Experience shows that solar resource prediction is a difficult task. The available solar irradiance where a photovoltaic plant is located or is planned to be installed depends mainly on the cloud incidence at the site. This incidence of clouds depends on the region's climate system, which is well known to be a non-linear, chaotic, and extremely complex, for which there is no exact mathematical model. The chaos level has been determined for various time series of wind and solar irradiance, and it turns out that the chaos level of the solar time series is higher than that of the wind series. A higher level of chaos indicates that the complexity of solar irradiance prediction is considerable. In previous works of solar irradiance prediction, using Artificial Neural Networks, it has been observed that the trained models fail to predict irradiance spikes in conditions of intermittent cloudiness. By conducting a study in this area, we have found that, for a given date, there exists a model to determine the ideal solar irradiance in any geographical location of the planet. These models, so-called clear-sky models, have been taken as a reference to predict not the solar irradiance, but the amount of irradiance occluded by the clouds. That is the difference between ideal irradiance and that measured by the weather station. The proposed model is called SolarDiff, which predicts this difference using Artificial Neural Networks. This article empirically demonstrates that the SolarDiff model exhibits better behavior than models based on direct data. The performance, as in most forecast models, is measured by quantifying the forecast error.