Optimizing complex systems, from discovering therapeutic drugs to designing high-performance materials, remains a fundamental challenge across science and engineering, as the underlying rules are often unknown and costly to evaluate. Offline optimization aims to optimize designs for target scores using pre-collected datasets without system interaction. However, conventional approaches may fail beyond training data, predicting inaccurate scores and generating inferior designs. This paper introduces ManGO, a diffusion-based framework that learns the design-score manifold, capturing the design-score interdependencies holistically. Unlike existing methods that treat design and score spaces in isolation, ManGO unifies forward prediction and backward generation, attaining generalization beyond training data. Key to this is its derivative-free guidance for conditional generation, coupled with adaptive inference-time scaling that dynamically optimizes denoising paths. Extensive evaluations demonstrate that ManGO outperforms 24 single- and 10 multi-objective optimization methods across diverse domains, including synthetic tasks, robot control, material design, DNA sequence, and real-world engineering optimization.

翻译：优化复杂系统，从发现治疗药物到设计高性能材料，始终是科学与工程领域的一项根本性挑战，因为其底层规则通常未知且评估成本高昂。离线优化的目标是在无需与系统交互的情况下，利用预先收集的数据集，针对目标评分优化设计方案。然而，传统方法在训练数据之外可能失效，预测出不准确的评分并生成次优设计。本文提出了ManGO，一个基于扩散的框架，它通过学习设计-评分流形，整体性地捕捉设计与评分之间的相互依赖关系。与现有方法将设计和评分空间孤立处理不同，ManGO统一了前向预测与后向生成，从而实现了对训练数据之外的泛化。其关键在于其用于条件生成的无导数指导，结合了自适应推理时间缩放，能够动态优化去噪路径。广泛的评估表明，在包括合成任务、机器人控制、材料设计、DNA序列以及现实世界工程优化在内的多个领域中，ManGO的性能优于24种单目标优化方法和10种多目标优化方法。