Retrieval Dwelling: A Principled Sampling Strategy for Exploiting Spurious State Exploration

Recent work has established that diffusion models can be interpreted as temperature-controlled Modern Hopfield Networks, where spurious states, historically viewed as detrimental artifacts, emerge at the boundary between memorization and generalization. We argue that these spurious attractors can be interpreted as low-curvature mixture manifolds that support interpolation between stored patterns. Building on this interpretation, we introduce \emph{retrieval dwelling}, a spectrally triggered sampling strategy that uses signatures of the score Jacobian spectrum to identify and prolong exploration in the putative spurious regime. Experiments on MNIST, FashionMNIST, CIFAR-10, and ImageNet-64 indicate that retrieval dwelling increases a measured spurious-state fraction by roughly 2-3$\times$, improves LPIPS diversity by 9-15\%, and yields comparable or modestly improved FID, while memorisation rates remain comparable to baseline in our runs.