reviews: 
Comments: The paper proposes an approach to diffusion modelling in which the covariance matrix of the time-reversal of the "noising" process is set to a diagonal approximation of the correct form estimated from the approximation of the "score". 

In order to do this a pair of neural networks are trained; one to estimate the score as usual and a second to estimate this diagonal matrix. The majority of parameters are shared between the two networks, allowing this to be accomplished with only a small additional computational cost. The properties of the objective function used to learn this covariance are explored to an extent in theoretical work.

Numerical results are presented for a toy model and for some more substantial image generation scenarios.
Strengths: To the best of my knowledge this approach to approximating the covariance matrix is novel and seems well motivated.

The numerical results do appear to show that this approach outperforms a number of alternative strategies and the settings of the image generation setting do seem reasonably challenging.

It seems that the additional implementation and training requirements of this approach over and above those of a more basic diffusion generative model are modest and so this approach could be incorporated into implementations of such approaches at small cost (both human and computational) which means that even modest improvements are potentially valuable.
Weaknesses: The paper doesn't seem to propose anything radically new; the introduction of sensible approximations of the covariance of the time reversal has been explored quite widely in recent years and so the contribution of this paper is the particular approach to doing that which, while well motivated and seemingly having good properties, does not seem particularly radical. 

There are some odd choices made presentationally at times which to my mind make the paper a bit less readable and hence a bit less accessible. For example, the description of diffusion processes in Section 2.1 takes as a starting point a discrete time process; (1) is not a diffusion process although it is described as one. It might be arrived at as the time discretisation of a diffusion, which may in this case be exact, but that's not the same thing.
These are minor points and haven't substantially influenced my view of the paper, but this seems the best box to put this in. The paper does contain quite a number of typos, strangely phrased sentences and similar; careful proofreading would make it more readable. E.g.
* Abstract: "diagonal covariances" is an odd phrase; covariances are the off-diagonal elements of the matrix. "diagonal covariance matrix" or similar might be clearer.
* Theorem 2: "objetcive"
* Theorem 2: "The objective in Equation (11) upper bounded the grounded objective." Didn't immediately seem to make sense to me; I /thought/ the intention was probably something like "The objective in Equation (11) upper bounds the base objective." or something of that sort, but it's not completely clear what the intended base objective was. It turns out that aside from the odd tense and phrasing, the statement of this theorem is using terms which are defined in the supplementary material!

The main evidence presented in support of the proposed approach is empirical and this evidence isn't completely overwhelming. E.g. from Table 3 it' seems that this method doesn't actually dominate other approaches in the literature although it often does well and doesn't seem to be outperformed by much when it is beaten. Of course, methods can be interesting without beating the state of the art uniformly, and there is the interesting suggestion that when other methods are outperforming this approach in terms of NLL they do less well in FID terms. That, of course, raises the question "why is this and what does it actually tell us?"
Recommendation: 8
Reviewer confidence: 3
Soundness/correctness: 3
Clarity: 2