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arXiv · 2604.10857

Query Lower Bounds for Diffusion Sampling

Zhiyang Xun·Eric Price
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Abstract

Diffusion models generate samples by iteratively querying learned score estimates. A rapidly growing literature focuses on accelerating sampling by minimizing the number of score evaluations, yet the information-theoretic limits of such acceleration remain unclear. In this work, we establish the first score query lower bounds for diffusion sampling. We prove that for $d$-dimensional distributions, given access to score estimates with polynomial accuracy $\varepsilon=d^{-O(1)}$ (in any $L^p$ sense), any sampling algorithm requires $\widetilde{\Omega}(\sqrt{d})$ adaptive score queries. In particular, our proof shows that any sampler must search over $\widetilde{\Omega}(\sqrt{d})$ distinct noise levels, providing a formal explanation for why multiscale noise schedules are necessary in practice.

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Zhiyang Xun, Eric Price. 2026-04-12. Query Lower Bounds for Diffusion Sampling. https://arxiv.org/abs/2604.10857

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