Scaling Bayesian Experimental Design to High-Dimensions with Information-Guided Diffusion

We present DiffBED, a Bayesian experimental design (BED) approach that scales to problems with high-dimensional design spaces. Our key insight is that current BED approaches typically cannot be scaled to real high--dimensional design problems because of the need to specify a likelihood model that remains accurate throughout the design space. We show that without this, their design optimisation procedures exploit deficiencies in the likelihood and produce implausible designs. We overcome this issue by introducing a generative prior over feasible designs using a diffusion model. By guiding this diffusion model using principled information-theoretic experimental design objectives, we are then able to generate highly informative yet realistic designs at an unprecedented scale: while previous applications of BED have been restricted to design spaces with a handful of dimensions, we show that DiffBED can successful scale to designing high-resolution images.