In this paper, we propose a noise-aware encoder-decoder framework to disentangle a clean saliency predictor from noisy training examples, where the noisy labels are generated by unsupervised handcrafted feature-based methods. The proposed model consists of two sub-models parameterized by neural networks: (1) a saliency predictor that maps input images to clean saliency maps, and (2) a noise generator, which is a latent variable model that produces noises from Gaussian latent vectors. The whole model that represents noisy labels is a sum of the two sub-models. The goal of training the model is to estimate the parameters of both sub-models, and simultaneously infer the corresponding latent vector of each noisy label. We propose to train the model by using an alternating back-propagation (ABP) algorithm, which alternates the following two steps: (1) learning back-propagation for estimating the parameters of two sub-models by gradient ascent, and (2) inferential back-propagation for inferring the latent vectors of training noisy examples by Langevin Dynamics. To prevent the network from converging to trivial solutions, we utilize an edge-aware smoothness loss to regularize hidden saliency maps to have similar structures as their corresponding images. Experimental results on several benchmark datasets indicate the effectiveness of the proposed model.