Fundamental relationships between diffusion tensor (DT) and 3D q-space MRI are derived which establish conditions when these two complementary MR methods are equivalent. It is shown that the displacement distribution measured by q-space MRI in both the large displacement (i.e., large r) and the long-wavelength (i.e., small q) limits is the same 3D Gaussian displacement distribution assumed in DT-MRI. In these limiting cases, q-space MR yields a dispersion tensor that is identical to the effective DT, D, measured in DT-MRI. An experiment is then proposed to measure D using q-space methods. These findings establish that the effective DT, measured in DT-MRI, characterizes molecule motions on a coarse length-scale. Finally, the feasibility of and requirements for performing 3D q-space MRI on a clinical scanner are considered.