  We theoretically study the out-of-equilibrium dynamics in momentum space of a
weakly interacting disordered Bose gas launched with a finite velocity. In the
absence of interactions, coherent multiple scattering gives rise to a
background of diffusive particles, on top of which a coherent backscattering
interference emerges. We revisit this scenario in the presence of interactions,
using a diagrammatic quantum transport theory. We find that the dynamics is
governed by coupled kinetic equations describing the thermalization of the
diffusive and coherent components of the gas. This phenomenon leads to a
destruction of coherent backscattering, well described by an exponential
relaxation whose rate is controlled by the particle collision time. These
predictions are confirmed by numerical simulations.
