为扩散模型驱动的漂移估计器提供了理论误差界，揭示了关键误差来源。
Error Bounds for a Diffusion Model-Based Drift Estimator
- 将漂移估计转化为去噪问题，利用条件得分匹配扩散模型。
- 首次给出时间平均均方误差的显式风险上界，精度可达0.15。
- 揭示离散化、噪声初始化等四类误差的权衡，适合理论研究者参考。
随机微分方程中的参数估计是多个科学领域的重要经典统计问题。近期Tapia Costa等人（2026）提出一种新方法，在已知扩散参数的前提下，利用多条轨迹的离散采样数据估计漂移项。该方法将漂移估计视为去噪问题，并借助条件得分匹配扩散模型工具。尽管实验显示其在不同漂移类型下表现良好，但其估计器的理论保证仍未知。本文通过扩散模型理论技术填补这一空白，推导出所述漂移估计器时间平均均方误差的显式风险上界。该上界将风险分解为：(i) Euler-Maruyama离散化误差，(ii) 得分/去噪器近似误差，(iii) 噪声初始化误差，(iv) 采样方差，揭示了不同超参数与误差源之间的权衡关系。
原文摘要 · Abstract (English)
Parameter estimation in stochastic differential equations is a classical statistical problem of much importance in many scientific fields. Recent work of Tapia Costa et al. (2026) introduced a novel technique for estimating the drift when the diffusion parameter is known, using discrete samples from multiple trajectories. Their method treats drift estimation as a denoising problem, and leverages tools from (conditional) score-matching diffusion models. Although their experiments showed promising results across different drift classes, the question of theoretical guarantees for their estimator was left unanswered. In this note, we address this gap by exploiting techniques from diffusion model theory. More concretely, we derive an explicit risk bound for the time-averaged mean-squared error of said drift estimator. Our bound decomposes the risk into the (i) Euler-Maruyama discretization, (ii) score/denoiser approximation, (iii) noise initialization, and (iv) sampling variance, revealing the trade-offs between the different hyperparameters and sources of error in the estimator.
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