This study proposes a deep generative adversarial architecture (GAA) for network-wide spatial-temporal traffic state estimation. The GAA is able to combine traffic flow theory with neural networks and thus improve the accuracy of traffic state estimation. It consists of two Long Short-Term Memory Neural Networks (LSTM NNs) which capture correlation in time and space among traffic flow and traffic density. One of the LSTM NNs, called a discriminative network, aims to maximize the probability of assigning correct labels to both true traffic state matrices (i.e., traffic flow and traffic density within a given spatial-temporal area) and the traffic state matrices generated from the other neural network. The other LSTM NN, called a generative network, aims to generate traffic state matrices which maximize the probability that the discriminative network assigns true labels to them. The two LSTM NNs are trained simultaneously such that the trained generative network can generate traffic matrices similar to those in the training data set. Given a traffic state matrix with missing values, we use back-propagation on three defined loss functions to map the corrupted matrix to a latent space. The mapping vector is then passed through the pre-trained generative network to estimate the missing values of the corrupted matrix. The proposed GAA is compared with the existing Bayesian network approach on loop detector data collected from Seattle, Washington and that collected from San Diego, California. Experimental results indicate that the GAA can achieve higher accuracy in traffic state estimation than the Bayesian network approach.