Large scale datasets created from crowdsourced labels or openly available data have become crucial to provide training data for large scale learning algorithms. While these datasets are easier to acquire, the data are frequently noisy and unreliable, which is motivating research on weakly supervised learning techniques. In this paper we propose original ideas that help us to leverage such datasets in the context of change detection. First, we propose the guided anisotropic diffusion (GAD) algorithm, which improves semantic segmentation results using the input images as guides to perform edge preserving filtering. We then show its potential in two weakly-supervised learning strategies tailored for change detection. The first strategy is an iterative learning method that combines model optimisation and data cleansing using GAD to extract the useful information from a large scale change detection dataset generated from open vector data. The second one incorporates GAD within a novel spatial attention layer that increases the accuracy of weakly supervised networks trained to perform pixel-level predictions from image-level labels. Improvements with respect to state-of-the-art are demonstrated on 4 different public datasets.