Asymptotic Learning Curves for Conditional Diffusion Models with Random Features

Conditional diffusion models have achieved remarkable success in generating novel, high-quality samples under prescribed conditions. Recent theoretical studies have examined memorization and generalization in unconditional diffusion models, but the theoretical understanding of conditional diffusion models, particularly with continuous conditions, remains limited. This distinction is important because conditional models must generalize to conditions not observed during training. We investigate these questions by deriving asymptotically precise training and test errors for a random-feature model of continuous conditional diffusion in the high-dimensional limit. Our findings motivate further investigation of memorization and generalization mechanisms specific to conditional diffusion models.