The authors examine qualitatively the requirement that field-particle interactions in turbulence be diffusive. The basic assumption necessary for turbulently dissipative (resonantly broadened) models is that the field-particle correlation time viewed along the particle orbit be much smaller than the field-field correlation time in the laboratory. They assume the orbit variables x(t) and v(t) are normally distribution, but the electric fields need not be. They then use simple arguments from probability theory to derive the particle propagator for a weakly turbulent plasma in a strong magnetic field. They use this propagator to find the effects of cross field diffusion on single wave pulses and plasma echoes.