Further Discussion
Dear Reviewer XoYX,
We appreciate your insightful response and are glad to clarify your concerns. We sincerely invite the reviewer to have further discussions.
> **Q1.** Why can't $\tau$-leaping be used in the discrete model? Can it be applied in other continuous graph generation such as GDSS?
**A1.** We clarify this as follows.
1. **$\tau$-leaping [1-3] is designed for continuous-time discrete-state** stochastic processes (CTMC). It **cannot** be applied to discrete-time models (e.g., Digress [4]) because $\tau$-leaping needs the rate matrices as input, but **discrete-time models do not have rate matrices**.
2. It **cannot** be applied to GDSS because GDSS is a **continuous-state** model, which is not characterized by the rate matrices.
> **Q2.** The result in Table 9 shows that the proposed method is robust to the sampling step and as mentioned in the paper, DIGRESS also has this property. This does not show there is an improvement in sampling efficiency.
**A2.** We would like to answer the reviewer' question from the following perspectives:
1. Theoretically, Digress cannot have such sampling flexibility. For example, **if the model is trained with 500 forward steps, technically, its reverse process has to include 500 steps**. In other words, for a Digress model trained with 500 forward steps, doing the reverse process in 100 steps is hard to ensure that the generated samples are from the desired generation distribution.
2. Empirically, we have conducted the following experiments to answer the reviewer's question better. We train a Digress model in **500 forward steps** and use it to **do reverse sampling in 500 steps**. We artificially freeze the reverse transition probability in every $\mathrm{round}(500/k)$ steps, where $k$ is the number of inferences. In this way, we have a fair comparison to show the sampling robustness regarding the number of model inferences in Table 1. The metric is validity, and the results of DisCo are shown in Table 4 of our submitted paper. Both DisCo and Digress use the graph Transformer as the backbone and the marginal distribution as the reference distribution. **DisCo is consistently more robust regarding the decrease in the number of inferences. In other words, DisCo has a better quality-efficiency tradeoff.**
| \# of inferences | DisCo | Digress |
|---|---|---|
| 500 | 99.3$\pm$0.6 | 98.9$\pm$0.4 |
| 100 | 98.7$\pm$0.5 | 95.0$\pm$1.1 |
| 30 | 97.9$\pm$1.2 | 92.1$\pm$0.7 |
| 10 | 95.3$\pm$1.9 | 87.9$\pm$0.8 |
| 5 | 93.0$\pm$1.7 | 80.1$\pm$1.4 |
| 1 | 76.1$\pm$2.3 | 67.1$\pm$2.9 |
Table 1. Quality-efficiency tradeoff comparison on QM9
3. In addition, we did not find results from the Digress paper [4] showing that Digress is robust to the step size. If the reviewer could kindly give us a point on related results/statements, we will be happy to check them out.
> **Q3.** As the main motivation for using a continuous Markov model instead of a discrete one is to improve the sampling efficiency, one should expect to see more evaluation and evidence to support and validate that this has been achieved.
**A3.** As we mentioned in the submitted paper, Tables 4 and 9 show that the model's performance is robust when the sampling steps are decreased, achieving a decent generation quality-efficiency tradeoff. Lines 844-846 in the appendix detail the sampling steps used to search for the best results, much smaller than Digress's number of sampling steps. In addition, the results from Table 1 in this response should be supplementary to show the generation efficiency of DisCo, which will be included in the revised paper.
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Reference:
[1] Campbell, Andrew, et al. "A continuous time framework for discrete denoising models." NeurIPS 2022.
[2] Gillespie, Daniel T. "Approximate accelerated stochastic simulation of chemically reacting systems." The Journal of chemical physics 115.4 (2001): 1716-1733.
[3] Wilkinson, Darren J. Stochastic modelling for systems biology. Chapman and Hall/CRC, 2018
[4] Vignac, Clement, et al. "DiGress: Discrete Denoising diffusion for graph generation." ICLR 2023.
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