The scatter (sigma(sSFR)) of the specific star formation rates of galaxies is a measure of the diversity in their star formation histories (SFHs) at a given mass. In this paper, we employ the Evolution and Assembly of GaLaxies and their Environments (EAGLE) simulations to study the dependence of the sigma(sSFR) of galaxies on stellar mass (M-*) through the sigma(sSFR)-M-* relation in z similar to 0-4. We find that the relation evolves with time, with the dispersion depending on both stellar mass and redshift. The models point to an evolving U-shaped form for the sigma(sSFR)-M-* relation, with the scatter being minimal at a characteristic mass M*( )of 10(9.5) M-circle dot and increasing both at lower and higher masses. This implies that the diversity of SFHs increases toward both the low- and high-mass ends. We find that feedback from active galactic nuclei is important for increasing the sigma(sSFR) for high-mass objects. On the other hand, we suggest that feedback from supernovae increases the sigma(sSFR) of galaxies at the low-mass end. We also find that excluding galaxies that have experienced recent mergers does not significantly affect the sigma(sSFR)-M-* relation. Furthermore, we employ the EAGLE simulations in combination with the radiative transfer code SKIRT to evaluate the effect of SFR/stellar mass diagnostics in the sigma(sSFR)-M-* relation, and find that the SFR/M(* )methodologies (e.g., SED fitting, UV+IR, UV+IRX-beta) widely used in the literature to obtain intrinsic properties of galaxies have a large effect on the derived shape and normalization of the sigma(sSFR)-M-* relation.