In recent years, the use of permutation-diffusion architecture for digital image encryption has become increasingly popular. The permutation procedure scrambles the pixel locations, while the diffusion phase modifies the pixel values and gives rise to the avalanche effect. Various diffusion techniques have been developed, and their strength strongly impacts the security of the overall cryptosystem. In this paper, we re-evaluate the security of a family of image diffusion mechanisms that are based on mixing modulo addition with bitwise exclusive OR operations. The recovery of the encryption element of these diffusion mechanisms is comprehensively demonstrated, and the accuracy bounds under various conditions are proved mathematically. Compared to the state-of-the-art methods, our work improves the recovery accuracy of the encryption element while the required prior knowledge is decreased. The proposed analysis of the diffusion mechanisms is further used to cryptanalyze the whole cryptosystem theoretically and experimentally.