  We study the temporal evolution of speckle patterns in transmission of short
wave pulses through a disordered waveguide. In the diffuse regime, the
short-range spatial structure of speckles is the same as for continuous wave
(cw) illumination, whereas the long-range correlation between distant speckle
spots grows linearly with time and can exceed its cw value. We discuss the
physical origin of this phenomenon, compare our results to recent microwave
experiments, and suggest that a similar linear growth with time should also be
characteristic for other mesoscopic interference phenomena.
