Ever since the work of May, almost 50 years ago, ecologists have sought to find the mech- anisms underlying the stability of species-rich communities. In order to reconcile empirical observations of highly diverse systems with theoretical models, many such mechanisms were proposed. Yet, recent refinements of May’s work suggest that stability in large systems re- quires a large degree of fine-tuning. As such, rich ecosystems are, in theory, very susceptible to perturbations in the model parameters, hindering their ability to persist. What has been largely overlooked, however, is that the set of species we observe is actually the end prod- uct of a process. This process, called community assembly, is a complex interplay between immigration from a regional pool of species to a local habitat and local extinctions fueled by species interactions. Explicitly considering the whole process allows us to gain a deeper understanding of how highly diverse communities exist. In this work, we study community assembly models under Lotka-Volterra dynamics and a constant regional pool of invaders. Under different parameterizations and modes of invasion, we show that the observation of highly speciose communities is possible without any need of fine-tuning—simply by letting the system assemble itself. Thus, while an arbitrary set of species cannot coexist, the pro- cess of assembly allows an arbitrary regional pool of species to give rise to species-rich local communities. In other words, a diverse regional pool gives rise to diverse local communities.