The exciton lifetimes $T_1$ in arrays of InAs/GaAs vertically coupled quantum dot pairs have been measured by time-resolved photoluminescence. A considerable reduction of $T_1$ by up to a factor of $\sim$ 2 has been observed as compared to a quantum dots reference, reflecting the inter-dot coherence. Increase of the molecular coupling strength leads to a systematic decrease of $T_1$ with decreasing barrier width, as for wide barriers a fraction of structures shows reduced coupling while for narrow barriers all molecules appear to be well coupled. The coherent excitons in the molecules gain the oscillator strength of the excitons in the two separate quantum dots halving the exciton lifetime. This superradiance effect contributes to the previously observed increase of the homogeneous exciton linewidth, but is weaker than the reduction of $T_2$. This shows that as compared to the quantum dots reference pure dephasing becomes increasingly important for the molecules.