How corner is a corner case? Percentile control for highway scenario generation
Jiaxi Liu, Hang Zhou, Hangyu Li, Yifan Wang, Keke Long, Chengyuan Ma, Bin Ran, Xiaopeng Li
University of Wisconsin–Madison
Published October 4, 2026 · on the feed October 8, 2026 · ▲ 2 · arXiv 2610.05003
The abstract
Generating corner-case scenarios with appropriate adversity in a simulation environment is critical for testing an autonomous vehicle (AV) software stack's safety performance before deployment. Existing autonomous-driving scenario generators can enforce specific behavior, adversity, or feasibility conditions, but they provide limited control over how extreme a generated scenario is relative to plausible futures in the same traffic context. This study represents the adversity of a generated scenario as its percentile in the conditional distribution of future risk given the observed history. This view supports calibrated answers to two questions: how "corner" a generated corner-case scenario is and how its "cornerness" can be fine-tuned. To this end, we formulate history-conditioned risk-percentile requests and learn a reference risk distribution that maps each requested percentile to a physical risk target. We then use a percentile-conditioned joint diffusion model with sampling-time risk guidance to generate multi-agent futures, together with a reference-based criterion for evaluating percentile realization. Experiments use the minimum post-encroachment time (PET) between the ego and its surrounding vehicles as the risk surrogate on highD. On the primary evaluation set, our method realizes 1,422 of 1,440 requests within a 0.05 percentile tolerance (98.75%), with mean percentile error 0.00673 and PET-target error 0.00991 seconds. The resulting interface connects context-relative risk specification, physical realization, and evaluation through a common risk scale. Project website and videos of generated scenarios are available at https://hhj233.github.io/CornerPercentile/.
The Brief
2:45A short podcast summary of the paper. Written and voiced by AI.
Transcript
How corner is a corner case? Percentile control for highway scenario generation. By Jiaxi Liu and seven others, from the University of Wisconsin-Madison. Published on the fourth of October. Its code repository is worked out: about one hundred and eighty source files, with a readme and a licence.
Before an autonomous vehicle's software goes on the road, its safety has to be tested, and a critical part of that is generating corner-case scenarios in simulation with the right amount of adversity. Existing scenario generators can enforce particular behaviours, adversity levels or feasibility conditions. What they offer little control over is how extreme a generated scenario is, compared with the futures that are plausible in that same traffic context. A scenario can be dangerous without anyone being able to say how unusual it is for the situation it starts from.
The study's answer is to measure adversity as a percentile, which makes it relative rather than absolute. The same physical risk could be routine in one traffic context and extreme in another, and a percentile says which. Given the history observed so far, there is a conditional distribution over future risk. A generated scenario's adversity is its position in that distribution. Framed like that, two questions get calibrated answers. How corner is a given corner case. And how can its cornerness be dialled up or down.
The pipeline has three parts. First, requests are written as history-conditioned risk percentiles, and the system learns a reference risk distribution that turns each requested percentile into a physical risk target. Second, a percentile-conditioned joint diffusion model, steered by risk guidance at sampling time, generates the futures of multiple agents at once. Third, a reference-based criterion judges whether the requested percentile was actually realized. Each part answers a different question. What does the tester want, stated relative to the context. What physical risk does that correspond to. And did the generated scenario deliver it.
The experiments run on highD, using as the risk surrogate the minimum post-encroachment time, or PET, between the ego vehicle and the vehicles around it. On the primary evaluation set, the method realizes one thousand four hundred and twenty-two of one thousand four hundred and forty requests within a tolerance of zero point zero five percentile.
That is a rate of ninety-eight point seven five percent. The mean percentile error is zero point zero zero six seven three. The error against the PET target is zero point zero zero nine nine one seconds.
The result is an interface with one common risk scale running through it. Someone specifies risk relative to the context, the generator realizes it physically, and the evaluation checks it on the same scale. Asking for a scenario at a chosen percentile becomes a request that can be made precisely and then verified.
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