Learning Where to Steer: Noise-Space Geometry for Efficient Offline Multi-Objective Optimization with Generative Models

2026-09-30

AI Summary

This study addresses the high sampling cost and difficulty of steering toward the Pareto front when applying diffusion models to offline multi-objective optimization. To overcome these limitations, this work proposes a novel guidance paradigm grounded in geometric analysis of the noise space. Specifically, the method employs a recursive feature machine to estimate sensitive directions and introduces data-adaptive, Pareto-aware guidance operators. By imposing only a directional displacement on the initial noise, it effectively steers generation without requiring stepwise intervention during the ODE sampling process. Experimental results demonstrate that the proposed approach achieves the best average hypervolume ranking across 47 tasks while substantially reducing sampling costs, comprehensively outperforming existing generative methods.

Abstract

Offline multi-objective optimization (MOO) seeks solutions with better objective trade-offs using only a fixed dataset, without querying the objectives. Diffusion models trained on such data have emerged as a promising approach, but their samples are not inherently better than the data and must be steered toward the Pareto front. Existing methods guide or condition every sampling step. We instead act on the initial noise and leave the sampling process unchanged. Across Off-MOO-Bench, we observe that the objectives, as functions of the noise, are sensitive to only a few directions. We estimate these directions once per task via a Recursive Feature Machine using function values alone, and a small cache serves every trade-off, so each candidate costs one noise displacement and one ODE solve. We prove that this displacement increases the learned scalarized objective in expectation, and that sweeping trade-offs recovers the flow's attainable front up to proxy and steering errors. With additional guidance, for which we introduce novel data-adaptive and Pareto-aware operators, our method attains the best average hypervolume rank among generative methods on 47 tasks, at comparable or lower sampling cost. Steering alone outranks the best prior generative method at a fraction of its sampling cost.

Problem

• Offline Multi-Objective Optimization
• Diffusion Models
• Pareto Front
• Sampling Efficiency

Innovation

• Offline Multi-Objective Optimization
• Noise-Space Steering
• Diffusion Models
• Recursive Feature Machine
• Pareto-aware Operators