Amplify and forward (AF) relaying is a viable strategy to extend the coverage of sub-terahertz (sub-THz) links, but inevitably propagates noise, leading to cumulative degradation across multiple hops. At the receiver, optimal decoding is desirable, yet challenging under non-Gaussian input distributions (video, voice, etc), for which neither the Minimum Mean Square Error (MMSE) estimator nor the mutual information admits a closed form. A further open question is whether knowledge of Channel State Information (CSI) and noise statistics at the intermediate relays is necessary for optimal detection. Aiming for an optimal decoder, this paper introduces a new framework that interprets the AF relay chain as a variance-preserving diffusion process and employs denoising diffusion implicit models (DDIMs) for signal recovery. We show that each AF hop is mathematically equivalent to a diffusion step with hop-dependent attenuation and noise injection. Consequently, the entire multi-hop chain collapses to an equivalent Gaussian channel fully described by only three real scalars per block: the cumulative complex gain and the effective noise variance. At the receiver, these end-to-end sufficient statistics define a matched reverse schedule that guides the DDIM-based denoiser, enabling near-optimal Bayesian decoding without per-hop CSI. We establish the information-theoretic foundation of this equivalence, proving that decoding performance depends solely on the final effective Signal-to-Noise-Ratio (SNR), regardless of intermediate noise/channel allocation or prior distribution. Simulations under AWGN and Rician fading confirm that the proposed AF-DDIM decoder reduces mean-squared error, symbol error rate, and bit error rate, particularly at moderate SNRs and for higher-order constellations.

翻译：放大转发（AF）中继是扩展亚太赫兹（sub-THz）链路覆盖范围的有效策略，但不可避免地会传播噪声，导致多跳累积性能劣化。在接收端，期望实现最优解码，但在非高斯输入分布（视频、语音等）下极具挑战性，因为此时最小均方误差（MMSE）估计器与互信息均无闭式解。另一个悬而未决的问题是，中间中继节点是否需要已知信道状态信息（CSI）和噪声统计量以实现最优检测。为构建最优解码器，本文提出一种新框架，将AF中继链解释为方差保持的扩散过程，并采用去噪扩散隐式模型（DDIMs）进行信号恢复。我们证明每个AF跳在数学上等价于一个具有跳变相关衰减和噪声注入的扩散步骤。因此，整个多跳链可简化为一个仅需每块三个实标量（累积复增益和等效噪声方差）即可完整描述的等效高斯信道。在接收端，这些端到端充分统计量定义了匹配的反向调度方案，用以指导基于DDIM的去噪器，从而在无需每跳CSI的情况下实现接近最优的贝叶斯解码。我们建立了该等价关系的信息论基础，证明解码性能仅取决于最终的有效信噪比（SNR），而与中间噪声/信道分配或先验分布无关。在加性高斯白噪声（AWGN）和莱斯衰落信道下的仿真实验表明，所提出的AF-DDIM解码器能有效降低均方误差、符号错误率和误码率，在中低信噪比和高阶调制场景下效果尤为显著。