We investigate applications of optimal transport theory to Kyle–Back models. First, we introduce a general methodology for constructing Kyle–Back equilibria from an optimal transport problem between the insider’s private signal and the market maker’s filtered beliefs. Using Monge–Kantorovich duality and backward stochastic partial differential equations (BSPDEs), we characterize equilibrium prices and trading strategies through Kantorovich potentials and transport maps, providing a unified framework that encompasses nearly all known continuous-time Kyle–Back models, including those with dynamic information and activist trading. Our second project develops a variational formulation of the Kyle model that accommodates stochastic and multidimensional liquidity. The equilibrium is reinterpreted as an optimal liquidation of information, where the insider’s control variable is the rate of information release rather than inventory. This formulation links market microstructure to optimal execution and clarifies the dual role of the adjoint process identified by Collin-Dufresne and Fos (2016) as the co-state variable in the stochastic maximum principle.