  The self-diffusion constant D is expressed in terms of transitions among the
local minima of the potential (inherent structure, IS) and their correlations.
The formulae are evaluated and tested against simulation in the supercooled,
unit-density Lennard-Jones liquid. The approximation of uncorrelated
IS-transition (IST) vectors, D_{0}, greatly exceeds D in the upper temperature
range, but merges with simulation at reduced T ~ 0.50. Since uncorrelated IST
are associated with a hopping mechanism, the condition D ~ D_{0} provides a new
way to identify the crossover to hopping. The results suggest that theories of
diffusion in deeply supercooled liquids may be based on weakly correlated IST.
