Generative Priors for High-Dimensional BOED
Pretrained diffusion models as flexible priors for scalable BOED in non-Gaussian, high-dimensional inverse problems
Classical EIG estimation becomes computationally prohibitive when the unknown parameter is high-dimensional and the posterior is non-Gaussian. This ongoing work addresses this by using pretrained diffusion models as flexible priors for sequential BOED.
The key idea is to interpret posterior sampling as a guided diffusion trajectory, where the accumulated likelihood guidance along the latent path serves as a tractable surrogate for information gain. Building on mutual information estimation via score-based diffusion (Franzese et al., 2024), the MINDE-DPS estimator enables efficient EIG estimation alongside posterior sampling.
We validate the approach on source localization and Darcy flow parameter estimation, including high-dimensional PDE-constrained settings where classical methods struggle. For the function-space setting, we leverage FunDPS (Yao et al., 2025), enabling posterior sampling over PDE solution fields from extremely sparse observations. Ongoing work explores flow matching as a faster alternative for posterior sampling and EIG accumulation.