  Earth system forecasting has traditionally relied on complex physical models
that are computationally expensive and require significant domain expertise. In
the past decade, the unprecedented increase in spatiotemporal Earth observation
data has enabled data-driven forecasting models using deep learning techniques.
These models have shown promise for diverse Earth system forecasting tasks but
either struggle with handling uncertainty or neglect domain-specific prior
knowledge, resulting in averaging possible futures to blurred forecasts or
generating physically implausible predictions. To address these limitations, we
propose a two-stage pipeline for probabilistic spatiotemporal forecasting: 1)
We develop PreDiff, a conditional latent diffusion model capable of
probabilistic forecasts. 2) We incorporate an explicit knowledge alignment
mechanism to align forecasts with domain-specific physical constraints. This is
achieved by estimating the deviation from imposed constraints at each denoising
step and adjusting the transition distribution accordingly. We conduct
empirical studies on two datasets: N-body MNIST, a synthetic dataset with
chaotic behavior, and SEVIR, a real-world precipitation nowcasting dataset.
Specifically, we impose the law of conservation of energy in N-body MNIST and
anticipated precipitation intensity in SEVIR. Experiments demonstrate the
effectiveness of PreDiff in handling uncertainty, incorporating domain-specific
prior knowledge, and generating forecasts that exhibit high operational
utility.
