Partial multi-label learning (PML) aims to learn a multilabel predictive model from the PML training examples, each of which is associated with a set of candidate labels where only a subset is valid. The common strategy to induce a predictive model is identifying the valid labels in each candidate label set. Nonetheless, this strategy ignores considering the essential label distribution corresponding to each instance as label distributions are not explicitly available in the training dataset. In this article, a novel partial multilabel learning method is proposed to recover the latent label distribution and progressively enhance it for predictive model induction. Specifically, the label distribution is recovered by considering the observation model for logical labels and the sharing topological structure from feature space to label distribution space. Besides, the latent label distribution is progressively enhanced by recovering latent labeling information and supervising predictive model training alternatively to make the label distribution appropriate for the induced predictive model. Experimental results on PML datasets clearly validate the effectiveness of the proposed method for solving partial multilabel learning problems. In addition, further experiments show the high quality of the recovered label distributions and the effectiveness of adopting label distributions for partial multilabel learning.