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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.17375 |
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| _version_ | 1866914277545213952 |
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| author | Liu, Peiyi Liu, Zhaoqiang Gu, Yiqi |
| author_facet | Liu, Peiyi Liu, Zhaoqiang Gu, Yiqi |
| contents | In this paper, we develop a class of samplers for the diffusion model using the operator-splitting technique. The linear drift term and the nonlinear score-driven drift of the probability flow ordinary differential equation are split and applied by flow maps alternatively. Moreover, we conduct detailed analyses for the second-order sampler, establishing a non-asymptotic total variation distance error bound of order $O(d/T^2+\sqrt{d}\varepsilon_{\mathrm{score}}+d\varepsilon_{\mathrm{Jac}})$, where $d$ is the data dimension; $T$ is the number of sampling steps; $\varepsilon_{\mathrm{score}}$ and $\varepsilon_{\mathrm{Jac}}$ measure the discrepancy between the actual score function and learned score function. Our bound is sharper than existing works, yielding bounds of $O(d^p/T^2)$ with some $p>1$ for specific second-order samplers. Numerical experiments on a two-dimensional synthetic dataset corroborate the established quadratic dependence on the step size $1/T$ in the error bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17375 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Operator splitting based diffusion samplers and improved convergence analysis Liu, Peiyi Liu, Zhaoqiang Gu, Yiqi Numerical Analysis In this paper, we develop a class of samplers for the diffusion model using the operator-splitting technique. The linear drift term and the nonlinear score-driven drift of the probability flow ordinary differential equation are split and applied by flow maps alternatively. Moreover, we conduct detailed analyses for the second-order sampler, establishing a non-asymptotic total variation distance error bound of order $O(d/T^2+\sqrt{d}\varepsilon_{\mathrm{score}}+d\varepsilon_{\mathrm{Jac}})$, where $d$ is the data dimension; $T$ is the number of sampling steps; $\varepsilon_{\mathrm{score}}$ and $\varepsilon_{\mathrm{Jac}}$ measure the discrepancy between the actual score function and learned score function. Our bound is sharper than existing works, yielding bounds of $O(d^p/T^2)$ with some $p>1$ for specific second-order samplers. Numerical experiments on a two-dimensional synthetic dataset corroborate the established quadratic dependence on the step size $1/T$ in the error bound. |
| title | Operator splitting based diffusion samplers and improved convergence analysis |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2601.17375 |