Pareto-Conditioned Diffusion Models for Offline Multi-Objective Optimization

TL;DR

This work reframes offline multi-objective optimization as conditional sampling by proposing Pareto-Conditioned Diffusion (PCD), a diffusion-based generator that conditions on target trade-offs to produce high-quality Pareto-front samples without explicit surrogate models. It introduces a multi-objective reweighting scheme to bias learning toward promising regions and an NSGA-III–inspired reference-direction method to generate diverse conditioning points beyond the observed data. Through extensive benchmarks across synthetic, MORL, real-world engineering, scientific design, and MONAS tasks, PCD demonstrates competitive performance and exceptional consistency with a single set of hyperparameters, while ablations confirm the value of its two core components. The approach offers a principled, end-to-end alternative to surrogate-guided offline MOO and has implications for efficient, data-driven design optimization in settings where objective evaluations are costly or unavailable during optimization.

Abstract

Multi-objective optimization (MOO) arises in many real-world applications where trade-offs between competing objectives must be carefully balanced. In the offline setting, where only a static dataset is available, the main challenge is generalizing beyond observed data. We introduce Pareto-Conditioned Diffusion (PCD), a novel framework that formulates offline MOO as a conditional sampling problem. By conditioning directly on desired trade-offs, PCD avoids the need for explicit surrogate models. To effectively explore the Pareto front, PCD employs a reweighting strategy that focuses on high-performing samples and a reference-direction mechanism to guide sampling towards novel, promising regions beyond the training data. Experiments on standard offline MOO benchmarks show that PCD achieves highly competitive performance and, importantly, demonstrates greater consistency across diverse tasks than existing offline MOO approaches.

Figures (9)

• Figure 1: Overview of the PCD framework, which reframes offline MOO as a conditional sampling problem.Training: A conditional diffusion model is trained on a static dataset, using a novel reweighting strategy to emphasize high-quality solutions near the Pareto front. Sampling: At inference, the model directly generates novel designs conditioned on target objectives. This end-to-end approach sidesteps the need for the explicit surrogate models and separate optimizers required by prior methods.
• Figure 2: Overview of the conditioning points generation procedure: a) The objective space is partitioned via direction vectors, and points are ranked based on non-dominated sorting. b) Each direction vector is paired with the point closest to it in perpendicular distance (black arrow). Rest of the points are paired to vector with the least amount of assigned points (gray arrow). c) A diverse set of conditioning points is generated by extrapolating the assigned points along the direction vectors and adding Gaussian noise.
• Figure 3: Effect of the guidance scale $\gamma$ on the normalized HV ratio across five representative tasks. Performance saturates quickly, showing limited benefit from strong guidance.
• Figure 4: Normalized dominance number distributions reveal dataset quality differences. The narrow distributions of C10/MOP2 and MO-Hopper indicate consistently high-quality datasets, whereas the long-tailed distribution of ZDT2 signals high variance in sample quality.
• Figure 5: Effect of the reweighting temperature $\tau$ on normalized performance. For the high-variance ZDT2 dataset, increasing $\tau$ significantly improves performance. The effect is minimal on the low-variance datasets.

Theorems & Definitions (2)

• Definition 1: Pareto Dominance
• Definition 2: Pareto Optimality