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arXiv 2503.08028stat.MLcs.LG
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去噪扩散中的计算瓶颈

Computational bottlenecks for denoising diffusions

Department of Statistics and Department of Mathematics, Stanford University(斯坦福大学统计系与数学系);Department of Statistics, Stanford University(斯坦福大学统计系)

Andrea Montanari, Viet Vu

AI总结:

研究探讨了是否所有可采样的分布都能通过扩散过程采样,发现某些分布虽易采样但扩散过程的漂移项难以计算。

摘要:

去噪扩散通过构造随机过程(ˆx_t:t≥0)在R^d中采样概率分布μ。该过程的漂移项m:R^d×R→R^d通过最小化分数匹配目标进行学习。我们提供证据表明,并非所有可采样的分布都能通过扩散过程采样。通过研究一个易于采样但扩散过程漂移项难以计算的分布,我们展示存在漂移项在多项式时间内接近最优值但生成样本分布与目标分布相差很远的情况。

英文摘要:

Denoising diffusions sample from a probability distribution $μ$ in $\mathbb{R}^d$ by constructing a stochastic process $({\hat{\boldsymbol x}}_t:t\ge 0)$ in $\mathbb{R}^d$ such that ${\hat{\boldsymbol x}}_0$ is easy to sample, but the distribution of $\hat{\boldsymbol x}_T$ at large $T$ approximates $μ$. The drift ${\boldsymbol m}:\mathbb{R}^d\times\mathbb{R}\to\mathbb{R}^d$ of this diffusion process is learned my minimizing a score-matching objective. Is every probability distribution $μ$, for which sampling is tractable, also amenable to sampling via diffusions? We provide evidence to the contrary by studying a probability distribution $μ$ for which sampling is easy, but the drift of the diffusion process is intractable -- under a popular conjecture on information-computation gaps in statistical estimation. We show that there exist drifts that are superpolynomially close to the optimum value (among polynomial time drifts) and yet yield samples with distribution that is very far from the target one.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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