This newsgroup, despite being focused on just polymers, and despite having some really knowledgeable people with decades of great experience, does have some blinds spots. You are seeing one such case right here, what with the long delays in getting an answer, and the easy-out Google suggestions. Most of the 119 hits are using the term "center of diffusion" in a non-technical sense as well making them useless to you.
That said, it appears that the center of diffusion is a point approximation for the diffusivity of a large molecule, in the same way that the center of mass is the point approximation for a 3D object. For spherical objects (including spherically shaped polymers), the center of diffusion will be the same as the center of mass. For nonspherical objects, they will differ, as certain parts of the macromolecule will be able to diffuse faster than other parts. The center of diffusion is a point that represents an "average" diffusion point for the molecule.