2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121947A maximal coupling of two diffusion processes makes two diffusion particles meet as early as possible. We study the uniqueness of maximal couplings under a sort of "reflection structure" which ensures the existence of such couplings. In this framework, the uniqueness in the class of Markovian couplings holds for the Brownian motion on a Riemannian manifold whereas it fails in more singular cases. We also prove that a Kendall-Cranston coupling is maximal under the reflection structure.23 pagesProbability60J60; 58J65text