Quantum dots (QDs) and quantum dot molecules (QDMs) are nanostructures that spontaneously self-assemble under different heteroepitaxial growth conditions to reduce the strain in the system. In the silicon–germanium system, QDs form when the rate of deposition is low, whereas QDMs form at higher deposition rates. In this work, the theoretical model of silicon–germanium heteroepitaxy is modified by explicitly incorporating noise in a continuum theory for surface evolution in molecular beam epitaxy. Using the connection between higher deposition flux and a higher noise amplitude, it is possible to explain how changing flux can lead to a transition from QD to QDM formation, as seen in experiments. In these systems, increasing the noise amplitude leads to formation of pits on the surface, as opposed to QDs. These pits serve as nucleation sites for eventual QDM formation and subsequent refinement during annealing. On the other hand, in the case of pre-patterned films with existing pits, QDMs form under low stochasticity, whereas QDs form when the noise amplitude is large. Thus, we illustrate a dual role of noise in nanostructure growth: one where it promotes formation of QDMs via pit nucleation and another where it curtails QDM formation due to stochastic effects.