The sensitivity of a wave field's evolution to small perturbations is of fundamental interest. For simple chaotic systems, there are multiple distinct regimes of either exponential or Gaussian overlap decay in time. We develop a semiclassical approach for understanding these regimes, and give a theory that interpolates between them. The wave field's evolution is considerably more stable than the exponential instability of chaotic trajectories seem to suggest. The resolution of this paradox lies in the collective behavior of the appropriate set of trajectories. Results are given for the standard map.