Multi-label image classification has generated significant interest in recent years and the performance of such systems often suffers from the not so infrequent occurrence of incorrect or missing labels in the training data. In this paper, we extend the state-of the-art of training classifiers to jointly deal with both forms of errorful data. We accomplish this by modeling noisy and missing labels in multi-label images with a new Noise Modeling Network (NMN) that follows our convolutional neural network (CNN), integrates with it, forming an end-to-end deep learning system, which can jointly learn the noise distribution and CNN parameters. The NMN learns the distribution of noise patterns directly from the noisy data without the need for any clean training data. The NMN can model label noise that depends only on the true label or is also dependent on the image features. We show that the integrated NMN/CNN learning system consistently improves the classification performance, for different levels of label noise, on the MSR-COCO dataset and MSR-VTT dataset. We also show that noise performance improvements are obtained when multiple instance learning methods are used.