High-Accuracy Sampling for Diffusion Models and Log-Concave Distributions

Fan Chen, Sinho Chewi, Constantinos Costis Daskalakis, Alexander Rakhlin
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:13835-13869, 2026.

Abstract

We present algorithms for diffusion model sampling which obtain $\delta$-error in $\mathrm{polylog}(1/\delta)$ steps, given access to $\widetilde O(\delta)$-accurate score estimates in $L^2$. This is an exponential improvement over all previous results. Specifically, under minimal data assumptions, the complexity is $\widetilde O(d\mathrm{polylog}(1/\delta))$ where $d$ is the dimension of the data; under a non-uniform $L$-Lipschitz condition, the complexity is $\widetilde O(\sqrt{dL}\mathrm{polylog}(1/\delta))$; and if the data distribution has intrinsic dimension $d_\star$, then the complexity reduces to $\widetilde O(d_\star\mathrm{polylog}(1/\delta))$. Our approach also yields the first $\mathrm{polylog}(1/\delta)$ complexity sampler for general log-concave distributions using only gradient evaluations.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-chen26p, title = {High-Accuracy Sampling for Diffusion Models and Log-Concave Distributions}, author = {Chen, Fan and Chewi, Sinho and Daskalakis, Constantinos Costis and Rakhlin, Alexander}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {13835--13869}, 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/chen26p/chen26p.pdf}, url = {https://proceedings.mlr.press/v306/chen26p.html}, abstract = {We present algorithms for diffusion model sampling which obtain $\delta$-error in $\mathrm{polylog}(1/\delta)$ steps, given access to $\widetilde O(\delta)$-accurate score estimates in $L^2$. This is an exponential improvement over all previous results. Specifically, under minimal data assumptions, the complexity is $\widetilde O(d\mathrm{polylog}(1/\delta))$ where $d$ is the dimension of the data; under a non-uniform $L$-Lipschitz condition, the complexity is $\widetilde O(\sqrt{dL}\mathrm{polylog}(1/\delta))$; and if the data distribution has intrinsic dimension $d_\star$, then the complexity reduces to $\widetilde O(d_\star\mathrm{polylog}(1/\delta))$. Our approach also yields the first $\mathrm{polylog}(1/\delta)$ complexity sampler for general log-concave distributions using only gradient evaluations.} }
Endnote
%0 Conference Paper %T High-Accuracy Sampling for Diffusion Models and Log-Concave Distributions %A Fan Chen %A Sinho Chewi %A Constantinos Costis Daskalakis %A Alexander Rakhlin %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-chen26p %I PMLR %P 13835--13869 %U https://proceedings.mlr.press/v306/chen26p.html %V 306 %X We present algorithms for diffusion model sampling which obtain $\delta$-error in $\mathrm{polylog}(1/\delta)$ steps, given access to $\widetilde O(\delta)$-accurate score estimates in $L^2$. This is an exponential improvement over all previous results. Specifically, under minimal data assumptions, the complexity is $\widetilde O(d\mathrm{polylog}(1/\delta))$ where $d$ is the dimension of the data; under a non-uniform $L$-Lipschitz condition, the complexity is $\widetilde O(\sqrt{dL}\mathrm{polylog}(1/\delta))$; and if the data distribution has intrinsic dimension $d_\star$, then the complexity reduces to $\widetilde O(d_\star\mathrm{polylog}(1/\delta))$. Our approach also yields the first $\mathrm{polylog}(1/\delta)$ complexity sampler for general log-concave distributions using only gradient evaluations.
APA
Chen, F., Chewi, S., Daskalakis, C.C. & Rakhlin, A.. (2026). High-Accuracy Sampling for Diffusion Models and Log-Concave Distributions. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:13835-13869 Available from https://proceedings.mlr.press/v306/chen26p.html.

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