reviews: 
Comments: This paper introduce a diffusion-based method for simulating PDEs. The method performs diffusion in the latent space, and incorporate physics priors into the model. Experiments are conducted in various number of datasets in PDE-Bench and 2 introduced datasets.
Strengths: Significance: The paper addresses the important problem of improving the generalizability and long-horizon predictive performance of simulating PDEs. The diffusion has advantage compared to prior approaches.

Novelty: The introduction of latent diffusion to PDE simulation, to my knowledge, is novel. 

Clarity: The introduction of the method is mostly clear.
Weaknesses: My most concern with the paper is the soundness of the paper, since I find that there are many errors in the tables in the experiment section. 

Errors:
1. The most obvious is in Table 2 and Table 3, where the PDE diffusion has exactly THE SAME results for all the different datasets, and even the same results in Table 2 and Table 3. This is clearly impossible.

2. Table 2 lacks the results for dataset CFD2D turbo2 for FNO, with MAE metric.

3. in Table 1, the bold font should make the best result across all methods. However, CFD2D turbo2, the proposed method is clearly has higher MAE and MSE than FNO.

Other places:
1. in Table 1, DR2D lacks the bold font for any method for 2-step.

2. In section 5.3, in the third last row, it lacks the numbers: "The MSE decrease is x% (at 2), x% (at 4), x%..."

3. In Fig 2, "Double shock" should be "Double Mach"?

These errors and unfinished parts seems be due to the time rush, so the paper is not polished enough. I strongly suggest the authors to double and triple check the paper, to make sure everything is correct, before submitting. I believe that if the paper is properly and carefully done and well-polished, it can be a strong paper. In its current form, I have to suggest rejection.

Besides, it would be great if the authors can analyze why the proposed method outperforms VDM. A comparison with existing work DYffusion [1] may also be preferable. There are also many neural PDE works that evolves the system in latent space, e.g., [2][3][4][5][6]. It may be preferable to discuss them.

[1] DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting, NeurIPS 2023

[2] Multiscale simulations of complex systems by learning their effective dynamics, Nature Machine Intelligence

[3] Learning to Accelerate Partial Differential Equations via Latent Global Evolution, NeurIPS 2022

[4] Latent space subdivision: stable and controllable time predictions for fluid flow, in Computer Graphics Forum

[5] Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders,” Journal of Computational Physics

[6] Deep fluids: A generative network for parameterized fluid simulations,” in Computer Graphics Forum
Recommendation: 1: strong reject
Reviewer confidence: 4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.
Soundness/correctness: 1 poor
Clarity: 2 fair