A Spatial Interpolation Method Based on Denoising Diffusion Probabilistic Model

Abstract

Spatial interpolation is critical in geographic information systems (GIS) and environmental science, particularly when dealing with high-dimensional and nonlinear data. Classical methods like Kriging and inverse distance weighting (IDW) often struggle with the complexities of irregular terrain and sparse datasets, and they are inadequate for capturing the nonlinear characteristics of high-dimensional spatial data. In this paper, we introduce a novel interpolation method based on the Denoising Diffusion Probabilistic Model (DDPM), which incorporates ConvNeXt V2 blocks within a UNet architecture. To validate the performance of our model, we employ the Copernicus Digital Elevation Model (COP-DEM) dataset for simulation experiments. Experimental results demonstrate that the proposed DDPM method significantly outperforms classical interpolation techniques, particularly in scenarios with high-density control points, producing high-quality interpolation results with strong transferabgeogeoility. This approach shows considerable promise for spatial interpolation in high-dimensional, complex terrains, offering a more robust alternative to traditional methods. It not only addresses key challenges in interpolation accuracy but also opens up new possibilities for applying generative models in other spatial data processing domains, including environmental monitoring and geospatial modeling.