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In this paper, we propose a computationally tractable and theoretically supported non-linear low-dimensional generative model to represent real-world data in the presence of noise and sparse outliers. The non-linear low-dimensional manifold discovery of data is done through describing a joint distribution over observations, and their low-dimensional representations (i.e. manifold coordinates). Our model, called generative low-dimensional background model (G-LBM) admits variational operations on the distribution of the manifold coordinates and simultaneously generates a low-rank structure of the latent manifold given the data. Therefore, our probabilistic model contains the intuition of the non-probabilistic low-dimensional manifold learning. G-LBM selects the intrinsic dimensionality of the underling manifold of the observations, and its probabilistic nature models the noise in the observation data. G-LBM has direct application in the background scenes model estimation from video sequences and we have evaluated its performance on SBMnet-2016 and BMC2012 datasets, where it achieved a performance higher or comparable to other state-of-the-art methods while being agnostic to the background scenes in videos. Besides, in challenges such as camera jitter and background motion, G-LBM is able to robustly estimate the background by effectively modeling the uncertainties in video observations in these scenarios.