Analysis of human sketches in deep learning has advanced immensely through the use of waypoint-sequences rather than raster-graphic representations. We further aim to model sketches as a sequence of low-dimensional parametric curves. To this end, we propose an inverse graphics framework capable of approximating a raster or waypoint based stroke encoded as a point-cloud with a variable-degree Bézier curve. Building on this module, we present Cloud2Curve, a generative model for scalable high-resolution vector sketches that can be trained end-to-end using point-cloud data alone. As a consequence, our model is also capable of deterministic vectorization which can map novel raster or waypoint based sketches to their corresponding high-resolution scalable Bézier equivalent. We evaluate the generation and vectorization capabilities of our model on Quick, Draw! and K-MNIST datasets.