Network traffic demand matrix is a critical input for capacity planning, anomaly detection and many other network management related tasks. The demand matrix is often computed from link load measurements. The traffic matrix (TM) estimation problem is the determination of the traffic demand matrix from link load measurements. The relationship between the link loads and the traffic matrix that generated the link load can be modeled as an under-determined linear system and has multiple feasible solutions. Therefore, prior knowledge of the traffic demand pattern has to be used in order to find a potentially feasible demand matrix. In this paper, we consider the TM estimation problem where we have information about the distribution of the demand sizes. This information can be obtained from the analysis of a few traffic matrices measured in the past or from operator experience. We develop an iterative projection based algorithm for the solution of this problem. If large number of past traffic matrices are accessible, we propose a Generative Adversarial Network (GAN) based approach for solving the problem. We compare the strengths of the two approaches and evaluate their performance for several networks using varying amounts of past data.