This work develops a distributed optimization algorithm with guaranteed exact convergence for a broad class of left-stochastic combination policies. The resulting exact diffusion strategy is shown to have a wider stability range and superior convergence performance than the EXTRA consensus strategy. The exact diffusion solution is also applicable to non-symmetric left-stochastic combination matrices, while most earlier developments on exact consensus implementations are limited to doubly-stochastic matrices or right-stochastic matrices; these latter policies impose stringent constraints on the network topology. Stability and convergence results are noted, along with numerical simulations to illustrate the conclusions.