发表机构
University of Waterloo; Royal Bank of Canada（滑铁卢大学; 加拿大皇家银行）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于控制Radon-Nikodym导数的分数式异常值生成方法，通过似然重加权修改扩散分数，无需重新训练即可生成低似然样本，并保持数据几何一致性。
AI 中文摘要
异常值对于压力测试算法和理解罕见条件下的系统行为至关重要。尽管异常值通常被描述为低似然事件，但现有的生成方法很少显式控制似然。在本工作中，我们引入了一种基于对数似然值分布的测度论异常值概念，该概念保证以可指定的幅度将更高的概率质量分配给低似然事件。基于此公式，我们推导了似然重加权如何修改扩散分数，并利用这一关系来激励对反向时间动力学的受控修改。特别地，似然重加权意味着分数函数按从似然分布的Radon-Nikodym导数导出的控制项进行缩放。相应地，更新后的分数函数无需重新训练扩散模型即可获得。我们利用扩散模型底层的Ornstein-Uhlenbeck半群来激励一个指数插值控制器，该控制器近似真实控制。实验证明，在保持与数据几何一致性的同时，能够受控生成低似然样本。
英文摘要
Outliers are important for stress-testing algorithms and understanding system behaviour under rare conditions. Despite being commonly described as low-likelihood events, existing generative approaches rarely control likelihood explicitly. In this work, we introduce a measure-theoretic notion of outliers based on the distribution of log-likelihood values, which is guaranteed to assign higher probability mass to low-likelihood events with a specifiable magnitude. Building on this formulation, we derive how likelihood reweighting modifies the diffusion score and use this relation to motivate a controlled modification of the reverse-time dynamics. In particular, likelihood reweighting implies a scaling of the score function with a control term derived from the Radon-Nikodym derivative of the likelihood distributions. Correspondingly, the updated score function can be obtained with no retraining of the diffusion model. We exploit the Ornstein-Uhlenbeck semigroup underlying diffusion models to motivate an exponentially interpolated controller which approximates the true control. Experiments demonstrate controlled generation of low-likelihood samples while remaining consistent with the data geometry.
Journal refIEEE Conference on Decision and Control (CDC), 2026
