Strong generalization in diffusion models

High-quality samples generated with score-based reverse diffusion algorithms provide evidence that deep neural networks (DNNs) trained for denoising can learn high-dimensional densities, despite the curse of dimensionality. However, recent reports of memorization of the training set raise the question of whether these networks are learning the ``true'' continuous density of the data. Here, we show that two denoising DNNs trained on non-overlapping subsets of a dataset learn nearly the same score function, and thus the same density, with a surprisingly small number of training images. This strong generalization demonstrates an alignment of powerful inductive biases in the DNN architecture and/or training algorithm with properties of the data distribution. Our method is general and can be applied to assess generalization vs.\ memorization in any generative model.