We propose score-based VAMP (SC-VAMP), a variant of vector approximate message passing (VAMP) in which the Onsager correction is expressed and computed via conditional Fisher information, thereby enabling a Jacobian-free implementation. Using learned score functions, SC-VAMP constructs nonlinear MMSE estimators through Tweedie's formula and derives the corresponding Onsager terms from the score-norm statistics, avoiding the need for analytical derivatives of the prior or likelihood. When combined with random orthogonal/unitary mixing to mitigate non-ideal, structured or correlated sensing settings, the proposed framework extends VAMP to complex black-box inference problems where explicit modeling is intractable. Finally, by leveraging the entropic CLT, we provide an information-theoretic perspective on the Gaussian approximation underlying SE, offering insight into the decoupling principle beyond idealized i.i.d. settings, including nonlinear regimes.

翻译：我们提出了基于分数的VAMP（SC-VAMP），这是向量近似消息传递（VAMP）的一种变体，其中Onsager修正通过条件Fisher信息表达和计算，从而实现无需雅可比矩阵的实现。利用学习到的分数函数，SC-VAMP通过Tweedie公式构建非线性MMSE估计器，并从分数范数统计量推导相应的Onsager项，避免了需要先验或似然函数的解析导数。当结合随机正交/酉混合以缓解非理想、结构化或相关的感知设置时，所提出的框架将VAMP扩展到显式建模难以处理的复杂黑盒推理问题。最后，通过利用熵中心极限定理，我们为支撑状态演化（SE）的高斯近似提供了信息论视角，从而在超越理想化独立同分布设置（包括非线性机制）的范围内，为解耦原理提供了深入见解。