Title: Weakly Supervised Label Learning Flows. Abstract: Supervised learning usually requires a large amount of labelled data. However, attaining ground-truth labels is costly for many tasks. Alternatively, weakly supervised methods learn with only cheap weak signals that only approximately label some data. Many existing weakly supervised learning methods learn a deterministic function that estimates labels given the input data and weak signals. In this paper, we develop label learning flow (LLF), a general framework for weakly supervised learning problems. Our method is a generative model based on normalizing flows. The main idea of LLF is to optimize the conditional likelihoods of all possible labelings of the data within a constrained space defined by weak signals. We develop a training method for LLF that trains the conditional flow inversely and avoids estimating the labels. Once a model is trained, we can make predictions with a sampling algorithm. We apply LLF to three weakly supervised learning problems. Experiment results show that our method outperforms many state-of-the-art alternatives.