The influence of dipolar interactions on the longitudianl relaxation of deuteron spin systems is investigated. Spin diffusion rates are evaluated, including approximate rates due to double quantum spin diffusion and three-spin flip-flop transitions. It is shown that slow molecular rotations in supercooled liquids do not affect the spin diffusion rates significantly provided that the motional correlation times are below the average spin lattice relaxation time T-l which becomes on the order of one second close to the glass transition temperature T-g. However, the broad distribution of deuteron T-l values at T < T-g results in a large effect of spin diffusion upon the long time decay of the longitudinal magnetization in T-l experiments. These effects are estimated in terms of a simple model in agreement with recent experiments. It is also shown that the initial decay determining the average rate [T-l(-l)] remains unaffected by spin diffusion. Finally, we show that small amplitude motions on a time scale of 10(-6)-10(-3) s may cause temperature dependent spin diffusion effects.