First introduced by Fernholz in stochastic portfolio theory, functionally generated portfolio allows its investment performance to be attributed to directly observable and easily interpretable market quantities. In previous works we showed that Fernholz’s multiplicatively generated portfolios have deep connections with optimal transport and the information geometry of exponentially concave functions. Recently, Karatzas and Ruf introduced a new additive portfolio generation whose relation with optimal transport was studied by Vervuurt. We show that additively generated portfolios can be interpreted in terms of the celebrated dually flat information geometry of Bregman divergence. Moreover, we introduce a unified framework of functional portfolio construction containing the two known cases and characterize all possible forms. Each construction involves a divergence functional on the unit simplex measuring the volatility captured, and admits a pathwise decomposition for the portfolio value.