Recently, there has been a great deal of research attention on understanding the convergence behavior of first-order methods using tools from continuous dynamical systems. The alternating direction method of multipliers (ADMM) is a widely used first-order method for solving optimization problems arising from machine learning and statistics, and the stochastic versions of ADMM plays a key role in many modern large-scale machine learning problems. We introduce a unified algorithmic framework called generalized stochastic ADMM and investigate it via a continuous-time analylsis. We rigorously proved that under some proper scaling, the trajectory of stochastic ADMM weakly converges to the trajectory of the stochastic differential equation with small noise parameters. Our analysis also provides a theoretical explanation on why the relaxation parameter should be chosen between 0 and 2.