The ability to make accurate social inferences makes humans able to navigate and act in their social environment effortlessly. Converging evidence shows that motion is one of the most informative cues in shaping the perception of social interactions. However, the scarcity of parameterized generative models for the generation of highly-controlled stimuli has slowed down both the identification of the most critical motion features and the understanding of the computational mechanisms underlying their extraction and processing from rich visual inputs. In this work, we introduce a novel generative model for the automatic generation of an arbitrarily large number of videos of socially interacting agents for comprehensive studies of social perception. The proposed framework, validated with three psychophysical experiments, allows generating as many as 15 distinct interaction classes. The model builds on classical dynamical system models of biological navigation and is able to generate visual stimuli that are parametrically controlled and representative of a heterogeneous set of social interaction classes. The proposed method represents thus an important tool for experiments aimed at unveiling the computational mechanisms mediating the perception of social interactions. The ability to generate highly-controlled stimuli makes the model valuable not only to conduct behavioral and neuroimaging studies, but also to develop and validate neural models of social inference, and machine vision systems for the automatic recognition of social interactions. In fact, contrasting human and model responses to a heterogeneous set of highly-controlled stimuli can help to identify critical computational steps in the processing of social interaction stimuli.