Detecting changes that occurred in a pair of 3D airborne LiDAR point clouds, acquired at two different times over the same geographical area, is a challenging task because of unmatching spatial supports and acquisition system noise. Most recent attempts to detect changes on point clouds are based on supervised methods, which require large labelled data unavailable in real-world applications. To address these issues, we propose an unsupervised approach that comprises two components: Neural Field (NF) for continuous shape reconstruction and a Gaussian Mixture Model for categorising changes. NF offer a grid-agnostic representation to encode bi-temporal point clouds with unmatched spatial support that can be regularised to increase high-frequency details and reduce noise. The reconstructions at each timestamp are compared at arbitrary spatial scales, leading to a significant increase in detection capabilities. We apply our method to a benchmark dataset of simulated LiDAR point clouds for urban sprawling. The dataset offers different challenging scenarios with different resolutions, input modalities and noise levels, allowing a multi-scenario comparison of our method with the current state-of-the-art. We boast the previous methods on this dataset by a 10% margin in intersection over union metric. In addition, we apply our methods to a real-world scenario to identify illegal excavation (looting) of archaeological sites and confirm that they match findings from field experts.