  We discuss the effects of diffusion of high energy cosmic rays in turbulent
extra-galactic magnetic fields. We find an approximate expression for the low
energy suppression of the spectrum of the different mass components (with
charge $Z$) in the case in which this suppression happens at energies below
$\sim Z$ EeV, so that energy losses are dominated by the adiabatic ones.
  The low energy suppression appears when cosmic rays from the closest sources
take a time comparable to the age of the Universe to reach the Earth. This
occurs for energies $E< Z\, {\rm EeV}\,(B/{{\rm G}})\sqrt{l_c/{\rm
Mpc}}(d_s/70\ {\rm Mpc})$ in terms of the magnetic field RMS strength $B$, its
coherence length $l_c$ and the typical separation between sources $d_s$.
  We apply this to scenarios in which the sources produce a mixed composition
and have a relatively low maximum rigidity ($E_{max}\sim (2$--$10) Z $ EeV),
finding that diffusion has a significant effect on the resulting spectrum, the
average mass and on its spread, in particular reducing this last one. For
reasonable values of $B$ and $l_c$ these effects can help to reproduce the
composition trends observed by the Auger Collaboration for source spectra
compatible with Fermi acceleration.
