While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for training diffusion models for dynamics forecasting that leverages the temporal dynamics encoded in the data, directly coupling it with the diffusion steps in the network. We train a stochastic, time-conditioned interpolator and a backbone forecaster network that mimic the forward and reverse processes of conventional diffusion models, respectively. This design choice naturally encodes multi-step and long-range forecasting capabilities, 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 imposes a strong inductive bias, allowing for improved computational efficiency compared to traditional Gaussian noise-based diffusion models. Our approach performs competitively on probabilistic skill score metrics in complex dynamics forecasting of 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。我们提出了一种训练扩散模型用于动力学预测的方法，该方法利用数据中编码的时间动态信息，直接将其与网络中的扩散步骤耦合。我们训练了一个随机、时间条件插值器和一个主干预测网络，它们分别模拟传统扩散模型的正向和反向过程。这种设计选择自然地编码了多步和长程预测能力，支持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进行性能权衡。此外，基于动力学信息的扩散过程引入了强归纳偏置，使得与基于高斯噪声的传统扩散模型相比，计算效率得以提升。我们的方法在海表温度、纳维-斯托克斯流和弹簧网格系统的复杂动力学预测中，在概率技能评分指标上表现出有竞争力的性能。