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Score-based Outlier Generation via Controlling the Radon-Nikodym Derivative

arXiv · AI, language, vision and robotics · article · Sep 10, 2026 · UTC

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 co

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