Single Image Super-Resolution (SISR) aims to improve resolution of small-size low-quality image from a single one. With popularity of consumer electronics in our daily life, this topic has become more and more attractive. In this paper, we argue that the curse of dimensionality is the underlying reason of limiting the performance of state-of-the-art algorithms. To address this issue, we propose Progressive Adversarial Network (PAN) that is capable of coping with this difficulty for domain-specific image super-resolution. The key principle of PAN is that we do not apply any distance-based reconstruction errors as the loss to be optimized, thus free from the restriction of the curse of dimensionality. To maintain faithful reconstruction precision, we resort to U-Net and progressive growing of neural architecture. The low-level features in encoder can be transferred into decoder to enhance textural details with U-Net. Progressive growing enhances image resolution gradually, thereby preserving precision of recovered image. Moreover, to obtain high-fidelity outputs, we leverage the framework of the powerful StyleGAN to perform adversarial learning. Without the curse of dimensionality, our model can super-resolve large-size images with remarkable photo-realistic details and few distortions. Extensive experiments demonstrate the superiority of our algorithm over state-of-the-arts both quantitatively and qualitatively.