  We explore in stochastic gravity theory whether non-Gaussian noises from the
higher order correlation functions of the stress tensor for quantum matter
fields when back-reacting on the spacetime may reveal hints of multi-scale
structures. Anomalous diffusion may depict how a test particle experiences in a
fractal spacetime. The hierarchy of correlations in quantum matter field
induces the hierarchy of correlations in geometric objects via the set of
Einstein-Langevin equations for each correlation order. This correlation
hierarchy kinetic theory conceptual framework, aided by the characteristics of
stochastic processes, may serve as a conduit for connecting the low energy
`Bottom-Up' approach with the `Top-Down' theories of quantum gravity which
predict the appearance of fractal spacetimes at the Planck scale.
