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Iris recognition systems transform an iris image into a feature vector. The seminal pipeline segments an image into iris and non-iris pixels, normalizes this region into a fixed-dimension rectangle, and extracts features which are stored and called a template (Daugman, 2009). This template is stored on a system. A future reading of an iris can be transformed and compared against template vectors to determine or verify the identity of an individual. As templates are often stored together, they are a valuable target to an attacker. We show how to invert templates across a variety of iris recognition systems. That is, we show how to transform templates into realistic looking iris images that are also deemed as the same iris by the corresponding recognition system. Our inversion is based on a convolutional neural network architecture we call RESIST (REconStructing IriSes from Templates). We apply RESIST to a traditional Gabor filter pipeline, to a DenseNet (Huang et al., CVPR 2017) feature extractor, and to a DenseNet architecture that works without normalization. Both DenseNet feature extractors are based on the recent ThirdEye recognition system (Ahmad and Fuller, BTAS 2019). When training and testing using the ND-0405 dataset, reconstructed images demonstrate a rank-1 accuracy of 100%, 76%, and 96% respectively for the three pipelines. The core of our approach is similar to an autoencoder. However, standalone training the core produced low accuracy. The final architecture integrates into an generative adversarial network (Goodfellow et al., NeurIPS, 2014) producing higher accuracy.