Bayesian optimization (BO) is a widely used approach for black-box optimization that uses a Gaussian process (GP) as a surrogate and guides sequential evaluations via an acquisition function, with the ultimate goal of locating the global optimum $\mathbf{x}^{\star}$. To align with this goal, information-based acquisition functions such as Predictive Entropy Search (PES) model $\mathbf{x}^{\star}$ as a random variable and reduce the entropy of its distribution, but approximating this distribution via traditional GP posterior sampling is computationally expensive. To address this limitation, we leverage Conditional Diffusion Models (CDMs) to efficiently approximate the distribution of $\mathbf{x}^{\star}$ and develop BO-inherent training strategies for CDMs. Motivated by the structural properties of the CDM-learned distribution, we further develop an acquisition strategy termed Diffusion-based Mode Seeking (DMS) to guide the sequential evaluation. We establish a sub-optimality guarantee for the CDM-learned distribution and demonstrate through extensive experiments that DMS outperforms standard BO baselines.

翻译：贝叶斯优化（BO）是一种广泛用于黑箱优化的方法，它采用高斯过程（GP）作为代理模型，并通过采集函数引导序列评估，其最终目标是定位全局最优点$\mathbf{x}^{\star}$。为实现这一目标，基于信息的采集函数（如预测熵搜索PES）将$\mathbf{x}^{\star}$建模为随机变量，并降低其分布的熵，但通过传统GP后验采样逼近该分布的计算成本高昂。为解决此局限，我们利用条件扩散模型（CDMs）高效逼近$\mathbf{x}^{\star}$的分布，并开发了面向CDM的BO固有训练策略。受CDM学习所得分布的结构特性启发，我们进一步提出基于扩散的模态搜索（DMS）采集策略来引导序列评估。我们为CDM学习所得分布建立了次优性保障，并通过大量实验证明DMS优于标准BO基线方法。