Many problems in real-world applications involve predicting continuous-valued random variables that are statistically related. In this paper, we propose a powerful deep structured model that is able to learn complex non-linear functions which encode the dependencies between continuous output variables. We show that inference in our model using proximal methods can be efficiently solved as a feed-foward pass of a special type of deep recurrent neural network. We demonstrate the effectiveness of our approach in the tasks of image denoising, depth refinement and optical flow estimation.