We consider solving multi-objective optimization problems in a distributed manner over a network of nodes. The problem is equivalent to optimizing a global cost that is the sum of individual components. Diffusion adaptation enables the nodes to cooperate locally through in-network processing in order to approach Pareto-optimality. We analyze the mean-square-error performance of the diffusion strategy and show that, at steady-state, all nodes can be made to approach a Pareto-optimal solution.