Latent-Time Steering for Bayesian Optimal Experimental Design

Bayesian optimal experimental design (BOED) selects experiments to maximally reduce uncertainty about unknown physical parameters, but the expected information gain (EIG) objective commonly used in BOED is often computationally expensive and difficult to estimate under complex priors. In this work, we propose a steering-cost surrogate for EIG that leverages pretrained diffusion-based generative priors over parameters and estimates EIG as a latent-time steering cost induced by likelihood guidance. Specifically, we combine the MINDE score–KL identity with a diffusion posterior sampling (DPS) plug-in approximation, yielding a tractable integral of squared likelihood guidance. The same pretrained prior supports posterior inference and design scoring without training a separate design policy. Additionally, we characterize the approximation error introduced by the proposed estimator. We validate our method on a range of design problems, including source localization, constant elasticity of substitution, and Darcy flow parameter estimation. For Darcy source-position design on a $64\times 64$ grid, our method reduces mean relative $L_2$ reconstruction error by $24.7\%$ and $24.9\%$ after the first and second measurements, respectively, compared with ALINE at the same resolution over 20 test cases.