We demonstrate the conversion of cold Cs_{2} molecules initially distributed over several vibrational levels of the lowest triplet state a^{3}Sigma_{u}^{+} into the singlet ground state X^{1}Sigma_{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 througtextcolor{black}{h two sequential single-photon emission steps: Th}e first photon populates levels with mixed triplet-singlet character, making possible a second spontaneous emission down to several vibrational levels of the X^{1}Sigma_{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.
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