We introduce a new tool for analyzing data from normal or anomalous
 diffusion processes: The distribution of generalized diffusivities
 P(D,t) is defined as the probability density of finding a squared
 displacement of duration t, rescaled by its asymptotic
 time-dependence. It contains information of all even moments of the
 process for all times and characterizes the fluctuations around the
 mean diffusivity, i.e. the generalized diffusion constant appearing
 in the asymptotic behavior of the mean square displacement, which is
 also equal to the first moment of P(D,t) for large t. The statistics
 may be taken along a single trajectory or over an ensemble of random
 walkers and therefore allows comparing e.g. data from single particle
 tracking experiments with NMR data. In this contribution we apply
 this idea to diffusive transport in simple Hamiltonian systems and
 show how the transporting structures in phase space are reflected in
 the distribution of generalized diffusivities P(D,t). On the basis of
 this distribution we make a comparison with continuous time random
 walks and show, how the latter can be refined to capture the observed
 structures.