Although we have shown in the main paper that DAG-GFlowNet is capable of learning an accurate approximation of the posterior distribution P (G | D) when the size of the dataset D is moderate (a situation where the benefits of a Bayesian treatment of structure learning are larger), we observed that as the size of the dataset increases, fitting the detailed-balance loss in (10) was more challenging. This can be explained by the fact that with a larger amount of data, the posterior distribution becomes very peaky (Koller and Friedman, 2009). As a consequence, in this situation, the delta-score in (9), which is required to calculate the loss, can take a wide range of values: adding an edge to a graph can drastically increase or decrease its score. In turn, the neural network parametrizing Pθ(Gt+1 | Gt) needs to compensate for these large fluctuations, making it harder to train.