In this note we show that the relaxation mechanism for self diffusion in solid transition metals leads quite naturally to a minimum in self diffusion coefficient at the half filled 3d, 4d and 5d-bands. We also loosely apply this concept to liquid transition metals where the relaxation is modelled as a local region of vaporization in the liquid (i.e. S(q) for large q is locally fluctuating wildly) and show that, if one can assume an Arrhenius D = D0e−/kTto a liquid metal, then the relaxation mechanism also predicts a minimum in self diffusion coefficint at the half filled 3d, 4d and 5d-bands for liquid transition metals. This prediction is shown to agree with the limited, scattered data for self diffusion in liquid transition metals