A general expression is derived for the NMR signal from a fluid undergoing random directional flow such as encountered within the microcirculation. The dependence of the echo amplitude on flow velocity, sample morphology, and experimental parameters are described in terms of a temporal velocity autocorrelation function. The width of the correlation function determines whether the flow can properly be described as diffusive. Comparison is made between the velocity autocorrelation method outlined here and the IVIM model for tissue perfusion. Conditions for the validity of the latter approach for extracting physiologic information from apparent diffusion measurements are discussed. The approach outlined leads to a more robust measure of microcirculatory blood velocity from NMR measurements.