dorsal/arxiv
View SchemaHigh-accuracy and dimension-free sampling with diffusions
| Authors | Khashayar Gatmiry, Sitan Chen, Adil Salim |
|---|---|
| Categories | |
| ArXiv ID | 2601.10708vv1 |
| URL | https://arxiv.org/abs/2601.10708 |
| 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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"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.\n 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\u0027\u0027 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.",
"arxiv_id": "2601.10708",
"authors": [
"Khashayar Gatmiry",
"Sitan Chen",
"Adil Salim"
],
"categories": [
"cs.LG",
"math.ST",
"stat.TH"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "High-accuracy and dimension-free sampling with diffusions",
"url": "https://arxiv.org/abs/2601.10708",
"version": "v1"
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"variant": "snapshot-2026-01-17",
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