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Point cloud segmentation is a fundamental task in 3D. Despite recent progress on point cloud segmentation with the power of deep networks, current learning methods based on the clean label assumptions may fail with noisy labels. Yet, class labels are often mislabeled at both instance-level and boundary-level in real-world datasets. In this work, we take the lead in solving the instance-level label noise by proposing a Point Noise-Adaptive Learning (PNAL) framework. Compared to noise-robust methods on image tasks, our framework is noise-rate blind, to cope with the spatially variant noise rate specific to point clouds. Specifically, we propose a point-wise confidence selection to obtain reliable labels from the historical predictions of each point. A cluster-wise label correction is proposed with a voting strategy to generate the best possible label by considering the neighbor correlations. To handle boundary-level label noise, we also propose a variant ``PNAL-boundary " with a progressive boundary label cleaning strategy. Extensive experiments demonstrate its effectiveness on both synthetic and real-world noisy datasets. Even with $60\%$ symmetric noise and high-level boundary noise, our framework significantly outperforms its baselines, and is comparable to the upper bound trained on completely clean data. Moreover, we cleaned the popular real-world dataset ScanNetV2 for rigorous experiment. Our code and data is available at https://github.com/pleaseconnectwifi/PNAL.