Kriging is the most widely used spatial interpolation method in geostatistics. For many environmental applications, kriging may have to satisfy the stationarity and isotropy hypothesis, and new techniques using machine learning suffer from a lack of labeled data. In this paper, we propose to use Deep Image Prior, which is a U-net-like deep neural network designed for image reconstruction, to perform spatial interpolation and conditional map generation without any prior learning. This approach allows to overcome the assumptions for kriging, as well as the lack of labeled data, while proposing uncertainty and probability above a certain threshold. The proposed method is based on a convolutional neural network that generates a map from random values by minimizing the difference between the output map and the observed values. From this new method of spatial interpolation, we generate n maps in order to have a map of uncertainty and a map of probability of exceeding the threshold. The conducted experiments demonstrate the relevance of the proposed methods for spatial interpolation, on both the well-known digital elevation model data and the more challenging case of pollution mapping. The obtained results with the three datasets demonstrate the competitive performance compared with state-of-the-art methods.