The measurement of translational diffusion coefficients by NMR generally makes use basically of two magnetic field gradient pulses separated by a so-called diffusion interval. The magnetic field gradient arises either from the static magnetic field (denoted by B0 used for polarizing the nuclear spins) or from the radio-frequency field (denoted by B1 used for inducing NMR transitions). The B0 method may be hampered by short effective transverse relaxation times ( T_2^*), by important gradient rise and fall times or by eddy currents. This does not occur with B1 gradients. Moreover, the effect of short transverse relaxation times during the gradient pulses is reduced by at least a factor of two. However, for B1 gradients, one might face with the limited volume in which the gradient is uniform and with the effect of short relaxation times which imply to reduce the various intervals in the diffusion experiment (this is as well true for the B0 method). Examples will be given for which the measurement of the diffusion coefficient by B0 gradients turned out to be impossible while a proper result was obtained with B1 gradients as far as a correction taking into account the limited volume is applied, together with a correction about the gradient calibration especially when dealing with samples containing paramagnetic species.