  Ultra-high energy cosmic rays can propagate diffusively in cosmic magnetic
fields. When their propagation time is comparable to the age of the universe, a
suppression in the flux relative to the case in the absence of magnetic fields
will occur. In this work we find an approximate parametrization for this
suppression for energies below $\sim$ Z EeV using several magnetic field
distributions obtained from cosmological simulations of the magnetized cosmic
web. We assume that the magnetic fields have a Kolmogorov power spectrum with
the field strengths distributed according to these simulations. We show that,
if magnetic fields are coupled to the matter distribution, low field strengths
will fill most of the volume, making the suppression milder compared to the
case of a constant magnetic field with strength equal to the mean value of this
distribution. We also derive upper limits for this suppression to occur for
some models of extragalactic magnetic fields, as a function of the coherence
length of these fields.
