Generative flow networks (GFNs) are a class of probabilistic models for sequential samplingof composite objects, proportional to a target distribution that is defined in terms of anenergy function or a reward. GFNs are typically trained using a flow matching or trajectorybalance objective, which matches forward and backward transition models over trajectories.In this work we introduce a variational objective for training GFNs, which is a convexcombination of the reverse- and forward KL divergences, and compare it to the trajectorybalance objective when sampling from the forward- and backward model, respectively. Weshow that, in certain settings, variational inference for GFNs is equivalent to minimizing thetrajectory balance objective, in the sense that both methods compute the same score-functiongradient. This insight suggests that in these settings, control variates, which are commonlyused to reduce the variance of score-function gradient estimates, can also be used with thetrajectory balance objective. We evaluate our findings and the performance of the proposedvariational objective numerically by comparing it to the trajectory balance objective on twosynthetic tasks.