SDE selection for different datasets & Steup of VESDE

[myu1999]

Dear authors,

Our team has been following your paper GDSS for the past six months. You have made tremendous contributions to the application of diffusion models in the graph domain. However, we have two questions that we hope to get answers from the original authors:

1.SDE selection for different datasets: For some small datasets like community_small and gdss_ego_small, you chose VPSDE for both nodes and edges. For larger datasets like QM9 and zinc250k, you selected VESDE for edges. We retrained QM9 using VPSDE, but the results were far inferior to VESDE. We'd like to ask: Why is VESDE chosen for large molecular datasets, and why does VPSDE perform poorly in these cases? Conversely, why is VPSDE typically chosen for smaller datasets?
2.Notably, in your experiments, you set sigma_min to 0.1 and sigma_max to 1 for VESDE. However, the original SDE paper states that sigma_max for VESDE is usually quite large to perturb and cover as much space as possible. Additionally, since in VESDE, x_t = x_0 + sigma_i * z, we have x_N = x_0 + sigma_max * z = x_0 + 1 * z. This makes it difficult to ensure that x_N follows a standard Gaussian distribution. Yet, the sampling starting point for VESDE is a standard Gaussian distribution. This seems somewhat contradictory. Could you explain the reasoning behind this?

We look forward to your new works and send our best wishes!