Why diffusion models get stuck sampling from their own data

Sampling from learned distributions using diffusion models often gets stuck on fragmented parts of the data manifold. This work introduces U-turn chains—iterative forward-backward diffusion steps with Metropolis-Hastings corrections—and uncovers a sharp transition: tiny moves fail to explore globally, but larger U-turn magnitudes restore mixing. The effect appears across synthetic languages, natural images, and text, with high-level features (like semantic concepts in LLM representations) relaxing last only when noise is large enough. The findings suggest diffusion samplers face fundamental constraints from their learned geometry.