  The goal of offline black-box optimization (BBO) is to optimize an expensive
black-box function using a fixed dataset of function evaluations. Prior works
consider forward approaches that learn surrogates to the black-box function and
inverse approaches that directly map function values to corresponding points in
the input domain of the black-box function. These approaches are limited by the
quality of the offline dataset and the difficulty in learning one-to-many
mappings in high dimensions, respectively. We propose Denoising Diffusion
Optimization Models (DDOM), a new inverse approach for offline black-box
optimization based on diffusion models. Given an offline dataset, DDOM learns a
conditional generative model over the domain of the black-box function
conditioned on the function values. We investigate several design choices in
DDOM, such as re-weighting the dataset to focus on high function values and the
use of classifier-free guidance at test-time to enable generalization to
function values that can even exceed the dataset maxima. Empirically, we
conduct experiments on the Design-Bench benchmark and show that DDOM achieves
results competitive with state-of-the-art baselines.
