We have used nuclear reaction analysis to measure diffusion coefficients D in couples consisting of hydrogenated polybutadienes of structure (C2H3(C2H5))(x)(C4H8)(1-x) and their partly deuterated counterparts. The 1,2- and 1,4-olefinic isomers are randomly distributed along the chains and the mean vinyl fraction x varies between 0.38 and 0.94. We find that the effective monomeric mobility D-0 [defined by D = D-0(N-e/N-2) for each copolymer, where N is the backbone length and N, the entanglement spacing] decreases monotonically with increasing vinyl content x. Over the range of microstructures and temperatures T (-14-40 degrees C) investigated we find log(D-0/T) varies smoothly with (T - T-g), where T-g is the glass transition temperature of the respective melts. An analysis of our data in terms of a simple activated rate process model suggests that D-0 is controlled by thermally activated hopping of segments whose effective volume is close to that of the respective statistical segment lengths of the copolymeric chains.