Existence of $q$-Bass martingales in the semidiscrete setting

What the math gives to ML

The paper identifies a distinguished martingale coupling by minimizing the expected squared Wasserstein distance between each conditional transition law and a fixed reference distribution q. This imposes conditional mean preservation while selecting transition kernels that remain close to a simple reference noise law. A transferable use is to regularize conditional generative or latent-transition networks so their stochastic outputs preserve prescribed barycenters and change the reference distribution only as much as needed to match the target marginal.