In this paper, we consider the problem of learning two-dimensional spatial models of gas distributions. To build models of gas distributions that can be used to accurately predict the gas concentration at query locations is a challenging task due to the chaotic nature of gas dispersal. We formulate this task as a regression problem. To deal with the specific properties of gas distributions, we propose a sparse Gaussian process mixture model, which allows us to accurately represent the smooth background signal and the areas with patches of high concentrations. We furthermore integrate the sparsification of the training data into an EM procedure that we apply for learning the mixture components and the gating function. Our approach has been implemented and tested using datasets recorded with a real mobile robot equipped with an electronic nose. The experiments demonstrate that our technique is well-suited for predicting gas concentrations at new query locations and that it outperforms alternative and previously proposed methods in robotics.