We use observations of high-energy (>1 MeV) protons and electrons in the core of Saturn's magnetosphere (R≲4 Rs) to investigate the hypothesis that the trapped radiation is accelerated and maintained by inward diffusion in violation of the third adiabatic invariant. When the intensity profiles are converted to density of particles in phase space at constant magnetic moment as a function of magnetic shell parameter L, we find that the phase space density increases inward both in narrow regions associated with satellite absorption and, more generally, over extended regions between absorption features for L≲4. Such behavior is inconsistent with inward diffusion as a model for population of the radiation zone and has led to the suggestion that there may be internal sources of high-energy particles, such as cosmic ray albedo neutron decay for protons. Calculations have shown, however, that Crand is too weak to account for observed intensities of >35-MeV protons (Cooper and Simpson, this issue), and no source has been suggested for high-energy electrons. In our analysis we employ Monte Carlo simulations to examine the assumptions concerning particle motion implicit in a diffusion model. We find from our simulations that the regions of negative phase space density associated with satellite absorption features may be explained if diffusion proceeds in an episodic manner, via brief periods of enhanced radial motion separated by longer periods when little radial motion takes place. We further show that the general density increase inward is not inconsistent with particle propagation by a random walk process between an external source and an inner absorbing boundary if the 'diffusion coefficient' decreases inward from the source. Specific conditions for the particle random walk are found which determine whether the density increases or decreases inward, and it is argued that for episodic diffusion the density must increase inward. We argue that episodic diffusion, though not proven as a model, reproduces major features of the density profiles of both protons and electrons in Saturn's magnetosphere for which standard diffusion theory is unable to account.