We present a detail-driven deep neural network for point set upsampling. A high-resolution point set is essential for point-based rendering and surface reconstruction. Inspired by the recent success of neural image super-resolution techniques, we progressively train a cascade of patch-based upsampling networks on different levels of detail end-to-end. We propose a series of architectural design contributions that lead to a substantial performance boost. The effect of each technical contribution is demonstrated in an ablation study. Qualitative and quantitative experiments show that our method significantly outperforms the state-of-the-art learning-based and optimazation-based approaches, both in terms of handling low-resolution inputs and revealing high-fidelity details.