* The proposed method is not well-positioned in literature. It's worth pointing out that the key idea of representing the marginal score as the expectation of scores of distributions conditioned on inputs is actually quite well-known. It has been used, for example, to develop the original denoising score matching objective [1]. It is also used in the literature as "score-interpolation" [2]. I just named a few but I would recommend the authors to do a thorough literature review as I believe this property is used in many more works.
* The definition of the notation \hat{c}_k (baycenters) is missing.
* The exponential dependence of the sampling error on T is concerning. Although empirical evidence is provided to justify that this error bound is pessimistic, it also renders the bound unnecessary. Meanwhile, it's unclear if the conclusion that under sigma < 0.4, a large starting T is harmless will generalize to other datasets.
* The 3D point cloud experiment is interesting but I don't understand why the proposed method fills the gap there. Could the authors elaborate on this?
* The practical utility of the proposed closed-form models is also unclear. Given that the model can only sample from baycenters of data point tuples, is there a clear case where we would prefer such a model over a trained score model?
* This is minor, but the readability of section 3 can be greatly improved if not going to the notation convention used by rectified flow, as the proposed method can be described using the standard diffusion model formulation (where the time is reversed and stochastic transition is used).
[1] Vincent, Pascal. "A connection between score matching and denoising autoencoders." Neural computation 23.7 (2011): 1661-1674.
[2] Dieleman, Sander, et al. "Continuous diffusion for categorical data." arXiv preprint arXiv:2211.15089 (2022).
* The proposed method is not well-positioned in literature. It's worth pointing out that the key idea of representing the marginal score as the expectation of scores of distributions conditioned on inputs is actually quite well-known. It has been used, for example, to develop the original denoising score matching objective [1]. It is also used in the literature as "score-interpolation" [2]. I just named a few but I would recommend the authors to do a thorough literature review as I believe this property is used in many more works.