论文概要
研究领域: ML 作者: Zhifeng Chen, Chenyang Jiang, Yazhen Wang 发布时间: 2026-09-25 arXiv: 2609.31612
中文摘要
近期文献揭示了优化与采样之间的深刻联系。我们为扩散模型建立了相应的一阶理论。第一，只要前向过程的平稳势函数强凸——这是对所选取噪过程的条件，而非对数据的条件——过阻尼与欠阻尼 Langevin 扩散基于 SDE 的逆时间流就能以显式的指数速率收缩相对 Fisher 散度。这是基于 SDE 的逆扩散独有的优势，在基于 ODE 的逆过程中并不存在。第二，我们引入离散化分析，为两类扩散模型的采样器建立了平均一阶平稳性界——即非凸优化中“平均梯度范数”保证的采样版本。与非凸优化中一样，这一无凸性条件的证书是局部的：它保证的是 score 的一致性，而非全局的模态权重。
原文摘要
Recent literature has shown a strong connection between optimization and sampling. We develop the corresponding first-order theory for diffusion models. First, the SDE-based reverse-time flows of overdamped and underdamped Langevin diffusions contract relative Fisher divergences at explicit exponential rates whenever the stationary potential of the forward process is strongly convex—a condition on the noising process one chooses, not on the data. This is a unique advantage of SDE-based reverse diffusion, absent in the reverse process based on ODEs. Second, we incorporate discretization and establish averaged first-order stationarity bounds—the sampling analog of averaged gradient-norm guarantees in nonconvex optimization—for samplers of both overdamped and underdamped diffusion model…
— 自动采集于 2026-09-29
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