This paper analyzes the implementation of least-mean-squares (LMS)-based, adaptive diffusion algorithms over networks in the frequency-domain (FD). We focus on a scenario of noisy links and include a moving-average step for denoising after self-learning to enhance performance. The mean-square-error convergence behavior of the resulting algorithm is investigated and the theoretical results are illustrated through simulations. In particular, the proposed denoised recursions are shown to perform favorably when compared with partial diffusion LMS (PD-LMS) and diffusion LMS algorithms, in terms of both complexity and performance.