Visualizing Thought: Conceptual Diagrams Enable Robust Planning in LMMs

Human reasoning relies on constructing and manipulating mental models -- simplified internal representations of situations used to understand and solve problems. Conceptual diagrams (e.g., a sketch drawn to aid reasoning) externalize these mental models, abstracting irrelevant details to efficiently capture how entities interact. In contrast, Large Language Models (LLMs) and Large MultiModal Models (LMMs) predominantly reason through text, limiting their effectiveness on complex multi-step tasks. In this paper, we propose Visual Thinking, a generalizable framework that enables LMMs to reason through multiple chains of self-generated conceptual diagrams, significantly enhancing their combinatorial planning capabilities. Our approach requires no human input beyond the natural language description of the task. It integrates textual and diagrammatic reasoning within an optimized Graph-of-Thought inference framework, enhanced by beam search and depth-wise backtracking. Evaluated on multiple challenging PDDL planning domains, our method substantially improves LMM performance (e.g., GPT-4o: 35.5% -> 90.2% in Blocksworld) and consistently outperforms text-only search-based inference methods. On more difficult domains with solution depths up to 40, it also surpasses the o1-preview reasoning model (e.g., 16 percentage points improvement in Floor Tiles). These results demonstrate the power of conceptual diagrams as a reasoning medium in LMMs.