In this paper, we introduce a conceptually simple network for generating\ndiscriminative tissue-level segmentation masks for the purpose of breast cancer\ndiagnosis. Our method efficiently segments different types of tissues in breast\nbiopsy images while simultaneously predicting a discriminative map for\nidentifying important areas in an image. Our network, Y-Net, extends and\ngeneralizes U-Net by adding a parallel branch for discriminative map generation\nand by supporting convolutional block modularity, which allows the user to\nadjust network efficiency without altering the network topology. Y-Net delivers\nstate-of-the-art segmentation accuracy while learning 6.6x fewer parameters\nthan its closest competitors. The addition of descriptive power from Y-Net's\ndiscriminative segmentation masks improve diagnostic classification accuracy by\n7% over state-of-the-art methods for diagnostic classification. Source code is\navailable at: https://sacmehta.github.io/YNet.\n