Deep learning-based image registration approaches have shown competitive performance and run-time advantages compared to conventional image registration methods. However, existing learning-based approaches mostly require to train separate models with respect to different regularization hyperparameters for manual hyperparameter searching and often do not allow spatially-variant regularization. In this work, we propose a learning-based registration approach based on a novel conditional spatially adaptive instance normalization (CSAIN) to address these challenges. The proposed method introduces a spatially-variant regularization and learns its effect of achieving spatially-adaptive regularization by conditioning the registration network on the hyperparameter matrix via CSAIN. This allows varying of spatially adaptive regularization at inference to obtain multiple plausible deformations with a single pre-trained model. Additionally, the proposed method enables automatic hyperparameter optimization to avoid manual hyperparameter searching. Experiments show that our proposed method outperforms the baseline approaches while achieving spatially-variant and adaptive regularization.