  The success of the shear-transformation-zone (STZ) theory in accounting for
broadly peaked, frequency-dependent, glassy viscoelastic response functions is
based on the theory's first-principles prediction of a wide range of internal
STZ transition rates. Here, I propose that the STZ's are the dynamic
heterogeneities frequently invoked to explain Stokes-Einstein violations and
stretched-exponential relaxation in glass-forming materials. I find that, to be
consistent with observations of Fickian diffusion near $T_g$, an STZ-based
diffusion theory must include cascades of correlated events, but that the
temperature dependence of the Stokes-Einstein ratio is determined by an
STZ-induced enhancement of the viscosity. Stretched-exponential relaxation of
density fluctuations emerges from the same distribution of STZ transition rates
that predicts the viscoelastic behavior.
