We study the motion of cold atoms in a pulsed standing wave of light, which
constitutes an experimental realization of the quantum kicked rotor. This
system exhibits dynamical localization, where quantum effects suppress clas
sical momentum diffusion. As we introduce amplitude noise, the coherences t
hat lead to localization are destroyed, resulting in restored diffusion. Fo
r high levels of noise, we find that the experiment is well described by a
classical model, suggesting that classical behavior has been restored. We p
resent a detailed experimental study of this noise-induced transition from
quantum to classical behavior.