arXiv：cs.LG· Qiuyun Zhu·· 13 小时前
全离散条件扩散模型的有限样本保证
Finite-Sample Guarantees for Fully Discrete Conditional Diffusion Models
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研究为基于数据学习、且以有限去噪步数实现的条件扩散模型建立了有限样本保证，将分数训练目标与采样网格对齐，使统计估计误差与数值离散化误差可联合分析。在平滑条件密度假设下，对任意平滑指数 β>0，适当网格可使平均条件 KL 散度达到 O_p(n^{-2β/(d_x+d_y+2β)})，使用或不使用早停均成立。
正文
Abstract:We establish finite-sample guarantees for conditional diffusion models learned from data and implemented with finitely many denoising steps. Our approach aligns the score-training objective with the sampling grid, allowing statistical estimation and numerical discretization errors to be analyzed together. Under a smooth conditional density model, we derive high-probability bounds on the generated distribution's error and quantify the required number of score evaluations. For every smoothness index $\beta>0$, a suitable grid yields averaged conditional Kullback--Leibler (KL) divergence $\widetilde O_p(n^{-2\beta/(d_x+d_y+2\beta)})$ relative to the original target with or without early stopping. Both the full and early-stopped samplers attain average target total-variation (TV) error $\widetilde O_p(n^{-\beta/(d_x+d_y+2\beta)})$. Here $n$ is the sample size, $d_x,d_y$ are the data and conditioning dimensions, and errors are averaged over the conditioning variable. The total-variation bound matches the rate established in existing conditional distribution-estimation theory, up to logarithmic factors.
| Comments: | 31 pages |
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.13851 [stat.ML] |
| (or arXiv:2610.13851v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.13851 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Qiuyun Zhu [view email]
[v1]
Fri, 9 Oct 2026 16:59:18 UTC (35 KB)
来源：arXiv：cs.LG · arxiv.org