In this paper, we investigate cascaded channel estimation for reconfigurable intelligent surface (RIS)-aided millimeter-wave multi-user communication systems. Since the complex channel gains of the cascaded RIS channel are generally non-Gaussian, the use of the linear minimum mean squared error (LMMSE) estimator leads to inevitable performance degradation. To tackle this issue, we propose a variational inference-based framework that approximates the complex channel gains using a complex adaptive Laplace prior, which effectively captures their probability distributions in a tractable way. Numerical results demonstrate that the proposed estimator outperforms conventional estimators including least squares and LMMSE in terms of cascaded channel estimation error.