We propose a mechanism for a velocity-selective device which would allow packets of cold atoms traveling in one direction through a pulsed optical lattice to pass undisturbed, while dispersing atoms traveling in the opposite direction. The mechanism is generic and straightforward: for a simple quantum kicked rotor pulsed with unequal periods, the quantum suppression of momentum diffusion (dynamical localization) yields momentum localization lengths L which are no longer isotropic, as in the standard case, but vary smoothly and controllably with initial momentum.