This article presents a Convolutional Neural Network (CNN) method to enable autonomous navigation of low-cost Micro Aerial Vehicle (MAV) platforms along dark underground mine environments. The proposed CNN component provides on-line heading rate commands for the MAV by utilising the image stream from the on-board camera, thus allowing the platform to follow a collision-free path along the tunnel axis. A novel part of the developed method consists of the generation of the data-set used for training the CNN. More specifically, inspired from single image haze removal algorithms, various image data-sets collected from real tunnel environments have been processed offline to provide an estimation of the depth information of the scene, where ground truth is not available. The calculated depth map is used to extract the open space in the tunnel, expressed through the area centroid and is finally provided in the training of the CNN. The method considers the MAV as a floating object, thus accurate pose estimation is not required. Finally, the capability of the proposed method has been successfully experimentally evaluated in field trials in an underground mine in Sweden.