  The propagation of high-energy cosmic rays through giant molecular clouds
constitutes a fundamental process in astronomy and astrophysics. The diffusion
of cosmic-rays through these magnetically turbulent environments is often
studied through the use of energy-dependent diffusion coefficients, although
these are not always well motivated theoretically. Now, however, it is feasible
to perform detailed numerical simulations of the diffusion process
computationally. While the general problem depends upon both the field
structure and particle energy, the analysis may be greatly simplified by
dimensionless analysis. That is, for a specified purely turbulent field, the
analysis depends almost exclusively on a single parameter -- the ratio of the
maximum wavelength of the turbulent field cells to the particle gyration
radius. For turbulent magnetic fluctuations superimposed over an underlying
uniform magnetic field, particle diffusion depends on a second dimensionless
parameter that characterizes the ratio of the turbulent to uniform magnetic
field energy densities. We consider both of these possibilities and parametrize
our results to provide simple quantitative expressions that suitably
characterize the diffusion process within molecular cloud environments. Doing
so, we find that the simple scaling laws often invoked by the high-energy
astrophysics community to model cosmic-ray diffusion through such regions
appear to be fairly robust for the case of a uniform magnetic field with a
strong turbulent component, but are only valid up to $\sim 50$ TeV particle
energies for a purely turbulent field. These results have important
consequences for the analysis of cosmic-ray processes based on TeV emission
spectra associated with dense molecular clouds.
