We introduce Neural Input Modeling (NIM), a generative-neural-network framework that exploits modern data-rich environments to automatically capture simulation input distributions and then generate samples from them. Experiments show that our prototype architecture NIM-VL, which uses a novel variational-autoencoder architecture with LSTM components, can accurately, and with no prior knowledge, automatically capture a range of complex stochastic processes and efficiently generate sample paths. Moreover, we show that the outputs from a queueing model with (known) complex inputs are statistically close to outputs from the same queueing model but with the inputs learned via NIM. Known distributional properties such as i.i.d. structure and nonnegativity can be exploited to increase accuracy and speed. NIM can thus help overcome one of the key barriers to simulation for non-experts.