The quality of an image affects the performance of computer vision applications. The presence of haze often greatly depreciates the visual effect of images. It is a traditional and critical vision challenge to remove haze from a single image. This paper proposes a trainable end-to-end de-hazing connectionist model with a special design. First, feature learning is conducted using hierarchical convolutional layers with nested structures. Cascaded haze-relevant tasks are then sequentially performed via a physics-driven sub-network. In particular, to break the assumption of a homogeneous atmosphere, a branch of the sub-network estimates the scattering factor in the form of a two-dimensional tensor. Finally, a chromatic adaptation layer is proposed for color adjustment, which is often neglected in existing de-hazing methods. In addition, we integrate different training criteria based on the characteristics of the haze-relevant variables in our model. For a fully actionable optimization, an asynchronous learning paradigm is designed for the fusion of different de-hazing tasks, and the joint model is further facilitated by a cyclic restoration. The effectiveness of the proposed de-hazing model was verified via extensive experiments, and most results of our method are remarkable.