The multistage model of carcinogenesis explains the steep rise of cancer incidence with age through accumulated events, and reliability theory extends this principle to systems whose failure requires several components. We asked whether the same idea could explain why chronic diseases differ in how rapidly incidence rises with age, and whether multimorbidity could independently reveal the processes involved. In UK Biobank, linked health records allowed pre-assessment disease co-occurrence and subsequent incidence to be analysed separately. Using generative representation learning, we derived functional units (FUs) from co-occurrence patterns across 232 diagnoses in 502,355 participants. For each diagnosis, we counted linked FUs and compared this breadth with subsequent incidence. Diagnoses linked to more FUs showed steeper age dependence of incidence (Spearman {rho} = 0.50; 0.4618 among 196 diagnoses with rising hazards), and this relationship persisted in an age-free representation. The FUs had distinct genetic architectures, with lead-variant directions preserved in FinnGen and the Million Veteran Program. Their GWAS reached 34 regions missed by diagnosis and BMI comparators, while fine-mapping and molecular evidence connected FU loci to candidate genes enriched for approved drug targets. Together, these results extend a multistage principle from cancer to chronic disease and show that multimorbidity structure explains variation in age-dependent incidence.