AbstractNetwork tomography aims at estimating source–destination traffic rates from link traffic measurements. This inverse problem was formulated by Vardi in 1996 for Poisson traffic over networks operating under deterministic as well as random routing regimes. In this article, we expand Vardi's second‐order moment matching rate estimation approach to higher‐order cumulant matching with the goal of increasing the column rank of the mapping and consequently improving the rate estimation accuracy. We develop a systematic set of linear cumulant matching equations and express them compactly in terms of the Khatri–Rao product. Both least squares estimation and iterative minimum I‐divergence estimation are considered. We develop an upper bound on the mean squared error (MSE) in least squares rate estimation from empirical cumulants. We demonstrate that supplementing Vardi's approach with the third‐order empirical cumulant reduces its minimum averaged normalized MSE in rate estimation by almost 20% when iterative minimum I‐divergence estimation was used.