The impulsive‐source distribution or Green’s function for an unboundedn‐dimensional Euclidean space filled by a material medium which undergoes a time‐dependent homogeneous deformation and which is characterized by a time‐dependent anisotropic diffusion tensor is derived. The special case of time‐independent velocity gradients is considered (motions with constant stretch history), in which the anisotropic diffusivity is assumed to arise from the distortion of the otherwise isotropic medium supporting the diffusion process. Explicit reductions are given for steady simple‐shearing (viscometric) flows. Also, a brief discussion is given of the relevance to general linear Brownian dynamical systems and the associated Taylor dispersion processes.