ParetoTransport: Generative Optimization by Mass Transport Toward The Pareto Front

Offline multi-objective optimization requires not only moving the objective vectors of candidate designs toward the Pareto front, but also distributing them effectively along it. Generative methods have recently emerged as a natural approach because they learn a distribution over feasible designs while allowing generation to be steered toward promising designs. Existing methods, however, largely retain classical sample-wise guidance strategies, leaving the distribution-level modeling capability of generative methods underused. We propose ParetoTransport, a training-free guidance method for pre-trained flow-matching models that formulates guidance over the induced probability path, transporting the empirical offline distribution toward the Pareto front under Wasserstein matching to intermediate proxy distributions. This directly controls distributional displacement and mass allocation. We establish a convergence result and demonstrate state-of-the-art performance on standard offline MOO benchmarks, evaluating beyond hypervolume with generational distance, inverted generational distance, and Wasserstein distance.