Spatial time series imputation is of great importance to various real-world applications. As the state-of-the-art generative models, diffusion models (e.g. CSDI) have outperformed statistical and autoregressive based models in time series imputation. However, diffusion models may introduce unstable noise owing to the inherent uncertainty in sampling, leading to the generated noise deviating from the intended Gaussian distribution. Consequently, the imputed data may deviate from the real data. To this end, we propose a Self-adaptive noise Scaling Diffusion Model named SaSDim for spatial time series imputation. Specifically, we introduce a novel Probabilistic High-Order SDE Solver Module to scale the noise following the standard Gaussian distribution. The noise scaling operation helps the noise prediction module of the diffusion model to more accurately estimate the variance of noise. To effectively learn the spatial and temporal features, a Spatial guided Global Convolution Module (SgGConv) for multi-periodic temporal dependencies learning with the Fast Fourier Transformation and dynamic spatial dependencies learning with dynamic graph convolution is also proposed. Extensive experiments conducted on three real-world spatial time series datasets verify the effectiveness of SaSDim.