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The scatter (${\rm\sigma_{\text{sSFR}}}$) of the specific star formation rates (sSFRs) of galaxies is a measure of the diversity in their star formation histories (SFHs) at a given mass. In this paper we employ the EAGLE simulations to study the dependence of the ${\rm \sigma_{\text{sSFR}}}$ of galaxies on stellar mass (${\rm M_{\star}}$) through the ${\rm \sigma_{\text{sSFR}}}$-${\rm M_{\star}}$ relation in $ {\rm z \sim 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-shape form for the ${\rm \sigma_{\text{sSFR}}}$-${\rm M_{\star}}$ relation with the scatter being minimal at a characteristic mass $M^{\star}$ of ${\rm 10^{9.5}}$ ${\rm M_{\odot}}$ and increasing both at lower and higher masses. This implication is that the diversity of SFHs increases towards both at the low- and high-mass ends. We find that active galactic nuclei feedback is important for increasing the ${\rm \sigma_{\text{sSFR}}}$ for high mass objects. On the other hand, we suggest that SNe feedback increases the ${\rm \sigma_{\text{sSFR}}}$ of galaxies at the low-mass end. We also find that excluding galaxies that have experienced recent mergers does not significantly affect the ${\rm \sigma_{\text{sSFR}}}$-${\rm M_{\star}}$ relation. Furthermore, we employ the combination of the EAGLE simulations with the radiative transfer code SKIRT to evaluate the effect of SFR/stellar mass diagnostics in the ${\rm \sigma_{\text{sSFR}}}$-${\rm M_{\star}}$ relation and find that the ${\rm SFR/M_{\star}}$ 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 ${\rm \sigma_{\text{sSFR}}}$-${\rm M_{\star}}$ relation.