Diversity in one group of species or genotypes is often correlated with diversity in a second group – prominent examples including native vs exotic species, and genetic diversity in a focal species vs species diversity in the rest of the community. I used simulation models to investigate the roles of competition and facilitation among species or genotypes in creating diversity–diversity relationships, with a focus on facilitation, which has received little theoretical attention. When competitive interactions dominate, increasing diversity in one group reduces diversity in the second group via filling of available niche space. Facilitation can create positive diversity–diversity relationships via a sampling effect, whereby a strong facilitator of the second group is more likely to be present as diversity increases in the first group, and also via one group acting as a source of biotic heterogeneity (i.e. diversifying selection) on the second group. However, the biotic heterogeneity effect is expected only under restricted conditions – with asymmetric facilitation, only during a transient period, or only over a small range of species diversity levels – and therefore seems unlikely to operate within trophic levels in natural communities. More generally, the simultaneous operation of competition and facilitation results in several different diversity–diversity relationships and underlying mechanisms. The results clarify the potential roles of positive and negative interactions in creating diversity–diversity relationships, and in determining the outcome of community dynamics in general. This study also highlights some important difficulties in incorporating facilitation into ecological theory for communities with many species.