reviews: 
Comments: This paper introduces a new model (LGNSDE) for learning on graphs with uncertainty quantification. It leverages an Ornstein-Uhlenbeck prior and a posterior with drift parameterized by a GCN model that is trained through variational inference. This SDE approach is latent as it operates on node feature embeddings. Two novel theoretical results are shown, providing a bound on model output variance and a bound on solutions under node feature perturbations. Six graph models are then compared in various experiments on five standard graph datasets, including studies of OOD detection, test noise, and active learning. The proposed model performs favorably across these experiments.
Strengths: - The LGNSDE model description is clear, concise, and intuitive.
- The two theoretical results are important and original, providing a good deal of strength to the proposed methodology.
- The experiments clearly show this model has significant potential in delivering upon the promise of uncertainty quantification for graph-structured learning problems.
Weaknesses: - Some of the cited works (particularly Calvo-Ordoñez et al., 2024, and Xu et al., 2022) leverage SDEs in a very similar way, but do not consider the problem of learning on graphs. While the application to graphs is creative, the model definition is somewhat limited in novelty.
- The choice of a constant drift and diffusion function in the OU prior is not sufficiently explored. It would be great if there was mention of why this is a reasonable restriction if this is indeed the case.
- The experimental section would benefit from increased clarity and specificity, especially in regard to the structure and setup of experiments. Choices such as number of epochs and early stopping criteria, if any, are not explicitly stated.
- It is stated in Section 5 that hyperparameters that achieved the highest validation accuracy were chosen. It is unclear to me which validation accuracy is used here, and knowing the exact grid search setup would be ideal for improved reproducibility.
- Table 7 shows that uniform hyperparameters were chosen across all models; if the hyperparameter choice was performed via search for each model independently, the comparison results might be more fair.
- The most impactful perceived weakness of this paper was the lack of experimental comparison with the models referenced as related works, particularly those referenced in Section 6. The other methods used in comparison do not follow a stochastic approach, limiting the ability for a fair comparison. I would be extremely interested to see a comparative study against the referenced GNSD (Lin et al., 2024) method, for example.
- For OOD detection, comparison against methods built specifically for this task on graphs, like GNNSafe (Wu et al., 2023) would be enlightening.
- One of the theoretical claims was a resistance to small perturbations in graph structure. This might lead to a compelling experiment, but this claim is not tested.

There are two small writing nitpicks:
- In the first line of the introduction, "Before the widespread of neural networks" is missing a word. Perhaps use "widespread success" or similar?
- In Section 6, "Hence, constructing a different method." does not read as a complete sentence, and should probably be folded into the line before it.
Recommendation: 6
Reviewer confidence: 3
Soundness/correctness: 2
Clarity: 3