Many important physical phenomena involve subtle signals that are difficult to observe with the unaided eye, yet visualizing them can be very informative. Current motion magnification techniques can reveal these small temporal variations in video, but require precise prior knowledge about the target signal, and cannot deal with interference motions at a similar frequency. We present DeepMag an end-to-end deep neural video-processing framework based on gradient ascent that enables automated magnification of subtle color and motion signals from a specific source, even in the presence of large motions of various velocities. While the approach is generalizable, the advantages of DeepMag are highlighted via the task of video-based physiological visualization. Through systematic quantitative and qualitative evaluation of the approach on videos with different levels of head motion, we compare the magnification of pulse and respiration to existing state-of-the-art methods. Our method produces magnified videos with substantially fewer artifacts and blurring whilst magnifying the physiological changes by a similar degree.