The air quality inference problem aims to utilize historical data from a limited number of observation sites to infer the air quality index at an unknown location. Considering the sparsity of data due to the high maintenance cost of the stations, good inference algorithms can effectively save the cost and refine the data granularity. While spatio-temporal graph neural networks have made excellent progress on this problem, their non-Euclidean and discrete data structure modeling of reality limits its potential. In this work, we make the first attempt to combine two different spatio-temporal perspectives, fields and graphs, by proposing a new model, Spatio-Temporal Field Neural Network, and its corresponding new framework, Pyramidal Inference. Extensive experiments validate that our model achieves state-of-the-art performance in nationwide air quality inference in the Chinese Mainland, demonstrating the superiority of our proposed model and framework.