Motivation: Critical evaluation of methods for protein function prediction shows that data integration improves the performance of methods that predict protein function, but a basic BLAST-based method is still a top contender. We sought to engineer a method that modernizes the classical approach while avoiding pitfalls common to state-of-the-art methods. Results: We present a method for predicting protein function, Effusion, which uses a sequence similarity network to add context for homology transfer, a probabilistic model to account for the uncertainty in labels and function propagation, and the structure of the Gene Ontology (GO) to best utilize sparse input labels and make consistent output predictions. Effusion's model makes it practical to integrate rare experimental data and abundant primary sequence and sequence similarity. We demonstrate Effusion's performance using a critical evaluation method and provide an in-depth analysis. We also dissect the design decisions we used to address challenges for predicting protein function. Finally, we propose directions in which the framework of the method can be modified for additional predictive power. Availability and implementation: The source code for an implementation of Effusion is freely available at https://github.com/babbittlab/effusion. Supplementary information: Supplementary data are available at Bioinformatics online.