In this paper, we present a new learning framework for image style transforms. Considering that the images in different style representations constitute different vector spaces, we propose a novel framework called Coupled Space Learning to learn the relations between different spaces and use them to infer the images from one style to another style. Observing that for each style, only the components correlated to the space of the target style are useful for inference, we first develop the Correlative Component Analysis to pursue the embedded hidden subspaces that best preserve the inter-space correlation information. Then we develop the Coupled Bidirectional Transform algorithm to estimate the transforms between the two embedded spaces, where the coupling between the forward transform and the backward transform is explicitly taken into account. To enhance the capability of modelling complex data, we further develop the Coupled Gaussian Mixture Model to generalize our framework to a mixture-model architecture. The effectiveness of the framework is demonstrated in the applications including face super-resolution and bidirectional portrait style transforms.