This work proposes a generative modeling-aided channel estimator based on mixtures of factor analyzers (MFA). In an offline step, the parameters of the generative model are inferred via an expectation-maximization (EM) algorithm in order to learn the underlying channel distribution of a whole communication scenario inside a base station (BS) cell. Thereby, the wireless channels are effectively modeled on a piecewise linear subspace which is achieved by the low-rank structure of the learned covariances of the MFA. This suits the low-rank structure of wireless channels at high frequencies and additionally saves parameters and prevents overfitting. Afterwards, the trained MFA model is used online to perform channel estimation with a closed-form solution of the estimator which asymptotically converges to the minimum mean square error (MMSE) estimator. Numerical results based on real-world measurements demonstrate the great potential of the proposed approach for channel estimation.