DiffBED: Scaling Bayesian Experimental Design to High-Dimensions

Bayesian experimental design (BED) is a principled framework for intelligent data acquisition. However, current approaches do not scale to problems with high–dimensional designs, impeding its uptake. We show that this limitation arises predominantly from the difficulty in specifying a likelihood model that remains accurate throughout the design space, and that without this, standard design optimisation procedures lead to a reward-hacking-like behaviour that exploits deficiencies in the likelihood, producing implausible or unrealistic designs. To overcome this, we introduce DiffBED, an approach based on a novel BED objective that explicitly rewards realistic designs. Realism is captured by a diffusion model, which we guide using information-theoretic experimental design criteria to generate highly informative yet realistic designs. This enables BED at an unprecedented scale: while existing applications of BED have been restricted to design spaces with a handful of dimensions, we show that DiffBED can successfully scale to designing high–resolution images.