This paper focuses on weakly supervised image understanding, in which the semantic labels are available only at image-level, without the specific object or scene location in an image. Existing algorithms implicitly assume that image-level labels are error-free, which might be too restrictive. In practice, image labels obtained from the pretrained predictors are easily contaminated. To solve this problem, we propose a novel algorithm for weakly supervised segmentation when only noisy image labels are available during training. More specifically, a semantic space is constructed first by encoding image labels through a graphlet (i.e., superpixel cluster) embedding process. Then, we observe that in the semantic space, the distribution of graphlets from images with a same label remains stable, regardless of the noises in image labels. Therefore, we propose a generative model, called latent stability analysis, to discover the stable patterns from images with noisy labels. Inferring graphlet semantics by making use of these mid-level stable patterns is much more secure and accurate than directly transferring noisy image-level labels into different regions. Finally, we calculate the semantics of each superpixel using maximum majority voting of its correlated graphlets. Comprehensive experimental results show that our algorithm performs impressively when the image labels are predicted by either the hand-crafted or deeply learned image descriptors.