Can AI Understand the Language of Origami?

Building AI systems that can plan, act, and create in the physical world requires more than pattern recognition. Such systems must reason about the generative mechanisms and constraints governing physical processes, using structured representations that connect observations, actions, and their effects. Yet, many existing benchmarks study these capabilities separately, focusing either on visual recognition or on abstract symbolic or programmatic reasoning. Origami provides a natural testbed that integrates these abilities: constructing shapes through folds requires visual perception, reasoning about geometric and physical constraints, and sequential planning, while remaining sufficiently structured for systematic evaluation. We introduce OrigamiBench, a benchmark for evaluating programmatic understanding of the mechanisms underlying origami synthesis through a high-level language of physically grounded fold actions. Experiments with modern vision-language models reveal that scaling model size alone does not reliably improve reasoning about physical transformations. Moreover, models struggle to ground programmatic information in visual observations, suggesting that visual and language representations remain weakly integrated.