ParetoTransport: Generative Optimization by Mass Transport Toward The Pareto Front

• URL: http://arxiv.org/abs/2609.07706v1
• Date: Mon, 07 Sep 2026 16:19:23 GMT
• Title: ParetoTransport: Generative Optimization by Mass Transport Toward The Pareto Front
• Abstract summary: We propose a training-free guidance method for pre-trained flow-matching models that explicitly specifies and refines a population-level distribution in objective space.<n>We demonstrate state-of-the-art performance on standard offline MOO benchmarks.
• Score: 24.160834012321747
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 explicitly specifies and refines a population-level distribution in objective space. ParetoTransport guides a flow-matching sampler to iteratively transport the empirical offline distribution toward the Pareto front, with Wasserstein matching to intermediate proxy distributions. This directly controls distributional displacement and mass allocation along the front. We establish a convergence result and demonstrate state-of-the-art performance on standard offline MOO benchmarks, extending recent evaluations beyond hypervolume to generational distance, inverted generational distance, and Wasserstein distance.

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