We study the problem of mapping from acoustic to visual speech with the goal of generating accurate, perceptually natural speech animation automatically from an audio speech signal. We present a sliding window deep neural network that learns a mapping from a window of acoustic features to a window of visual features from a large audio-visual speech dataset. Overlapping visual predictions are averaged to generate continuous, smoothly varying speech animation. We outperform a baseline HMM inversion approach in both objective and subjective evaluations and perform a thorough analysis of our results.