By applying the concept of dynamical facilitation and analyzing the excitation lines that result from this facilitation; we investigate the origin of decoupling of transport coefficients in supercooled liquids. We illustrate our approach with two classes of models. One depicts diffusion in a strong glass former; and the other in a fragile glass former. At low temperatures; both models exhibit violation of the Stokes-Einstein relation; D ∼τ −1 ; where D is the self-diffusion constant and τ is the structural relaxation time. In the strong case; the violation is sensitive to dimensionality d ; going as D ∼τ −2∕3 for d =1 and as D ∼τ −0.95 for d =3 . In the fragile case; however; we argue that dimensionality dependence is weak; and show that for d =1 ; D ∼τ −0.73 . This scaling for the fragile case compares favorably with the results of a recent experimental study for a three-dimensional fragile glass former.