Sampling from discrete distributions specified by unnormalised probability functions is a classical statistical problem. GFlowNets address this problem by constructing objects sequentially, adding one discrete component at a time in either a predefined or a learned order. The choice of order determines which conditional distributions the neural network must learn, some of which may be easier to learn than others. Yet whether existing GFlowNet algorithms discover interpretable generation orders and make use of them during training remains unexplored. We introduce controlled problems where generation order is experimentally shown to affect convergence and standard GFlowNet training struggles to discover useful orders. To address this difficulty, we develop Learning-Order GFlowNet, a training recipe that learns interpretable generation orders without order annotations and improves convergence on these problems. Finally, we investigate gradient signal-to-noise ratio (SNR) as a possible explanation for order emergence: orders associated with faster convergence exhibit higher SNR at comparable validation loss, suggesting both a mechanism favouring their emergence and an SNR-based characterisation of a good generation order.

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