  Optical beam propagation in random media is characterized by familiar speckle
patterns generated by intricate interference effects. Such patterns may be
modified and possibly attenuated for partially coherent incident beam profiles.
In the weak-coupling regime of the It\^o-Schr\"odinger paraxial model of wave
propagation, we show how the spatio-temporal statistics of the partially
coherent beams interact with the statistics of the random medium to enhance or
suppress scintillation effects.
