Query Lower Bounds for Diffusion Sampling
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 $\widetildeΩ(\sqrt{d})$ adaptive score queries. In particular, our proof shows that, within any polynomial total-query budget, successful sampling requires searc...
| Authors | Zhiyang Xun, Eric Price |
|---|---|
| Primary category | cs.LG |
| Published | 12 April 2026 |
| Last updated at source | 29 September 2026 |
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