Current object detection approaches predict bounding boxes, but these provide little instance-specific information beyond location, scale and aspect ratio. In this work, we propose to directly regress to objects shapes in addition to their bounding boxes and categories. It is crucial to find an appropriate shape representation that is compact and decodable, and in which objects can be compared for higher-order concepts such as view similarity, pose variation and occlusion. To achieve this, we use a denoising convolutional auto-encoder to establish an embedding space, and place the decoder after a fast end-to-end network trained to regress directly to the encoded shape vectors. This yields what to the best of our knowledge is the first real-time shape prediction network, running at ~35 FPS on a high-end desktop. With higher-order shape reasoning well-integrated into the network pipeline, the network shows the useful practical quality of generalising to unseen categories similar to the ones in the training set, something that most existing approaches fail to handle.