  Diffusion models have demonstrated great potential in generating high-quality
content for images, natural language, protein domains, etc. However, how to
perform user-preferred targeted generation via diffusion models with only
black-box target scores of users remains challenging. To address this issue, we
first formulate the fine-tuning of the targeted reserve-time stochastic
differential equation (SDE) associated with a pre-trained diffusion model as a
sequential black-box optimization problem. Furthermore, we propose a novel
covariance-adaptive sequential optimization algorithm to optimize cumulative
black-box scores under unknown transition dynamics. Theoretically, we prove a
$O(\frac{d^2}{\sqrt{T}})$ convergence rate for cumulative convex functions
without smooth and strongly convex assumptions. Empirically, experiments on
both numerical test problems and target-guided 3D-molecule generation tasks
show the superior performance of our method in achieving better target scores.
