iUNets: Fully invertible U-Nets with Learnable Up- and Downsampling

U-Nets have been established as a standard architecture for image-to-image learning problems such as segmentation and inverse problems in imaging. For large-scale data, as it for example appears in 3D medical imaging, the U-Net however has prohibitive memory requirements. Here, we present a new fully-invertible U-Net-based architecture called the iUNet, which employs novel learnable and invertible up- and downsampling operations, thereby making the use of memory-efficient backpropagation possible. This allows us to train deeper and larger networks in practice, under the same GPU memory restrictions. Due to its invertibility, the iUNet can furthermore be used for constructing normalizing flows.