  We present experimental observations of diffusion resonances for the quantum
kicked rotor with weak decoherence. Cold caesium atoms are subject to a pulsed
standing wave of near-resonant light, with spontaneous emission providing
environmental coupling. The mean energy as a function of the pulse period is
determined during the late-time diffusion regime for a constant probability of
spontaneous emission per unit time. Structure in the late-time energy is seen
to increase with physical kicking strength. The observed structure is related
to Shepelyansky's predictions of the initial quantum diffusion rates.
