ParetoTransport: Generative Optimization by Mass Transport Towards the Pareto Front

Offline multi-objective optimization requires both convergence of a solution set towards the Pareto front and coverage along it. Generative methods have recently emerged as a promising approach due to their ability to approximate the inverse relation between objective vectors and feasible designs. Beyond this inverse-design capability, however, their inherently distributional nature remains largely underexploited: existing methods primarily rely on classical sample-wise guidance strategies. We propose $\textit{ParetoTransport}$, a training-free guidance method for pre-trained flow-matching models that explicitly refines the generated objective-space distribution. ParetoTransport transports the generated distribution by combining distributional displacement towards the Pareto front with Wasserstein matching. This enables explicit control over both convergence towards the Pareto front and mass allocation along it. We further provide theoretical support for this transport view by establishing a Wasserstein contraction result, showing geometric contraction of the objective-space distribution towards the Pareto front. ParetoTransport achieves state-of-the-art performance on standard offline MOO benchmarks, extending recent hypervolume-based evaluations with Generational Distance (GD) and Inverted Generational Distance (IGD).