We propose binary-quantized and spatio-temporally discretized network models of linear diffusion systems and investigate their filtering effect on single-bit sigma-delta (ΣΔ) modulated signals. The network consists of only one kind of elements that add ΣΔ modulated signals and quantize the sum in the form of single-bit signal. A basic one-dimensional network is constructed first. Then, the network is extended into two dimensions. These networks have characteristics equivalent to those of linear diffusion systems in both time and frequency domains. In addition, network noise caused by the quantization in the elements contains low-level low-frequency components and high-level high-frequency components. Therefore, the proposed networks have possibility to be used as signal propagation and diffusion media of ΣΔ domain filters.