Posterior Inference with Diffusion Models for High-dimensional Black-box Optimization

Optimizing high-dimensional and complex black-box functions is crucial in numerous scientific applications. While Bayesian optimization (BO) is a powerful method for sample-efficient optimization, it struggles with the curse of dimensionality and scaling to thousands of evaluations. Recently, leveraging generative models to solve black-box optimization problems has emerged as a promising framework. However, those methods often underperform compared to BO methods due to limited expressivity and difficulty of uncertainty estimation in high-dimensional spaces. To overcome these issues, we introduce \textbf{DiBO}, a novel framework for solving high-dimensional black-box optimization problems. Our method iterates two stages. First, we train a diffusion model to capture the data distribution and an ensemble of proxies to predict function values with uncertainty quantification. Second, we cast the candidate selection as a posterior inference problem to balance exploration and exploitation in high-dimensional spaces. Concretely, we fine-tune diffusion models to amortize posterior inference. Extensive experiments demonstrate that our method outperforms state-of-the-art baselines across various synthetic and real-world black-box optimization tasks. Our code is publicly available \href{this https URL}{here}

@article{yun2025_2502.16824,
  title={ Posterior Inference with Diffusion Models for High-dimensional Black-box Optimization },
  author={ Taeyoung Yun and Kiyoung Om and Jaewoo Lee and Sujin Yun and Jinkyoo Park },
  journal={arXiv preprint arXiv:2502.16824},
  year={ 2025 }
}