ParetoTransport: Generative Optimization by Mass Transport Toward The Pareto Front

Offline multi-objective optimization (MOO) seeks candidate designs whose objective vectors not only lie close to the Pareto front but are also effectively distributed along it. Generative methods have recently emerged as a promising approach because they learn a distribution over feasible designs while allowing generation to be guided toward desirable designs. Existing methods, however, largely retain classical sample-wise guidance strategies, leaving the distribution-level modeling capability of generative methods underused. We formulate offline MOO as a sampling problem and motivate the $2$-Wasserstein distance as a natural quality measure. Building on this view, we propose ParetoTransport, a training-free guidance method for pre-trained flow-matching models that formulates guidance directly over the population-level distribution in objective space, combining directional transport toward the Pareto front with Wasserstein matching that controls the allocation of probability mass along it. Under an exact-matching assumption, we prove that the transported distribution converges geometrically toward the Pareto front in $2$-Wasserstein distance. On offline MOO benchmarks, we extend the evaluation of recent generative methods beyond hypervolume to generational distance, inverted generational distance, and the $2$-Wasserstein distance. ParetoTransport achieves consistently strong performance, attaining the best average rank in convergence and probability-mass allocation across all benchmark families.