I will talk about generic identifiability of component analysis for pairwise mean independent source variables, which generalizes the classical result for independent component analysis (ICA) by relaxing the independence assumption. Our result implies generic identifiability of component analysis models with source variables that are weaker than independence but stronger than pairwise mean independence. We show that the pairwise mean independence assumption is minimal for generic identifiability: if we drop one mean independence assumption on the source variables, the model becomes generically unidentifiable. Just as independent distributions have diagonal cumulants, pairwise mean independent distributions have prescribed zeros in their cumulant tensors. Our results apply to any distributions with these zero patterns, and sufficiently generic nonzero entries, at any higher-order cumulant. This is joint work with Anna Seigal and Piotr Zwiernik.