Distributional Shrinkage II: Higher-Order Scores Encode Brenier Map
arXiv:2512.09295v3 Announce Type: replace-cross Abstract: Consider the additive Gaussian model $Y = X + sigma Z$, where $X sim P$ is an unknown signal, $Z sim N(0,1)$ is independent of $X$, and $sigma > 0$ is known. Let $Q$ denote the law of $Y$. We construct a hierarchy of denoisers $T_0, T_1, ldots, T_infty colon mathbb{R} to mathbb{R}$ that depend only on higher-order score functions $q^{(m)}/q$, $m geq 1$, of $Q$ and require no knowledge of the law […]