  The scattering of inertia-gravity waves by large-scale geostrophic turbulence
in a rapidly rotating, strongly stratified fluid leads to the diffusion of wave
energy on the constant-frequency cone in wavenumber space. We derive the
corresponding diffusion equation and relate its diffusivity to the wave
characteristics and the energy spectrum of the turbulent flow. We check the
predictions of this equation against numerical simulations of the
three-dimensional Boussinesq equations in initial-value and forced scenarios
with horizontally isotropic wave and flow fields. In the forced case,
wavenumber diffusion results in a $k^{-2}$ wave energy spectrum consistent with
as-yet-unexplained features of observed atmospheric and oceanic spectra.
