  The migration of magnetic bright point-like features (MBP) in the lower solar
atmosphere reflects the dispersal of magnetic flux as well as the horizontal
flows of the atmospheric layer they are embedded in. We analyse trajectories of
the proper motion of intrinsically magnetic, isolated internetwork Ca II H MBPs
(mean lifetime 461 +- 9 s) to obtain their diffusivity behaviour. We use
seeing-free high spatial and temporal resolution image sequences of quiet-Sun,
disc-centre observations obtained in the Ca II H 3968 {\AA} passband of the
Sunrise Filter Imager (SuFI) onboard the Sunrise balloon-borne solar
observatory. Small MBPs in the internetwork are automatically tracked. The
trajectory of each MBP is then calculated and described by a diffusion index
({\gamma}) and a diffusion coefficient (D). We further explore the distribution
of the diffusion indices with the help of a Monte Carlo simulation. We find
{\gamma} = 1.69 +- 0.08 and D = 257 +- 32 km^2/s averaged over all MBPs.
Trajectories of most MBPs are classified as super-diffusive, i.e., {\gamma} >
1, with the determined {\gamma} being to our knowledge the largest obtained so
far. A direct correlation between D and time-scale ({\tau}) determined from
trajectories of all MBPs is also obtained. We discuss a simple scenario to
explain the diffusivity of the observed, relatively short-lived MBPs while they
migrate within a small area in a supergranule (i.e., an internetwork area). We
show that the scatter in the {\gamma} values obtained for individual MBPs is
due to their limited lifetimes. The super-diffusive MBPs can be well-described
as random walkers (due to granular evolution and intergranular turbu- lence)
superposed on a large systematic (background) velocity, caused by granular,
mesogranular and supergranular flows.
