New AI Trick Makes Rare Events on Demand — No Retraining Needed

A team of researchers — Amartya Mukherjee, Tristan Milne, Kry Yik-Chau Lui, Stephanie Hazlewood, and Jun Liu — want to generate outliers on demand, and they have a new way to do it with diffusion models. Outliers matter: they're used for stress-testing algorithms and understanding how systems behave under rare conditions. But as the authors note, outliers are usually described as low-likelihood events, and existing generative approaches rarely control likelihood explicitly. Their answer is 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. From there, they derive how likelihood reweighting modifies the diffusion score — implying a scaling of the score function with a control term derived from the Radon-Nikodym derivative of the likelihood distributions — and use that to motivate a controlled modification of the reverse-time dynamics. The updated score function can be obtained with no retraining of the diffusion model. They also exploit the Ornstein-Uhlenbeck semigroup underlying diffusion models to motivate an exponentially interpolated controller that approximates the true control. Experiments demonstrate controlled generation of low-likelihood samples while remaining consistent with the data geometry. The work is arXiv:2609.12113, submitted 10 Sep 2026, with a journal reference to the IEEE Conference on Decision and Control (CDC), 2026.