High-Dimensional Black-Box Optimization via Guidance Sampling of Diffusion Models

Many real-world optimization problems involve optimizing black-box objectives for which only a limited number of evaluations are available. Bayesian optimization (BO) is a powerful framework for such problems, but its effectiveness often deteriorates in high-dimensional spaces. Recent work leverages diffusion models for black-box optimization, often through pre-training a reward-conditioned score network to steer generation towards high-reward samples. Alternatively, gradient-based guidance methods assume access to a differentiable reward function from which guidance gradients are queried. However, these approaches either require large amounts of labeled data for offline training or access to exact reward gradients, limiting their applicability in black-box settings. We propose BReaD (Black-box Reward-guided Sampling of Diffusion Model), a guidance sampling framework for optimizing black-box rewards without assuming access to a labeled dataset or reward gradients. The proposed method uses a Gaussian process (GP) as a differentiable surrogate for the unknown objective and actively queries labels for the generated samples. We provide a theoretical analysis of the total-variation distance between the generated distribution and the target distribution. Using Upper Confidence Bound (UCB) as guidance signals, our method balances exploration and exploitation during generation and enables the discovery of high-reward regions in the data space. Numerical experiments on scientific discovery and image generation tasks demonstrate that our framework can effectively optimize black-box rewards in low-data scenarios.