We demonstrate the conversion of cold Cs2 molecules initially distributed over several vibrational levels of the lowest triplet state a 3 Σ + u into the singlet ground state X 1 Σ + g . This conversion is realized by a broadband laser exciting the molecules to a well-chosen state from which they may decay to the singlet state through two sequential single-photon emission steps: The first photon populates levels with mixed triplet-singlet character, making possible a second spontaneous emission down to several vibrational levels of the X 1 Σ + g states. By adding an optical scheme for vibrational cooling, a substantial fraction of molecules are transferred to the ground vibrational level of the singlet state. The efficiency of the conversion process, with and without vibrational cooling, is discussed at the end of the article. The presented conversion is general in scope and could be extended to other molecules.PACS numbers: 33.15. Bh, 33.20.Tp, 33.70.Ca, The last decade has witnessed increasing experimental efforts to produce large samples of ultracold molecules in a well-defined quantum state. Such samples constitute a very interesting basis for a great variety of studies ranging from controlled molecular dynamics [1] and anisotropic long-range interactions [2] to precision measurements [3] and quantum computing [4]. Internal-state manipulation of ultracold alkali-metal molecules has been in the spotlight with the stimulated raman adiabatic passage (STIRAP) technique, which allows transfer, with nearunity efficiency, of weakly bound molecules produced by magneto-association in the lowest triplet state to the absolute singlet ground state [5,6]. However, this technique is not suited to samples of molecules distributed in several vibrational levels, such as those produced by the widespread technique of cold-atom photoassociation.Motivated by the goal of finding general methods to achieve this transfer, we propose an optical scheme to move a whole vibrational distribution from a specific electronic state to another one of different multiplicity and parity. By combining this technique with our vibrational cooling technique [7], we are able to produce large samples of ultracold molecules in the lowest vibrational level of the ground state. This successful combination demonstrates the versatility of the optical vibrational cooling. Our demonstration relies on photoassociated ultracold Cs 2 molecules stabilized in a vibrational distribution of the lowest triplet state a 3 Σ