In certain naturally aged aluminum alloys, significant strengthening can be obtained due to the decomposition of a super-saturated solid solution into clusters. The origins of such strengthening remain unclear due to the challenge of differentiating solute cluster strengthening from solid solution or precipitate strengthening. To shed light on the origin of cluster strengthening in aluminum alloys, the interaction between the smallest possible type of clusters (i.e. dimers) and moving dislocations in a model Al-Mg alloy is studied using atomistic simulations. Additionally, theoretical models for both the parelastic and dielastic interactions between clusters and dislocations is used to identify which factor among order strengthening, elastic interaction, and change of stacking fault energy controls cluster strengthening. The comparison of the results from these models to that of the atomistic simulations show that in the case of Mg dimers, the strength of the strongest ones are dominated by the dielastic contribution through the change of stacking fault energy.