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Process modeling is an important activity in business transformation projects. Free-form diagramming tools, such as PowerPoint and Visio, are the preferred tools for creating process models. However, the designs created using such tools are informal sketches, which are not amenable to automated analysis. Formal models, although desirable, are rarely created (during early design) because of the usability problems associated with formal-modeling tools. In this paper, we present an approach for automatically inferring formal process models from informal business process diagrams, so that the strengths of both types of tools can be leveraged. We discuss different sources of structural and semantic ambiguities, commonly present in informal diagrams, which pose challenges for automated inference. Our approach consists of two phases. First, it performs structural inference to identify the set of nodes and edges that constitute a process model. Then, it performs semantic interpretation, using a classifier that mimics human reasoning to associate modeling semantics with the nodes and edges. We discuss both supervised and unsupervised techniques for training such a classifier. Finally, we report results of empirical studies, conducted using flow diagrams from real projects, which illustrate the effectiveness of our approach.