Although single-image super-resolution (SISR) methods have achieved great success on single degradation, they still suffer performance drop with multiple degrading effects in real scenarios. Recently, some blind and non-blind models for multiple degradations have been explored. However, those methods usually degrade significantly for distribution shifts between the training and test data. Towards this end, we propose a conditional meta-network framework (named CMDSR) for the first time, which helps SR framework learn how to adapt to changes in input distribution. We extract degradation prior at task-level with the proposed ConditionNet, which will be used to adapt the parameters of the basic SR network (BaseNet). Specifically, the ConditionNet of our framework first learns the degradation prior from a support set, which is composed of a series of degraded image patches from the same task. Then the adaptive BaseNet rapidly shifts its parameters according to the conditional features. Moreover, in order to better extract degradation prior, we propose a task contrastive loss to decrease the inner-task distance and increase the cross-task distance between task-level features. Without predefining degradation maps, our blind framework can conduct one single parameter update to yield considerable SR results. Extensive experiments demonstrate the effectiveness of CMDSR over various blind, even non-blind methods. The flexible BaseNet structure also reveals that CMDSR can be a general framework for large series of SISR models. Our code is available at \url{https://github.com/guanghaoyin/CMDSR}.

Accepted by IEEE Transaction on Image Processing