Some diffusion parameters of water are computed with various thermal-neutron scattering laws. It is found that the diffusion cooling coefficient, in particular, is reasonably sensitive to the scattering law, but that the diffusion cooling coefficients predicted by the Radkowsky and Nelkin kernels are in fortuitious agreement. The coefficients computed for the Nelkin kernel, when treated in a manner consistent with the way in which experimental data are treated, are in reasonable agreement with the results of a recent experiment.