Stability of the Kim--Milman flow map
arXiv:2511.01154v12 citationsh-index: 15
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This addresses a theoretical problem in probability and analysis, but it appears incremental as it focuses on a specific stability characterization for an existing flow map.
The paper characterizes the stability of the Kim-Milman flow map with respect to variations in the target measure, showing that stability holds with respect to the relative Fisher information instead of the Wasserstein distance.
In this short note, we characterize stability of the Kim--Milman flow map -- also known as the probability flow ODE -- with respect to variations in the target measure. Rather than the Wasserstein distance, we show that stability holds with respect to the relative Fisher information