This paper proposes the diffusion circuit for Autonomous Ratio-Memory Cellular Nonlinear Networks (ARMCNNs). ARMCNNs can tolerate large variations of ratio weights which has been shown in our previous paper. However, in our previous circuit implementation, the synapse weight circuit between neighboring neurons was composed of two voltage to current converters (V/Is) and current mirrors. The layout area is still too large for a high density CNN array. Another issue is that for each subsystem of ARMCNNs, spurious memory points may exist besides two binary equilibrium points. The occurence of these spurious memory points will reduce the recognition rate (RR). So this paper proposes the diffusion circuit for synapse weights to extend the domain of attraction (DOA) and therefore eliminate these spurious memory points in comparison with our previous paper. In the literature, MOSFET transistors for the synapse weight circuit mostly either work in the weak inversion region, or in the strong inversion, but not both. Hence, the gate voltage has to be carefully desgined for MOSFET transistors working in the correct regions. On the contrary, in this paper, the synapse weight of a single MOSFET can work in either the weak inversion region or the strong inversion, making analog design more robust.