Understanding how genomic variation contributes to phenotypic complexity and disease requires approaches that overcome the linear assumptions of additive models and resolve the combinatorial nature of genome regulation. While genome-wide association studies (GWAS) have catalogued thousands of loci linked to complex traits, the functional interpretation of these regions remains limited by a lack of methods to integrate and deconvolve their cell-type-specific regulatory roles. Here, we analyse 833 EpiMap epigenomes spanning eight chromatin marks to construct a generalizable machine learning framework that models the modular architecture of genome regulation. We define 720 interpretable regulatory signatures, Epigenetically Co-Modulated Patterns, that delineate co-regulated genomic regions with tissue and cell-specific regulatory activity. We dissect underlying epigenomic signatures of genomic loci associated with cell-type specific enhancers, complex traits and diseases. We demonstrate utility of EpiCops to improve causal variant mapping across 25 GWAS traits. Additionally, we apply EpiCops to distinguish biological patterns within the mixture of GTEx eQTLs, ClinVar pathogenic variants, and UK Biobank GWAS traits. By applying EpiCops to variants associated with diabetes and asthma, we effectively dissect these complex diseases into distinct subgroups, outperforming state-of-the-art supervised benchmark methods. Finally, we demonstrate the utility of EpiCops in substantially enhancing polygenic risk score predictions compared to baseline models. Taken together, this study presents a scalable framework for interpreting the regulatory logic of genetic variation and advancing methods to resolve the cellular and molecular basis of trait heterogeneity and disease mechanisms.