  We formulate the the problem of persistent diffusion in three dimensions from
the perspective of the Frenet--Serret equations. In contrast to one and two
dimensional systems, in three dimensions persistent diffusion is, in general, a
third order process. In this paper we derive a Fokker--Planck equation for the
process and we calculate its effective diffusion constant. We also provide
expressions for the asymptotic average displacement of the walk, as well as
explicit expressions for the Fourier--Laplace transform of the correlations
between the tangent, normal and binormal vectors of the motion.
