Genome-wide in vivo protein-DNA interactions are routinely mapped using high-throughput chromatin immunoprecipitation (ChIP). ChIP-reported regions are typically investigated for enriched sequence-motifs, which are likely to model the DNA-binding specificity of the profiled protein and/or of co-occurring proteins. However, simple enrichment analyses can miss insights into the binding-activity of the protein. Note that ChIP reports regions making direct contact with the protein as well as those binding through intermediaries. For example, consider a ChIP experiment targeting protein X, which binds DNA at its cognate sites, but simultaneously interacts with four other proteins. Each of these proteins also binds to its own specific cognate sites along distant parts of the genome, a scenario consistent with the current view of transcriptional hubs and chromatin loops. Since ChIP will pull down all X-associated regions, the final reported data will be a union of five distinct sets of regions, each containing binding sites of one of the five proteins, respectively. Characterizing all five different motifs and the corresponding sets is important to interpret the ChIP experiment and ultimately, the role of X in regulation. We present diversity which attempts exactly this: it partitions the data so that each partition can be characterized with its own de novo motif. Diversity uses a Bayesian approach to identify the optimal number of motifs and the associated partitions, which together explain the entire dataset. This is in contrast to standard motif finders, which report motifs individually enriched in the data, but do not necessarily explain all reported regions. We show that the different motifs and associated regions identified by diversity give insights into the various complexes that may be forming along the chromatin, something that has so far not been attempted from ChIP data. Webserver at http://diversity.ncl.res.in/, standalone (Mac OS X/Linux) from https://github.com/NarlikarLab/DIVERSITY/releases/tag/v1.0.0.