Recently, several well-performing deep convolutional neural networks were proposed for remote sensing image super-resolution (SR). However, these methods rarely consider that remote sensing images are corruptible by additional noise, blurring, and other factors. Therefore, to eliminate the interference of these factors, especially the noise, we propose a novel information purification network (IPN) for remote sensing image SR. The proposed information purification block (IPB) can process channel-wise features differently by channel separation and rescale spatial-wise features adaptively through the proposed multi-scale spatial attention mechanism. We further design an information group to explore a more powerful expressive combination of IPBs. Moreover, long and short skip connections can transmit abundant low-frequency information, making IPBs pay more attention to high-frequency information. We mix the images under various degradation models as training data in the training phase. In this way, the network can directly reconstruct various degraded images. Experiments on AID and UC Merced Land-Use datasets under multiple degradation models demonstrate that the proposed IPN performs better than state-of-the-art methods.