  The Nelson stochastic mechanics of inhomogeneous quantum diffusion in flat
spacetime with a tensor of diffusion can be described as a homogeneous one in a
Riemannian manifold where this tensor of diffusion plays the role of a metric
tensor. It is shown that the such diffusion accelerates both a sample particle
and a local frame such that their mean accelerations do not depend on their
masses. This fact, explaining the principle of equivalence, allows one to
represent the curvature and gravitation as consequences of the quantum
fluctuations. In this diffusional treatment of gravitation it can be naturally
explained the fact that the energy density of the instantaneous Newtonian
interaction is negative defined.
