Mobile genetic elements (MGEs) and diversity-generating mechanisms (DGMs) are paramount in microbial and viral evolution. These elements provide evolutionary leaps, conferring novel phenotypes, including those detrimental to human health, such as antimicrobial resistance. Unfortunately, state-of-the-art algorithms to detect these elements have many limitations, including reliance on reference genomes, assemblers, and heuristics, resulting in computational bottlenecks and limiting the breadth of biological discoveries. Here we present DIVE, a novel statistical, reference-free paradigm for de novo discovery of MGEs and DGMs by identifying k-mer sequences associated with high rates of sequence diversification. We use DIVE to analyze hundreds of samples to rediscover thousands of known MGEs and DGMs, quantify their activity, study their within-element variability, and identify their preferential integration loci. Using DIVE, we rediscover CRISPR, identify previously unreported CRISPR direct repeats in Escherichia coli, discover a novel CRISPR direct repeat in Ruminococcus bromii, identify antisense RNA5 as a putative novel class of non-coding RNA prone to integrate MGEs and identify the boundaries of antibiotic resistance hotspots in SXT integrative and conjugative elements in Vibrio cholerae. DIVE also identifies thousands of sequences associated with high diversity rates that cannot be mapped to known MGEs or DGMs, pointing to a substantial gap in the characterization of the microbial sequence space.