UNet-AF: Alias-free UNet architectures

The simplicity and effectiveness of UNet architectures make them ubiquitous in image restoration, segmentation, and diffusion models. They are often assumed to be equivariant to translations, yet they traditionally consist of layers that are known to be prone to aliasing, which hinders their equivariance in practice. To overcome this limitation, we show how to build sub-pixel translation-equivariant UNet architectures by appropriately choosing their main components (convolution, pooling, downsampling, activation, and normalization layers) to be alias-free. We evaluate the proposed equivariant architectures against non-equivariant baselines on image restoration tasks and observe competitive performance with a significant increase in measured equivariance. Through extensive ablation studies, we also demonstrate the importance of every architectural choice to achieve high equivariance. Our implementation is available at https://github.com/jscanvic/UNet-AF