Initial state-independent phenotypic diversification will be a powerful tool for directing cells to multiple phenotypes in practical situation, in which initial cellular states are unknown. In this study, we designed Symmetric Diversity Generator (SDG) for the initial state-independent phenotypic diversification, in which homogenous cells diversify into two phenotypes and the ratio of the phenotypes do not depend on the initial cellular state. The SDG consists of two mechanisms: an intracellular mutual inhibition by repressors and an intercellular activation of the repressor productions by intercellular activators that are expected to compensate imbalance of repressor concentrations and of intercellular activator concentrations. We computationally evaluated the initial state dependence of the SDG in terms of the ratio of the two phenotypes after the diversification, and found the SDG still has initial state dependence. For lower dependence, we designed two kinds of symmetric diversity generator focusing on degradation rate of activators and responsiveness of repressor productions to transcription factors, activators and repressors. Our computational evaluation suggests that the latter approach is much more promising than the former one because the intercellular activators can compensate the imbalance of the transcription factors in advance of response of repressor productions. The former approach would be used for improvement of robustness of other synthetic genetic circuits already designed.