Stability of the Kim--Milman flow map

2025/11/03 by Sinho Chewi, Chewi, Sinho, Aram-Alexandre Pooladian +3 · 2 citations
Mathematics · #26D10 #FOS: Computer and information sciences #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Machine Learning (cs.LG) #Point processes and geometric inequalities #Probability (math.PR) #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2511.01154

openalex publication_date 2025/11/03 · openalex created_date 2025/11/06 · openalex updated_date 2026/07/28

Abstract

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 in relative Fisher information.

Citations

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Cited by

• A Dacorogna-Moser construction of transport maps on ℝ^d with application to geodesics on the space of couplings
• A Generalization of Caffarelli's Contraction Theorem to Nearly Spherical Manifolds

Related

• Lipschitz Transport Maps via the Follmer Flow
• Quantitative Stability of Optimal Transport Maps under Variations of the Target Measure
• Entropy and Fisher information in non-convex domains: one chain to rule them all
• Gradient Flows in Filtering and Fisher-Rao Geometry
• Fisher-Rao Gradient Flow: Geodesic Convexity and Functional Inequalities