The self-diffusion constant D is expressed in terms of transitions among th
e local minima (inherent structures, IS) of the N-body potential-energy sur
face or landscape, and their correlations. The formulas are evaluated and t
ested against simulation in the supercooled, unit-density Lennard-Jones liq
uid. The approximation of uncorrelated IS-transition (IST) vectors Do, grea
tly exceeds D for the highest T, but merges with simulation at reduced T si
milar to 0.50, close to the estimated mode-coupling temperature T-c. Since
uncorrelated IST's are associated with a hopping mechanism, the condition D
similar to D-o provides a new way to identify the crossover to hopping. Th
e results suggest that theories of diffusion in deeply supercooled liquids
may be based on weakly correlated IST's.