Video frame interpolation typically involves two steps: motion estimation and pixel synthesis. Such a two-step approach heavily depends on the quality of motion estimation. This paper presents a robust video frame interpolation method that combines these two steps into a single process. Specifically, our method considers pixel synthesis for the interpolated frame as local convolution over two input frames. The convolution kernel captures both the local motion between the input frames and the coefficients for pixel synthesis. Our method employs a deep fully convolutional neural network to estimate a spatially-adaptive convolution kernel for each pixel. This deep neural network can be directly trained end to end using widely available video data without any difficult-to-obtain ground-truth data like optical flow. Our experiments show that the formulation of video interpolation as a single convolution process allows our method to gracefully handle challenges like occlusion, blur, and abrupt brightness change and enables high-quality video frame interpolation.