Real-world data often contains intrinsic ambiguity that the common single-hard-label annotation paradigm ignores. Standard training using ambiguous data with these hard labels may produce overly confident models and thus leading to poor generalization. In this paper, we propose a novel framework called Quantized Label Learning (QLL) to alleviate this issue. First, we formulate QLL as learning from (very) ambiguous data with hard labels: ideally, each ambiguous instance should be associated with a ground-truth soft-label distribution describing its corresponding probabilistic weight in each class, however, this is usually not accessible; in practice, we can only observe a quantized label, i.e., a hard label sampled (quantized) from the corresponding ground-truth soft-label distribution, of each instance, which can be seen as a biased approximation of the ground-truth soft-label. Second, we propose a Class-wise Positive-Unlabeled (CPU) risk estimator that allows us to train accurate classifiers from only ambiguous data with quantized labels. Third, to simulate ambiguous datasets with quantized labels in the real world, we design a mixing-based ambiguous data generation procedure for empirical evaluation. Experiments demonstrate that our CPU method can significantly improve model generalization performance and outperform the baselines.