Hyperspectral (HS) cameras record the spectrum at multiple wavelengths for each pixel in an image, and are used, e.g., for quality control and agricultural remote sensing. We introduce a fast, cost-efficient and mobile method of taking HS images using a regular digital camera equipped with a passive diffraction grating filter, using machine learning for constructing the HS image. The grating distorts the image by effectively mapping the spectral information into spatial dislocations, which we convert into a HS image by a convolutional neural network utilizing novel wide dilation convolutions that accurately model optical properties of diffraction. We demonstrate high-quality HS reconstruction using a model trained on only 271 pairs of diffraction grating and ground truth HS images.