  The spectrum of electromagnetic emission generated by relativistic electrons
scattered on small-scale random magnetic fields, implied by current models of
the magnetic field generation in the gamma-ray burst sources, is considered.
The theory developed includes both perturbative and non-perturbative versions
and, therefore, suggests a general treatment of the radiation in arbitrary
small-scale random field. It is shown that a general treatment of the random
nature of the small-scale magnetic field, as well as angular diffusion of the
electrons due to multiple scattering by magnetic inhomogeneities (i.e.,
non-perturbative effects), give rise to a radiation spectrum that differs
significantly from so-called "jitter" spectrum. The spectrum of diffusive
synchrotron radiation seems to be consistent with the low energy spectral index
distribution of the gamma-ray bursts.
