An application programming interface (API) provides various software constructs that allow a developer to assemble a processing pipeline having arbitrary structure and complexity. Once assembled, the processing pipeline is configured to include a set of interconnected pipestages. Those pipestages are associated with one or more different CTAs that may execute in parallel with one another on a parallel processing unit. The developer specifies the configuration of the pipestages, including the configuration of the different CTAs across all pipestages, as well as the different processing operations performed by each different CTA.