Query Lower Bounds for Diffusion Sampling

Fuente: arXiv
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Autori principali: Xun, Zhiyang, Price, Eric
Natura: Preprint
Pubblicazione: 2026
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author Xun, Zhiyang
Price, Eric
author_facet Xun, Zhiyang
Price, Eric
contents 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 any sampler must search over $\widetildeΩ(\sqrt{d})$ distinct noise levels, providing a formal explanation for why multiscale noise schedules are necessary in practice.
format Preprint
id arxiv_https___arxiv_org_abs_2604_10857
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Query Lower Bounds for Diffusion Sampling
Xun, Zhiyang
Price, Eric
Machine Learning
Artificial Intelligence
Data Structures and Algorithms
Statistics Theory
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 any sampler must search over $\widetildeΩ(\sqrt{d})$ distinct noise levels, providing a formal explanation for why multiscale noise schedules are necessary in practice.
title Query Lower Bounds for Diffusion Sampling
topic Machine Learning
Artificial Intelligence
Data Structures and Algorithms
Statistics Theory
url https://arxiv.org/abs/2604.10857