Parallel Simulation for Log-concave Sampling and Score-based Diffusion Models

Huanjian Zhou, Masashi Sugiyama
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:79192-79225, 2025.

Abstract

Sampling from high-dimensional probability distributions is fundamental in machine learning and statistics. As datasets grow larger, computational efficiency becomes increasingly important, particularly in reducing adaptive complexity, namely the number of sequential rounds required for sampling algorithms. While recent works have introduced several parallelizable techniques, they often exhibit suboptimal convergence rates and remain significantly weaker than the latest lower bounds for log-concave sampling. To address this, we propose a novel parallel sampling method that improves adaptive complexity dependence on dimension $d$ reducing it from $\widetilde{\mathcal{O}}(\log^2 d)$ to $\widetilde{\mathcal{O}}(\log d)$. Our approach builds on parallel simulation techniques from scientific computing.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-zhou25x, title = {Parallel Simulation for Log-concave Sampling and Score-based Diffusion Models}, author = {Zhou, Huanjian and Sugiyama, Masashi}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {79192--79225}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/zhou25x/zhou25x.pdf}, url = {https://proceedings.mlr.press/v267/zhou25x.html}, abstract = {Sampling from high-dimensional probability distributions is fundamental in machine learning and statistics. As datasets grow larger, computational efficiency becomes increasingly important, particularly in reducing adaptive complexity, namely the number of sequential rounds required for sampling algorithms. While recent works have introduced several parallelizable techniques, they often exhibit suboptimal convergence rates and remain significantly weaker than the latest lower bounds for log-concave sampling. To address this, we propose a novel parallel sampling method that improves adaptive complexity dependence on dimension $d$ reducing it from $\widetilde{\mathcal{O}}(\log^2 d)$ to $\widetilde{\mathcal{O}}(\log d)$. Our approach builds on parallel simulation techniques from scientific computing.} }
Endnote
%0 Conference Paper %T Parallel Simulation for Log-concave Sampling and Score-based Diffusion Models %A Huanjian Zhou %A Masashi Sugiyama %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-zhou25x %I PMLR %P 79192--79225 %U https://proceedings.mlr.press/v267/zhou25x.html %V 267 %X Sampling from high-dimensional probability distributions is fundamental in machine learning and statistics. As datasets grow larger, computational efficiency becomes increasingly important, particularly in reducing adaptive complexity, namely the number of sequential rounds required for sampling algorithms. While recent works have introduced several parallelizable techniques, they often exhibit suboptimal convergence rates and remain significantly weaker than the latest lower bounds for log-concave sampling. To address this, we propose a novel parallel sampling method that improves adaptive complexity dependence on dimension $d$ reducing it from $\widetilde{\mathcal{O}}(\log^2 d)$ to $\widetilde{\mathcal{O}}(\log d)$. Our approach builds on parallel simulation techniques from scientific computing.
APA
Zhou, H. & Sugiyama, M.. (2025). Parallel Simulation for Log-concave Sampling and Score-based Diffusion Models. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:79192-79225 Available from https://proceedings.mlr.press/v267/zhou25x.html.

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