Diabetes complications often afflict diabetes patients seriously: over 68% of diabetes-related mortality is caused by diabetes complications. In this paper, we study the problem of automatically diagnosing diabetes complications from patients' lab test results. The objective problem has two main challenges: 1) feature sparseness: a patient only undergoes 1.26% lab tests on average, and 65.5% types of lab tests are performed on samples from less than 10 patients; 2) knowledge skewness: it lacks comprehensive detailed domain knowledge of the association between diabetes complications and lab tests. To address these challenges, we propose a novel probabilistic model called Sparse Factor Graph Model (SparseFGM). SparseFGM projects sparse features onto a lower-dimensional latent space, which alleviates the problem of sparseness. SparseFGM is also able to capture the associations between complications and lab tests, which help handle the knowledge skewness. We evaluate the proposed model on a large collections of real medical records. SparseFGM outperforms (+20% by F1) baselines significantly and gives detailed associations between diabetes complications and lab tests.