  Using a numerically exact method we study the stability of dynamical
localization to the addition of interactions in a periodically driven isolated
quantum system which conserves only the total number of particles. We find that
while even infinitesimally small interactions destroy dynamical localization,
for weak interactions density transport is significantly suppressed and is
asymptotically diffusive, with a diffusion coefficient proportional to the
interaction strength. For systems tuned away from the dynamical localization
point, even slightly, transport is dramatically enhanced and within the largest
accessible systems sizes a diffusive regime is only pronounced for sufficiently
small detunings.
