Research on methods for the inference of networks from biological data is making significant advances, but the adoption of network inference in biomedical research practice is lagging behind. Here, we present Cyni, an open-source fill-in-the-algorithm framework that provides common network inference functionality and user interface elements. Cyni allows the rapid transformation of Java-based network inference prototypes into apps of the popular open-source Cytoscape network analysis and visualization ecosystem. Merely placing the resulting app in the Cytoscape App Store makes the method accessible to a worldwide community of biomedical researchers by mouse click. In a case study, we illustrate the transformation of an ARACNE implementation into a Cytoscape app.