Aims: Electrocardiographic Imaging (ECGI) is a promising tool to map the electrical activity of the heart non-invasively using body surface potentials (BSP). However, it is still challenging due to the mathematically ill-posed nature of the inverse problem to solve. Novel approaches leveraging progress in artificial intelligence could alleviate these difficulties. Methods: We propose a Deep Learning (DL) formulation of ECGI in order to learn the statistical relation between BSP and cardiac activation. The presented method is based on Conditional Variational Autoencoders (CVAE) using deep generative neural networks. To quantify the accuracy of this method, we simulated activation maps and BSP data on six cardiac anatomies. Results: We evaluated our model by training it on five different cardiac anatomies (5 000 activation maps) and by testing it on a new patient anatomy over 200 activation maps. Due to the probabilistic property of our method, we predicted 10 distinct activation maps for each BSP data. The proposed method is able to generate volumetric activation maps with a good accuracy on the simulated data: the mean absolute error is 9.40 ms with 2.16 ms standard deviation on this testing set. Conclusion: The proposed formulation of ECGI enables to naturally include imaging information in the estimation of cardiac electrical activity from body surface potential. It naturally takes into account all the spatio-temporal correlations present in the data. We believe these features can help improve ECGI results.