  Following analogies with relativistic point particles, and Schild strings, we
show that the Einstein gravity and its strong coupling regime (or the Planck
mass going to 0) are related to each other through a Laplace transform. The
Feynman propagator of gravity in the strong coupling regime satisfies a
functional diffusion equation in the three-metric space with the evolution
parameter being the volume of spacetime. We conjecture that the relationship
between both regimes is consistent with the existence of an evolution operator
in which time is replaced by the volume of spacetime
