Driven by their remarkable success in computer vision and inverse problem solving, score-based models are increasingly applied to wireless communications, where they show promise across a range of physical-layer tasks. However, despite this growing interest, the current literature often lacks a rigorous analysis of when score-matching offers a tangible advantage over traditional discriminative learning. This paper aims to address this gap through the use-case of channel estimation, a fundamental inverse problem in wireless systems. We present a theoretically grounded interpretation of score-based channel estimation through the lens of the perception-distortion tradeoff, identifying the conditions where score matching excels as well as its key limitations. In particular, by modeling downstream wireless tasks (e.g., capacity maximization) as functionals of the channel estimation process, we quantify the excess risk incurred by standard distortion-minimization approaches. Extensive numerical results show that under high predictive uncertainty, the large excess risk gap can be offset by score-based estimation, enabling near Bayesian-optimal precoding via the learned posterior, whereas in the low predictive uncertainty regime, discriminative distortion-minimization approaches are preferable due to lower complexity and more efficient use of model capacity.

翻译：受其在计算机视觉和逆问题求解领域显著成功的驱动，基于分数的模型正越来越多地应用于无线通信，并在多种物理层任务中展现出潜力。然而，尽管兴趣日益浓厚，当前文献往往缺乏对分数匹配相较于传统判别学习何时能提供切实优势的严格分析。本文旨在通过信道估计这一无线系统中的基本逆问题用例来填补这一空白。我们通过感知-失真权衡的视角，对基于分数的信道估计提出了一种具有理论依据的解释，明确了分数匹配表现出色的条件及其关键局限性。具体而言，通过将下游无线任务（如容量最大化）建模为信道估计过程的泛函，我们量化了标准失真最小化方法导致的额外风险。大量数值结果表明，在高预测不确定性下，基于分数估计可弥补较大的额外风险差距，通过学习的后验实现接近贝叶斯最优的预编码；而在低预测不确定性区域，由于复杂度较低且模型容量利用更高效，判别式失真最小化方法更为可取。