level, preventing re-excitation from that state. We observe a fast and efficient accumulation, ∼ 70% of the initially detected molecules, in the lowest vibrational level, v = 0, of the singlet electronic state. The validity of this incoherent depopulation pumping method is very general and opens exciting prospects for laser cooling and manipulation of molecules.