Deep learning can be used to help reconstruct low frequencies in seismic data, and to directly infer velocity models in simple cases. In order to succeed with deep learning, a good training set of velocity models is critical. We present a new way to design random models that are statistically similar to a given guiding model. Our approach is based on shuffling the coefficients of a wavelet packet decomposition (WPD) of the guiding model, allowing us to replicate realistic textures from a synthetic model. We generate realistically random models from the BP 2004 and Marmousi II models for neural network training, and utilize the trained network to extrapolate low frequencies for the SEAM model. We apply full-waveform inversion to the extrapolated data to understand the limitations of our approach.