Considering the ill-posed nature, contrastive regularization has been developed for single image dehazing, introducing the information from negative images as a lower bound. However, the contrastive samples are nonconsensual, as the negatives are usually represented distantly from the clear (i.e., positive) image, leaving the solution space still under-constricted. Moreover, the interpretability of deep dehazing models is underexplored towards the physics of the hazing process. In this paper, we propose a novel curricular contrastive regularization targeted at a consensual contrastive space as opposed to a non-consensual one. Our negatives, which provide better lower-bound constraints, can be assembled from 1) the hazy image, and 2) corresponding restorations by other existing methods. Further, due to the different similarities between the embeddings of the clear image and negatives, the learning difficulty of the multiple components is intrinsically imbalanced. To tackle this issue, we customize a curriculum learning strategy to reweight the importance of different negatives. In addition, to improve the interpretability in the feature space, we build a physics-aware dual-branch unit according to the atmospheric scattering model. With the unit, as well as curricular contrastive regularization, we establish our dehazing network, named C2PNet. Extensive experiments demonstrate that our C2PNet significantly outperforms state-of-the-art methods, with extreme PSNR boosts of 3.94dB and 1.50dB, respectively, on SOTS-indoor and SOTS-outdoor datasets. Code is available at https://github.com/YuZheng9/C2PNet.