While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting, where generating stable and accurate rollout forecasts remains challenging, Our method, DYffusion, leverages the temporal dynamics in the data, directly coupling it with the diffusion steps in the model. We train a stochastic, time-conditioned interpolator and a forecaster network that mimic the forward and reverse processes of standard diffusion models, respectively. DYffusion naturally facilitates multi-step and long-range forecasting, allowing for highly flexible, continuous-time sampling trajectories and the ability to trade-off performance with accelerated sampling at inference time. In addition, the dynamics-informed diffusion process in DYffusion imposes a strong inductive bias and significantly improves computational efficiency compared to traditional Gaussian noise-based diffusion models. Our approach performs competitively on probabilistic forecasting of complex dynamics in sea surface temperatures, Navier-Stokes flows, and spring mesh systems.

翻译：尽管扩散模型能够成功生成数据并进行预测，但它们主要针对静态图像设计。我们提出了一种高效训练扩散模型进行概率性时空预测的方法，其中生成稳定且准确的滚动预测仍具有挑战性。我们的方法DYffusion利用数据中的时间动力学，将其直接与模型中的扩散步骤耦合。我们训练了一个随机的、时间条件化的插值器和一个预测器网络，分别模拟标准扩散模型的前向和反向过程。DYffusion自然支持多步和长程预测，允许高度灵活的连续时间采样轨迹，并能在推理时通过加速采样权衡性能。此外，DYffusion中基于动力学的扩散过程引入了强归纳偏置，与传统基于高斯噪声的扩散模型相比显著提升了计算效率。我们的方法在海面温度、纳维-斯托克斯流和弹簧网格系统的复杂动力学概率预测中表现出竞争力。