发表机构
University of Oxford; Princeton University; Max Planck Institute for Security and Privacy; University of Cambridge; Gonville & Caius College（牛津大学; 普林斯顿大学; 马克斯·普朗克安全与隐私研究所; 剑桥大学; 贡维尔与凯斯学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种带有解析方差调度的生成式扩散替代模型，将正向噪声化速率设为方差的时间导数，无需中间输运数据，即可校准仿真并实现基于似然的推断，在湍流等离子体输运中表现良好。
AI 中文摘要
随机输运描述了初始结构化分布在未解析的外力、散射或非均匀介质作用下扩散的物理系统，这类系统的实用替代模型需具备概率性、时间分辨能力，且能表征非高斯分布结构。生成式扩散模型通过高斯噪声破坏数据并学习反向流以回归结构化状态，具备上述特性。然而其噪声调度通常是启发式选择的：图像和音频生成作为典型用例，无物理时钟；而在输运领域，即便完整分布未知，方差（或均方位移）常可从宏观理论或经验标度中获取。本文将正向噪声化速率规定为该方差的时间导数，使生成时间成为校准后的输运时钟；该方差路径通过构造得到保证，学习到的得分场则表示从入口数据继承的非高斯结构沿该路径的平滑过程，无需中间时间的物理输运数据。针对湍流等离子体中的弹道扩散输运，该替代模型匹配测试粒子分布，复现实验室测量的方差标度，且无需调度调优即可跟踪模拟的峰度演化，支持校准仿真与基于似然的推断。
英文摘要
Stochastic transport describes physical systems in which an initially structured distribution spreads under unresolved forcing, scattering, or heterogeneous media. Useful surrogates for such systems should be probabilistic, time-resolved, and able to represent non-Gaussian distributional structure. Generative diffusion models, which corrupt data with Gaussian noise and learn a reverse flow back to structured states, have these properties. Their noise schedules, however, are usually chosen heuristically: image and audio generation---the canonical use cases---provide no physical clock. In transport, by contrast, the variance, or mean-square displacement, is often known from macroscopic theory or empirical scaling even when the full distribution is not. Here we prescribe the forward noising rate as the time derivative of this variance, turning generative time into a calibrated transport clock. The variance path is enforced by construction, while the learned score field represents how non-Gaussian structure inherited from entrance data is smoothed along that path, requiring no intermediate-time physical transport data. For ballistic-to-diffusive transport in turbulent plasmas, the surrogate matches test-particle distributions, reproduces the laboratory-measured variance scale, and tracks the simulated kurtosis evolution without schedule tuning, enabling calibrated emulation and likelihood-based inference.
CommentsAccepted for publication in Nature Communications
Journal refNature Communications 17 (2026) 10408
DOI：10.1038/s41467-026-77769-6
