The Diffusion Network(DN) is a stochastic recurrent network which has been shown capable of modeling the distributions of continuous-valued, continuous-time paths. However, the dynamics of the DN are governed by stochastic differential equations, making the DN unfavourable for simulation in a digital computer. This paper presents the implementation of the DN in analogue Very Large Scale Integration, enabling the DN to be simulated in real time. Moreover, the log-domain representation is applied to the DN, allowing the supply voltage and thus the power consumption to be reduced without limiting the dynamic ranges for diffusion processes. A VLSI chip containing a DN with two stochastic units has been designed and fabricated. The design of component circuits will be described, so will the simulation of the full system be presented. The simulation results demonstrate that the DN in VLSI is able to regenerate various types of continuous paths in real-time.