We introduce WiCluster, a new machine learning (ML) approach for passive indoor positioning using radio frequency (RF) channel state information (CSI). WiCluster can predict both a zone-level position and a precise 2D or 3D position, without using any precise position labels during training. Prior CSI-based indoor positioning work has relied on non-parametric approaches using digital signal-processing (DSP) and, more recently, parametric approaches (e.g., fully supervised ML methods). However these do not handle the complexity of real-world environments well and do not meet requirements for large-scale commercial deployments: the accuracy of DSP-based method deteriorates significantly in non-line-of-sight conditions, while supervised ML methods need large amounts of hard-to-acquire centimeter accuracy position labels. In contrast, WiCluster is precise, requires weaker label-information that can be easily collected, and works well in non-line-of-sight conditions. Our first contribution is a novel dimensionality reduction method for charting. It combines a triplet-loss with a multi-scale clustering-loss to map the high-dimensional CSI representation to a 2D/3D latent space. Our second contribution is two weakly supervised losses that map this latent space into a Cartesian map, resulting in meter-accuracy position results. These losses only require simple to acquire priors: a sketch of the floorplan, approximate access-point locations and a few CSI packets that are labelled with the corresponding zone in the floorplan. Thirdly, we report results and a robustness study for 2D positioning in two single-floor office buildings and 3D positioning in a two-story home.