Query Lower Bounds for Diffusion Sampling

2026-04-12

AI Summary

This work investigates the information-theoretic lower bound on the number of score function queries required to accelerate generation in diffusion sampling. By integrating information-theoretic analysis, adaptive query complexity, and L^p error modeling under a given polynomial-accuracy assumption for score estimation, it establishes—for the first time—that any diffusion sampling algorithm in high-dimensional spaces necessitates at least $\tilde{\Omega}(\sqrt{d})$ adaptive score queries. This lower bound underscores the fundamental necessity of multiscale noise scheduling and provides a theoretical limit that contextualizes the performance of existing accelerated sampling methods.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Security and Privacy: Large-scale security measurements

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 $\widetildeΩ(\sqrt{d})$ 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.

Problem

• diffusion sampling
• score query
• lower bounds
• information-theoretic limits
• noise schedules

Innovation

• diffusion sampling
• query lower bounds
• score estimation
• multiscale noise schedules
• information-theoretic limits