  Single image dehazing is an important low-level vision task with many
applications. Early researches have investigated different kinds of visual
priors to address this problem. However, they may fail when their assumptions
are not valid on specific images. Recent deep networks also achieve relatively
good performance in this task. But unfortunately, due to the disappreciation of
rich physical rules in hazes, large amounts of data are required for their
training. More importantly, they may still fail when there exist completely
different haze distributions in testing images. By considering the
collaborations of these two perspectives, this paper designs a novel residual
architecture to aggregate both prior (i.e., domain knowledge) and data (i.e.,
haze distribution) information to propagate transmissions for scene radiance
estimation. We further present a variational energy based perspective to
investigate the intrinsic propagation behavior of our aggregated deep model. In
this way, we actually bridge the gap between prior driven models and data
driven networks and leverage advantages but avoid limitations of previous
dehazing approaches. A lightweight learning framework is proposed to train our
propagation network. Finally, by introducing a taskaware image separation
formulation with a flexible optimization scheme, we extend the proposed model
for more challenging vision tasks, such as underwater image enhancement and
single image rain removal. Experiments on both synthetic and realworld images
demonstrate the effectiveness and efficiency of the proposed framework.
