In large population-based studies and in clinical routine, tasks like disease\ndiagnosis and progression prediction are inherently based on a rich set of\nmulti-modal data, including imaging and other sensor data, clinical scores,\nphenotypes, labels and demographics. However, missing features, rater bias and\ninaccurate measurements are typical ailments of real-life medical datasets.\nRecently, it has been shown that deep learning with graph convolution neural\nnetworks (GCN) can outperform traditional machine learning in disease\nclassification, but missing features remain an open problem. In this work, we\nfollow up on the idea of modeling multi-modal disease classification as a\nmatrix completion problem, with simultaneous classification and non-linear\nimputation of features. Compared to methods before, we arrange subjects in a\ngraph-structure and solve classification through geometric matrix completion,\nwhich simulates a heat diffusion process that is learned and solved with a\nrecurrent neural network. We demonstrate the potential of this method on the\nADNI-based TADPOLE dataset and on the task of predicting the transition from\nMCI to Alzheimer's disease. With an AUC of 0.950 and classification accuracy of\n87%, our approach outperforms standard linear and non-linear classifiers, as\nwell as several state-of-the-art results in related literature, including a\nrecently proposed GCN-based approach.\n