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Channel estimation is of great importance in realizing practical intelligent reflecting surface-assisted multi-user communication (IRS-MC) systems. However, different from traditional communication systems, an IRS-MC system generally involves a cascaded channel with a sophisticated statistical distribution, which hinders the implementations of the Bayesian estimators. To further improve the channel estimation performance, in this paper, we model the channel estimation as a denoising problem and adopt a data-driven approach to realize the channel estimation. Specifically, we propose a convolutional neural network (CNN)-based deep residual network (CDRN) to implicitly learn the residual noise for recovering the channel coefficients from the noisy pilot-based observations. In the proposed CDRN, a CNN denoising block equipped with an element-wise subtraction structure is designed to exploit both the spatial features of the noisy channel matrices and the additive nature of the noise simultaneously, which further improves the estimation accuracy. Simulation results demonstrate that the proposed method can almost achieve the same estimation accuracy as that of the optimal minimum mean square error (MMSE) estimator requiring the knowledge of the channel distribution.