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.
