Stability of the Kim--Milman flow map

Chewi, Sinho, Pooladian, Aram-Alexandre, Zhang, Matthew S.

arXiv.org Artificial Intelligence 

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