Owing to the remarkable development of deep learning technology, there have been a series of efforts to build deep learning-based climate models. Whereas most of them utilize recurrent neural networks and/or graph neural networks, we design a novel climate model based on two concepts, the neural ordinary differential equation (NODE) and the advection–diffusion equation. The advection–diffusion equation is widely used for climate modeling because it describes many physical processes involving Brownian and bulk motions in climate systems. On the other hand, NODEs are to learn a latent governing equation of ODE from data. In our presented method, we combine them into a single framework and propose a concept, called neural advection–diffusion equation (NADE). Our NADE, equipped with the advection–diffusion equation and one more additional neural network to model inherent uncertainty, can learn an appropriate latent governing equation that best describes a given climate dataset. In our experiments with three real-world and two synthetic datasets and fourteen baselines, our method consistently outperforms existing baselines by non-trivial margins.