  We propose a novel approach to nonequilibrium real-time dynamics of quantum
impurities models coupled to biased non-interacting leads, such as those
relevant to quantum transport in nanoscale molecular devices. The method is
based on a Diagrammatic Monte Carlo sampling of the real-time perturbation
theory along the Keldysh contour. We benchmark the method on a non-interacting
resonant level model and, as a first non-trivial application, we study zero
temperature non-equilibrium transport through a vibrating molecule.
