Simulating turbulent flows is crucial for a wide range of applications, and
machine learning-based solvers are gaining increasing relevance. However,
achieving stability when generalizing to longer rollout horizons remains a
persistent challenge for learned PDE solvers. We address this challenge by
introducing a fully data-driven fluid solver that utilizes an autoregressive
rollout based on conditional diffusion models. We show that this approach
offers clear advantages in terms of rollout stability compared to other learned
baselines. Remarkably, these improvements in stability are achieved without
compromising the quality of generated samples, and our model successfully
generalizes to flow parameters beyond the training regime. Additionally, the
probabilistic nature of the diffusion approach allows for inferring predictions
that align with the statistics of the underlying physics. We quantitatively and
qualitatively evaluate the performance of our method on a range of challenging
scenarios, including incompressible and transonic flows, as well as isotropic
turbulence.

基于条件扩散模型的全数据驱动流体求解器通过自回归预测实现了稳定的长期复现性，同时能够推广到训练范围之外的流动参数。