Satellite-based InSAR images have the potential to detect volcanic deformation prior to eruptions, but while a vast number of images are routinely acquired, only a small percentage contain volcanic deformation events. Manual inspection could miss these anomalies, and an automatic system modelled with supervised learning requires suitably labelled datasets. To tackle these issues, this paper explores the use of unsupervised deep learning on InSAR images for the purpose of identifying volcanic deformation as anomalies. We test three different state-of-the-art architectures, one convolutional neural network (PaDiM - Patch Distribution Modeling) and two generative models (GANomaly and DDPM). We propose a preprocessing approach to deal with noisy and incomplete data points. We further improve the performance of PaDiM by using a weighted distance, assigning greater importance to features from deeper layers. The final framework was tested with four different volcanoes, which have different characteristics and its performance was compared against an existing supervised learning method for volcanic deformation detection. The experiments show that our final anomaly detection outperforms the supervised learning, particularly where the characteristics of deformation are unknown. Our framework can thus be used to identify deformation at volcanoes without needing prior knowledge about the deformation patterns present there.