Before diffusion models generalize, they grow spurious attractors absent from training data but repeated in samples
As the training set grows, diffusion models move from memorizing training samples to generalizing, and between these phases an intermediate kind of attractor appears that matches no training image yet recurs in generated samples. Reading generation as retrieval in a dense associative memory predicts such spurious states once storage capacity is exceeded; on MNIST, FASHION-MNIST, CIFAR-10 and LSUN-CHURCH the spurious fraction rises and then falls at the memorization-to-generalization boundary, with basin volumes between those of memorized and generalized samples.