In this paper, we propose a computationally tractable and theoretically\nsupported non-linear low-dimensional generative model to represent real-world\ndata in the presence of noise and sparse outliers. The non-linear\nlow-dimensional manifold discovery of data is done through describing a joint\ndistribution over observations, and their low-dimensional representations (i.e.\nmanifold coordinates). Our model, called generative low-dimensional background\nmodel (G-LBM) admits variational operations on the distribution of the manifold\ncoordinates and simultaneously generates a low-rank structure of the latent\nmanifold given the data. Therefore, our probabilistic model contains the\nintuition of the non-probabilistic low-dimensional manifold learning. G-LBM\nselects the intrinsic dimensionality of the underling manifold of the\nobservations, and its probabilistic nature models the noise in the observation\ndata. G-LBM has direct application in the background scenes model estimation\nfrom video sequences and we have evaluated its performance on SBMnet-2016 and\nBMC2012 datasets, where it achieved a performance higher or comparable to other\nstate-of-the-art methods while being agnostic to the background scenes in\nvideos. Besides, in challenges such as camera jitter and background motion,\nG-LBM is able to robustly estimate the background by effectively modeling the\nuncertainties in video observations in these scenarios.\n