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Weakly-supervised object detection (WSOD) aims to train an object detector only requiring the image-level annotations. Recently, some works have managed to select the accurate boxes generated from a well-trained WSOD network to supervise a semi-supervised detection framework for better performance. However, these approaches simply divide the training set into labeled and unlabeled sets according to the image-level criteria, such that sufficient mislabeled or wrongly localized box predictions are chosen as pseudo ground-truths, resulting in a sub-optimal solution of detection performance. To overcome this issue, we propose a novel WSOD framework with a new paradigm that switches from weak supervision to noisy supervision (W2N). Generally, with given pseudo ground-truths generated from the well-trained WSOD network, we propose a two-module iterative training algorithm to refine pseudo labels and supervise better object detector progressively. In the localization adaptation module, we propose a regularization loss to reduce the proportion of discriminative parts in original pseudo ground-truths, obtaining better pseudo ground-truths for further training. In the semi-supervised module, we propose a two tasks instance-level split method to select high-quality labels for training a semi-supervised detector. Experimental results on different benchmarks verify the effectiveness of W2N, and our W2N outperforms all existing pure WSOD methods and transfer learning methods. Our code is publicly available at https://github.com/1170300714/w2n_wsod.