This paper tackles automated categorization of Age-related Macular Degeneration (AMD), a common macular disease among people over 50. Previous research efforts mainly focus on AMD categorization with a single-modal input, let it be a color fundus photograph (CFP) or an OCT B-scan image. By contrast, we consider AMD categorization given a multi-modal input, a direction that is clinically meaningful yet mostly unexplored. Contrary to the prior art that takes a traditional approach of feature extraction plus classifier training that cannot be jointly optimized, we opt for end-to-end multi-modal Convolutional Neural Networks (MM-CNN). Our MM-CNN is instantiated by a two-stream CNN, with spatially-invariant fusion to combine information from the CFP and OCT streams. In order to visually interpret the contribution of the individual modalities to the final prediction, we extend the class activation mapping (CAM) technique to the multi-modal scenario. For effective training of MM-CNN, we develop two data augmentation methods. One is GAN-based CFP/OCT image synthesis, with our novel use of CAMs as conditional input of a high-resolution image-to-image translation GAN. The other method is Loose Pairing, which pairs a CFP image and an OCT image on the basis of their classes instead of eye identities. Experiments on a clinical dataset consisting of 1,094 CFP images and 1,289 OCT images acquired from 1,093 distinct eyes show that the proposed solution obtains better F1 and Accuracy than multiple baselines for multi-modal AMD categorization. Code and data are available at https://github.com/li-xirong/mmc-amd.