用扩散模型估计随机微分方程的漂移项，可高效处理高维数据。
Drift Estimation for Stochastic Differential Equations with Denoising Diffusion Models
- 将漂移估计转化为基于历史观测的去噪问题。
- 在低维上媲美经典方法，高维下表现更优且非单纯架构优势。
- 适合需要高维动态建模的金融、生物等领域的研究人员。
研究在已知扩散系数条件下，从固定时间区间内高频观测的多轨迹数据中估计时齐漂移函数的问题。将漂移估计建模为基于先前观测的条件去噪问题，提出一种漂移函数估计器，该估计器是训练具备动态生成新轨迹能力的条件扩散模型的副产品。在不同漂移类型下，该方法在低维场景中与经典方法相当，在高维场景中保持稳定竞争力，性能提升无法仅归因于模型架构设计。
原文摘要 · Abstract (English)
We study the estimation of time-homogeneous drift functions in multivariate stochastic differential equations with known diffusion coefficient, from multiple trajectories observed at high frequency over a fixed time horizon. We formulate drift estimation as a denoising problem conditional on previous observations, and propose an estimator of the drift function which is a by-product of training a conditional diffusion model capable of simulating new trajectories dynamically. Across different drift classes, the proposed estimator was found to match classical methods in low dimensions and remained consistently competitive in higher dimensions, with gains that cannot be attributed to architectural design choices alone.
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