Dipole relaxation from thermally induced perturbations is investigated on different length scales for dielectric materials. From the continuum dynamical equations for the polarisation, expressions for the transverse and longitudinal dipole autocorrelation functions are derived in the limit where the cross coupling between the electric field fluctuations and dipole moment fluctuations can be ignored. The peak frequencies in the spectra of the autocorrelation functions are also derived. They depend on the wave vector squared which is a fingerprint of the underlying dipole diffusion mechanism. The theoretical predictions are compared with molecular dynamics simulation results for a model dielectric material and liquid water. For the transverse dipole autocorrelation function the agreement is excellent in the limit of small wave vectors and the presence of a diffusion mechanism is confirmed. For the longitudinal direction the simulation results show that the cross coupling between the electric field and the dipole moment is non-negligible compromising the theoretical predictions. The underlying mechanism for this coupling is not clear.