# Flow-of-Thought: A Framework for Visual Reasoning

arXiv: https://arxiv.org/abs/2610.09746 · HTML: https://mlsanity.com/paper/2610.09746/

## Key facts

- No citing papers in the map yet (data through 7 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 9 of its 20 references that are in the map.
- First posted on arXiv 7 Oct 2026.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)

## Builds on (most cited first, 9 of 9)

- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [On the Measure of Intelligence](https://mlsanity.com/paper/1911.01547/) (2019)
- [VSP: Assessing the dual challenges of perception and reasoning in spatial planning tasks for VLMs](https://mlsanity.com/paper/2407.01863/) (2024)
- [Latent Sketchpad: Sketching Visual Thoughts to Elicit Multimodal Reasoning in MLLMs](https://mlsanity.com/paper/2510.24514/) (2025)
- [Self-Supervised Visual Preference Alignment](https://mlsanity.com/paper/2404.10501/) (2024)
- [Chain-of-Sketch: Enabling Global Visual Reasoning](https://mlsanity.com/paper/2410.08165/) (2024)
- [TopoBench: Benchmarking LLMs on Hard Topological Reasoning](https://mlsanity.com/paper/2603.12133/) (2026)

## Abstract (arXiv)

Mental imagery, ``seeing with the mind's eye'' is an essential aspect of human cognition. Despite rapid progress Large Language Models (LLMs) and Vision Transformers (ViTs) still underperform on tasks requiring spatial understanding. To address this, we introduce Flow-of-Thought (FoT), a framework that integrates the generation of visual sketches as intermediate reasoning steps, mimicking mental imagery in humans. We train coordinate-aware trajectory flow fields on SO(2) group orbits and cumulative shortest paths, then freeze the learned dynamics; same vs. different decisions compare competing generative hypotheses using foreground-weighted reconstruction energy. On locked tests FoT reaches 100.0% accuracy on Tetris and 99.0% on colored shapes. Under frozen transfer, the orbit-trained 2D flow improves over its endpoint-only control on BLINK Multi-view (72.2% vs. 63.9% on 133 public validation pairs), supporting continuous visual traces as an effective and interpretable representation for spatial reasoning in some out-of-distribution settings.