With the current accelerating rate of biodiversity extinction, there is great interest in how species diversity influences ecosystem properties. In this article, we investigate the relationship between species diversity and the stability of community biomass in the face of stochastic perturbations of species' abundances. The model explicitly includes species' interactions. We show that the pattern of species' interactions affects whether the relationship between diversity and biomass stability is positive or negative. In particular, assumptions about community structure influence the relationship between species diversity and community biomass, which in turn influences the diversity-stability relationship. We also discuss the relationship between diversity and another type of stability, the proportional change in community biomass with the extinction or introduction of a species. Regardless of community type, diversity buffers the change in biomass when a species is added or removed.