We propose a fully automatic method to assess and improve the quality of the fat saturation in breast MR images. For this purpose, three deep neural networks were trained using both actual and synthetic breast MR data. Firstly, the poorly fat saturated cases were classified using a binary classification network. Then, the poorly fat saturated regions were localized using a segmentation network. Lastly, for the poor cases, the remaining fat signals were retrospectively suppressed using a correction network. The results showed that our networks successfully identified the poor cases and suppressed the remaining fat signals.