A general framework is presented to describe a resonant inelastic current inducing dynamics in the nuclear degrees of freedom of a molecule embedded between two electrodes. This approach makes use of the scattering theory of density matrices to account for the interaction between the scattering charge and the molecular modes to all orders and reduces in appropriate limits to both the standard master equation treatment for vibrational heating and the Landauer formalism for purely elastic transport. While the method presented here is equivalent to these approaches in limiting cases, it also goes well beyond their restrictions by incorporating the full quantum dynamics in the vibrational subspace in the presence of tunneling current. By application to the Au-C(60)-Au junction, it is shown that inclusion of vibrational coherences, which were previously neglected, is crucial to accurately predict the dynamics induced by current in molecular devices. Interaction with a bath of phonon modes is incorporated within the Bloch model and the competition between the bath-induced relaxation processes and the current-induced excitation is studied in detail over a range of temperatures.