Abstract

One of the core challenges in building general reasoning systems lies in generating diverse, human-aligned solution trajectories—different yet valid paths by which a problem can be solved. Prior approaches often rely on handcrafted templates, rule-based augmentations, or human demonstrations, which are limited in scalability and stylistic diversity. To address this, we explore the use of Generative Flow Networks (GFlowNets) for automated solution augmentation in reasoning tasks. We propose a framework that learns to generate diverse reasoning trajectories with probabilities proportional to their quality, guided by a human-inspired reward function and a novel geometric forward policy. This enables the generation of multiple plausible solution paths without relying on manual supervision. Moreover, our method supports efficient test-time augmentation from input-output examples alone, without access to ground-truth programs or external demonstrations—making it suitable for zero-shot settings. We evaluate our framework on the Abstraction and Reasoning Corpus (ARC-AGI), a benchmark designed to test compositional and abstract reasoning. Our results show that GFlowNets can effectively explore the space of valid reasoning processes, producing a variety of plausible reasoning trajectories, similar to how different individuals might solve the same problem using different intermediate steps. These trajectories are generated at scale-over 100k per task in under an hour, and follow a logarithmic yield trend, enabling practical tradeoffs between augmentation volume and novelty. Furthermore, fine-tuning a large language model (LLaMA 3.1 Instruct 8B) on these synthetic trajectories leads to a 28.6% improvement in reasoning accuracy on ARC tasks, demonstrating the downstream utility of our method. These findings suggest that GFlowNets offer a promising foundation for modeling structured reasoning in automated trajectory generation. Our code is here: https://github.com/GIST-DSLab/GFN_to_ARC