We present a scalable, generative framework for multi-label learning with missing labels. Our framework consists of a latent factor model for the binary label matrix, which is coupled with an exposure model to account for label missingness (i.e., whether a zero in the label matrix is indeed a zero or denotes a missing observation). The underlying latent factor model also assumes that the low-dimensional embeddings of each label vector are directly conditioned on the respective feature vector of that example. Our generative framework admits a simple inference procedure, such that the parameter estimation reduces to a sequence of simple weighted least-square regression problems, each of which can be solved easily, efficiently, and in parallel. Moreover, inference can also be performed in an online fashion using mini-batches of training examples, which makes our framework scalable for large data sets, even when using moderate computational resources. We report both quantitative and qualitative results for our framework on several benchmark data sets, comparing it with a number of state-of-the-art methods.