发表机构
University of Oxford; University of British Columbia（牛津大学; 不列颠哥伦比亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出DireSMC，一种序贯蒙特卡洛方法，引导扩散模型中的加权样本至稀有事件，提供概率校准估计，并在玩具问题和气候模拟器上验证，实现9至1413倍加速。
AI 中文摘要
扩散模型日益被用作天气预报、分子动力学和材料设计等领域中昂贵模拟器的替代品。在这些模型中，计算事件E的概率p0[E]是困难的，尤其是当感兴趣的事件是稀有事件时。使用蒙特卡洛的稳定估计在计算上变得难以处理，需要不断增加的样本量∝1/p0[E]来补偿日益增加的稀有性。在本文中，我们提出了稀有事件的扩散重要性采样（DireSMC），这是一种序贯蒙特卡洛方案，将一组加权样本引导至稀有事件，不仅提供样本，还提供其概率的校准估计。我们使用事件集的解析松弛来设置引导，使该方法易于扩展到广泛的用户自定义稀有事件。我们在一个具有解析解的玩具问题和一个基于分数的气候模拟器上验证了我们的方法，在从10^-3到10^-5的一系列稀有性范围内获得了准确的稀有事件概率，与蒙特卡洛相比实现了9倍到1413倍的净加速。
英文摘要
Diffusion models are increasingly used as surrogates for expensive simulators in weather prediction, molecular dynamics, and materials design. In these models, computing the probability $p_0[E]$ of an event $E$ is difficult, especially when the event of interest is rare. A stable estimate using Monte Carlo becomes computationally intractable, requiring a growing sample size $\propto\!1/p_0[E]$ to compensate for an increasing rarity. In this paper, we present Diffusion Importance Sampling of Rare Events or DireSMC, a sequential Monte Carlo scheme that guides a population of weighted samples towards the rare event, giving access not only to samples but also to a calibrated estimate of its probability. We set up our guidance using an analytical relaxation of the event set, allowing the method to easily extend to a wide range of user-defined rare events. We validate our method on a toy problem with analytical solutions and on a score-based climate emulator, where we obtain accurate rare-event probabilities on a range of rarities from $10^{-3}$ to $10^{-5}$, achieving net speed-ups of $9\times$ to $1413\times$ over Monte Carlo.
CommentsA previous version of this work was presented at the NeurIPS 2026: AI for Stochastic Dynamics workshop
