The diffusion term in the velocity gradient tensorAijevolution equation in homogeneous isotropic turbulence at moderate Reynolds number has been investigated using full direct numerical simulation (DNS) of the Navier–Stokes equations. This study also considered the diffusion terms associated with the strain rate tensorSijand the vorticity vector&ohgr;i.The statistics of the “diffusion frequency”&ohgr;0defined as&ohgr;0≡−&ngr;∇2Aij/Aij,which can be thought of as an inverse of a characteristic diffusion time scalet0,has been studied both for diagonal and off-diagonal elements of this tensor, forSijand for&ohgr;i.The probability density functions (PDF’s) of the diffusion frequency&ohgr;0for all the variables considered in this study have a distinct peak indicating a most probable positive value. It is found that the value of the frequency increases with larger absolute values of the velocity gradient. The conditional averages of&ngr;∇2Aij,&ngr;∇2Sijand&ngr;∇2&ohgr;iare found to be closely related by a cubic function ofAij,Sijand&ohgr;irespectively, which in the neighborhood of one standard deviation from the origin is very well approximated by the same linear relationship for all the variables. This latter result suggests that a linear approximation model [Dopazo &etal;,Ninth Symposium on Turbulent Shear Flows;J. Martin, Ph.D. dissertation] for the diffusion terms of velocity gradients may be appropriate in certain cases. ©1997 American Institute of Physics.