Abstract
Diffusion models have emerged as powerful generative frameworks by progressively adding noise to data through a forward process and then reversing this process to generate realistic samples. While these models have achieved strong performance across various tasks and modalities, their application to temporal predictive learning remains underexplored. Existing approaches treat predictive learning as a conditional generation problem, but often fail to fully exploit the temporal dynamics inherent in the data, leading to challenges in generating temporally coherent sequences. To address this, we introduce Dynamical Diffusion (DyDiff), a theoretically sound framework that incorporates temporally aware forward and reverse processes. Dynamical Diffusion explicitly models temporal transitions at each diffusion step, establishing dependencies on preceding states to better capture temporal dynamics. Through the reparameterization trick, Dynamical Diffusion achieves efficient training and inference similar to any standard diffusion model. Extensive experiments across scientific spatiotemporal forecasting, video prediction, and time series forecasting demonstrate that Dynamical Diffusion consistently improves performance in temporal predictive tasks, filling a crucial gap in existing methodologies. Code is available at this repository: this https URL.
Abstract (translated)
扩散模型作为一种强大的生成框架，通过逐步向数据添加噪声的正向过程和反向该过程以生成逼真的样本而兴起。尽管这些模型在各种任务和模态中表现出色，但它们在时间预测学习中的应用尚未得到充分探索。现有方法将预测学习视为条件生成问题，但由于未能充分利用数据内在的时间动态特性，通常难以生成具有连贯性的时间序列。为解决这一问题，我们引入了动力学扩散（DyDiff），这是一种理论依据坚实的框架，它包含了时间感知的正向和反向过程。动力学扩散在每次扩散步骤中显式建模时间转换，并基于先前的状态建立依赖关系，以更好地捕捉时间动态特性。通过重新参数化技巧，动力学扩散实现了类似标准扩散模型的有效训练和推理效率。跨科学时空预测、视频预测以及时间序列预测的广泛实验表明，动力学扩散在时间预测任务中始终提高了性能，填补了现有方法论的一个重要空白。代码可在以下仓库获取：此 https URL 链接。
URL
https://arxiv.org/abs/2503.00951
