High-accuracy and dimension-free sampling with diffusions

Khashayar Gatmiry, Sitan Chen, Adil Salim
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:34242-34274, 2026.

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 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, and we prove that its iteration complexity scales 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 only through the effective radius of the support of the target distribution.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-gatmiry26a, title = {High-accuracy and dimension-free sampling with diffusions}, author = {Gatmiry, Khashayar and Chen, Sitan and Salim, Adil}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {34242--34274}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/gatmiry26a/gatmiry26a.pdf}, url = {https://proceedings.mlr.press/v306/gatmiry26a.html}, 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 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, and we prove that its iteration complexity scales 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 only through the effective radius of the support of the target distribution.} }
Endnote
%0 Conference Paper %T High-accuracy and dimension-free sampling with diffusions %A Khashayar Gatmiry %A Sitan Chen %A Adil Salim %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-gatmiry26a %I PMLR %P 34242--34274 %U https://proceedings.mlr.press/v306/gatmiry26a.html %V 306 %X 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 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, and we prove that its iteration complexity scales 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 only through the effective radius of the support of the target distribution.
APA
Gatmiry, K., Chen, S. & Salim, A.. (2026). High-accuracy and dimension-free sampling with diffusions. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:34242-34274 Available from https://proceedings.mlr.press/v306/gatmiry26a.html.

Related Material