High-accuracy and dimension-free sampling with diffusions

• URL: http://arxiv.org/abs/2601.10708v1
• Date: Thu, 15 Jan 2026 18:58:50 GMT
• Title: High-accuracy and dimension-free sampling with diffusions
• Authors: Khashayar Gatmiry, Sitan Chen, Adil Salim,
• Abstract summary: We propose a new solver for diffusion models relying on a subtle interplay between low-degree approximation and the collocation method.<n>We prove that its complexity scales emphpolylogarithmically in $1/varepsilon$, yielding the first high-accuracy' guarantee for a diffusion-based sampler.
• Score: 27.7060066305274
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Diffusion models have shown remarkable empirical success in sampling from rich multi-modal distributions. Their inference relies on numerically solving a certain differential equation. This differential equation cannot be solved in closed form, and its resolution via discretization typically requires many small iterations to produce \emph{high-quality} samples. More precisely, prior works have shown that the iteration complexity of discretization methods for diffusion models scales polynomially in the ambient dimension and the inverse accuracy $1/\varepsilon$. In this work, we propose a new solver for diffusion models relying on a subtle interplay between low-degree approximation and the collocation method (Lee, Song, Vempala 2018), and we prove that its iteration complexity scales \emph{polylogarithmically} in $1/\varepsilon$, yielding the first ``high-accuracy'' guarantee for a diffusion-based sampler that only uses (approximate) access to the scores of the data distribution. In addition, our bound does not depend explicitly on the ambient dimension; more precisely, the dimension affects the complexity of our solver through the \emph{effective radius} of the support of the target distribution only.

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