Generative Boltzmann Optimization: Diffusion Models for Adaptive Gibbs Sampling

Black-box optimization requires efficiently balancing exploration and exploitation under limited access to expensive function evaluations. We propose Generative Boltzmann Optimization via Conditional Diffusion (GBO-CD), which combines diffusion models with distributional search to learn and propagate adaptive sampling distributions across iterations. By leveraging pseudo-labeled samples, the method constructs a large, low-cost training set, enabling effective refinement of the search distribution with minimal additional evaluations. We provide a distribution-level theoretical analysis showing that the estimated sampling distribution tracks the target Gibbs distribution and progressively concentrates near the global optimizer. Empirical results demonstrate competitive performance on benchmark problems.