Recent advances in deep learning have inspired numerous works on data-driven solutions to partial differential equation (PDE) problems. These neural PDE solvers can often be much faster than their numerical counterparts; however, each presents its unique limitations and generally balances training cost, numerical accuracy, and ease of applicability to different problem setups. To address these limitations, we introduce several methods to apply latent diffusion models to physics simulation. Firstly, we introduce a mesh autoencoder to compress arbitrarily discretized PDE data, allowing for efficient diffusion training across various physics. Furthermore, we investigate full spatio-temporal solution generation to mitigate autoregressive error accumulation. Lastly, we investigate conditioning on initial physical quantities, as well as conditioning solely on a text prompt to introduce text2PDE generation. We show that language can be a compact, interpretable, and accurate modality for generating physics simulations, paving the way for more usable and accessible PDE solvers. Through experiments on both uniform and structured grids, we show that the proposed approach is competitive with current neural PDE solvers in both accuracy and efficiency, with promising scaling behavior up to $\sim$3 billion parameters. By introducing a scalable, accurate, and usable physics simulator, we hope to bring neural PDE solvers closer to practical use.

本研究针对神经偏微分方程求解器在训练成本、数值精度和适用性方面的局限性，提出了几种新方法，采用潜在扩散模型进行物理模拟。通过引入网格自编码器、全时空解生成和基于文本提示的条件生成，证明了语言在生成物理模拟中的有效性与可解释性，展示了所提出方法在准确性和效率上的竞争力，推动了神经偏微分方程求解器向实际应用的迈进。

Text2PDE：用于可访问的物理模拟的潜在扩散模型