Plant architecture is shaped by the production of new organs, most of which emerge postembryonically. This process includes the formation of new lateral branches along existing shoots. Current evidence supports a detached-meristem model as the cellular basis of lateral shoot initiation. In this model, a small number of undifferentiated cells are sampled from the periphery of the shoot apical meristem (SAM) to act as precursors for axillary buds, which eventually develop into new shoots. Repeated branching thus creates cellular bottlenecks (i.e. somatic drift) that affect how de novo (epi)genetic mutations propagate through the plant body during development. Somatic drift could be particularly relevant for stochastic DNA methylation gains and losses (i.e. spontaneous epimutations), as they have been shown to arise rapidly with each cell division. Here, we formalize a special case of the detached-meristem model, where precursor cells are randomly sampled from the SAM periphery in a way that maximizes cell lineage independence. We show that somatic drift during repeated branching gives rise to a mixture of cellular phylogenies within the SAM over time. This process is dependent on the number of branch points, the strength of drift as well as the epimutation rate. Our model predicts that cell-to-cell DNA methylation heterogeneity in the SAM converges to nonzero states during development, suggesting that epigenetic variation is an inherent property of the SAM cell population. Our insights have direct implications for empirical studies of somatic (epi)genomic diversity in long-lived perennial and clonal species using bulk or single-cell sequencing approaches.