In partial label learning, each training example is assigned a set of candidate labels, only one of which is the ground-truth label. Existing partial label learning frameworks either assume each candidate label of equal confidence or consider the ground-truth label as a latent variable hidden in the indiscriminate candidate label set, while the different labeling confidence levels of the candidate labels are regrettably ignored. In this paper, we formalize the different labeling confidence levels as the latent label distributions, and propose a novel unified framework to estimate the latent label distributions while training the model simultaneously. Specifically, we present a biconvex formulation with constrained local consistency and adopt an alternating method to solve this optimization problem. The process of alternating optimization exactly facilitates the mutual adaption of the model training and the constrained label propagation. Extensive experimental results on controlled UCI datasets as well as real-world datasets clearly show the effectiveness of the proposed approach.