ExTrEMO-D: Diffusion Transfer for Expensive Multi-Objective Optimization

In transfer optimization of expensive multi-objective optimization (ExMO), effectively reusing structural knowledge from Pareto-optimal solutions of source tasks is crucial for improving sample efficiency. This work proposes Expensive Transfer Evolutionary Multi-Objective Optimizer with Diffusion (ExTrEMO-D), a generative transfer framework that models the Pareto-set distribution p(x) in the decision space. Compared with forward transfer based on supervised surrogate modeling, ExTrEMO-D captures cross-task similarity in the Pareto-set geometric structure, which provides more informative guidance for optimization. Meanwhile, ExTrEMO-D mitigates the model collapse issue in inverse transfer, which can arise from one-to-many mappings introduced by non-Pareto-optimal samples, by avoiding explicit pairing between preference vectors and solutions. ExTrEMO-D realizes diffusion transfer via two-stage training and targetguided sampling. In terms of the two-stage training process, (i) the optimal transport aligns source non-dominated solutions to the target domain, and (ii) diffusion learns a geometry-consistent prior from the aligned samples. Then, target-guided sampling injects gradients from target multi-objective surrogates into the denoising dynamics, steering generation towards the target Pareto front. Extensive experiments on synthetic benchmarks and three real-world applications spanning materials science, robotics, and machine learning demonstrate that ExTrEMO-D consistently outperforms state-of-the-art baselines and achieves improved sample efficiency in ExMO.