Enhanced convergence guarantees of score-based generative models in 𝒲2-distance beyond log-concavity
Abstract
Although score-based generative models (SGMs) have achieved remarkable success in real-world sample generation tasks, it is still far from sufficient to understand them from a mathematical perspective. In this paper, we aim to provide enhanced convergence guarantees for two existing SGMs in 𝒲2-distance beyond log-concavity. More precisely, we develop a novel framework of {\color{black}discretization} error analysis for Euler-Maruyama (EM) and Poisson midpoint (PM) time discretization schemes for SGMs. Under a non-log-concavity condition, we show that 𝒪̃(√d/ε) iterations suffice to approximate the target distributions in ε-accuracy for the classical EM-based SGM, considerably improving upon the existing iteration complexity 𝒪̃(d/ε2). Notably, the novel framework of error analysis also enables us to establish an 𝒪̃(√d/ε2/3) iteration complexity for the PM-based SGM in ε-accuracy, significantly outperforming current state-of-the-art Wasserstein convergence guarantees for SDE-based diffusion samplers.
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BibTeX
@misc{zhang2026enhanced,
title = {{Enhanced convergence guarantees of score-based generative models in $\mathcalW_2$-distance beyond log-concavity}},
author = {Xiaoyan Zhang and Chenxu Pang and Xiaojie Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40308},
eprint = {2610.40308},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40308},
}
RIS
TY - UNPB
TI - Enhanced convergence guarantees of score-based generative models in 𝒲_2-distance beyond log-concavity
AU - Xiaoyan Zhang
AU - Chenxu Pang
AU - Xiaojie Wang
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40308
UR - https://arxiv.org/abs/2610.40308
AB - Although score-based generative models (SGMs) have achieved remarkable success in real-world sample generation tasks, it is still far from sufficient to understand them from a mathematical perspective. In this paper, we aim to provide enhanced convergence guarantees for two existing SGMs in 𝒲_2-distance beyond log-concavity. More precisely, we develop a novel framework of {\color{black}discretization} error analysis for Euler-Maruyama (EM) and Poisson midpoint (PM) time discretization schemes for SGMs. Under a non-log-concavity condition, we show that 𝒪̃(√d/ε) iterations suffice to approximate the target distributions in ε-accuracy for the classical EM-based SGM, considerably improving upon the existing iteration complexity 𝒪̃(d/ε^2). Notably, the novel framework of error analysis also enables us to establish an 𝒪̃(√d/ε^2/3) iteration complexity for the PM-based SGM in ε-accuracy, significantly outperforming current state-of-the-art Wasserstein convergence guarantees for SDE-based diffusion samplers.
ER -