Depending on their mechanism of self-propulsion, active particles can exhibit time-dependent, often periodic, propulsion velocity. The precise propulsion velocity profile determines their mean square displacement and their effective diffusion coefficient at long times. Here, we demonstrate that any periodic propulsion profile results in a larger diffusion coefficient than the corresponding case with constant propulsion velocity. We investigate, in detail, periodic exponentially decaying velocity pulses, expected in propulsion mechanisms based on sudden absorption of finite amounts of energy. We show, both analytically and with numerical simulations, that in these cases the effective diffusion coefficient can be arbitrarily enhanced with respect to the case with constant velocity equal to the average speed. Our results may help interpret, in a new light observations on the diffusion enhancement of active particles.