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arXiv Machine Learning By Yiwen Kou, Yimeng Wang

Lower Bounds for Parallel Diffusion Sampling

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The paper establishes the first polynomial lower bounds on the number of parallel rounds required for diffusion sampling with approximate scores. It proves a “~Ω(d^{1/3})” lower bound for sampling smooth, near‑isotropic Gaussian mixtures in ℝ^d, and an Ω(d) lower bound for uniform sampling from anisotropic axis‑aligned boxes inside the unit ball. These bounds apply to any randomized algorithm that can make polynomially many queries per round at arbitrary locations and noise levels, while maintaining inverse‑polynomial score error and constant total variation accuracy.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

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