Deep image generation is becoming a tool to enhance artists and designers creativity potential. In this paper, we aim at making the generation process more structured and easier to interact with. Inspired by vector graphics systems, we propose a new deep image reconstruction paradigm where the outputs are composed from simple layers, defined by their color and a vector transparency mask. This presents a number of advantages compared to the commonly used convolutional network architectures. In particular, our layered decomposition allows simple user interaction, for example to update a given mask, or change the color of a selected layer. From a compact code, our architecture also generates vector images with a virtually infinite resolution, the color at each point in an image being a parametric function of its coordinates. We validate the efficiency of our approach by comparing reconstructions with state-of-the-art baselines given similar memory resources on CelebA and ImageNet datasets. Most importantly, we demonstrate several applications of our new image representation obtained in an unsupervised manner, including editing, vectorization and image search.