# Unrolled Flow Models for Reasoning

arXiv: https://arxiv.org/abs/2610.09759 · HTML: https://mlsanity.com/paper/2610.09759/

## Key facts

- No citing papers in the map yet (data through 7 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 21 of its 29 references that are in the map.
- First posted on arXiv 7 Oct 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)
- Diffusion models / [Discrete and text diffusion](https://mlsanity.com/diffusion/discrete-and-text-diffusion/)

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Hierarchical Reasoning Model](https://mlsanity.com/paper/2506.21734/) (2025)
- [Reasoning by Superposition: A Theoretical Perspective on Chain of Continuous Thought](https://mlsanity.com/paper/2505.12514/) (2025)
- [Flow Map Language Models: One-step Language Modeling via Continuous Denoising](https://mlsanity.com/paper/2602.16813/) (2026)
- [Grokking at the Edge of Numerical Stability](https://mlsanity.com/paper/2501.04697/) (2025)
- [Less is More: Recursive Reasoning with Tiny Networks](https://mlsanity.com/paper/2510.04871/) (2025)
- [Categorical Flow Maps](https://mlsanity.com/paper/2602.12233/) (2026)
- [ELF: Embedded Language Flows](https://mlsanity.com/paper/2605.10938/) (2026)
- [Fixed-Point Reasoners: Stable and Adaptive Deep Looped Transformers](https://mlsanity.com/paper/2606.18206/) (2026)
- [Generative Recursive Reasoning](https://mlsanity.com/paper/2605.19376/) (2026)
- [Probabilistic Tiny Recursive Model](https://mlsanity.com/paper/2605.19943/) (2026)
- [Language Modeling with Hyperspherical Flows](https://mlsanity.com/paper/2605.11125/) (2026)
- [Equilibrium Reasoners: Learning Attractors Enables Scalable Reasoning](https://mlsanity.com/paper/2605.21488/) (2026)
- [Universal Reasoning Model](https://mlsanity.com/paper/2512.14693/) (2025)
- [Solve the Loop: Attractor Models for Language and Reasoning](https://mlsanity.com/paper/2605.12466/) (2026)
- [Self-conditioned Flow Map Language Models via Fixed-point Flows](https://mlsanity.com/paper/2607.00714/) (2026)
- [Scaling Categorical Flow Maps](https://mlsanity.com/paper/2605.07820/) (2026)
- [Thinking with Looped Flows](https://mlsanity.com/paper/2609.11801/) (2026)
- [Flow Reasoning Models: Turning Flows Into Efficient Recurrent Reasoners](https://mlsanity.com/paper/2606.29150/) (2026)

## Abstract (arXiv)

Flow matching enables language generation in few steps, but whether additional integration steps improve reasoning remains unclear. We prove that a flow parameterized by a two-layer Transformer can solve graph reachability, with the required number of integration steps increasing with the target's distance from the root. Yet, standard flow language models can fail to benefit from additional steps on reasoning tasks. We attribute this limitation to objectives that supervise each time point independently, without explicitly training successive steps to build on one another. To address this, we instead train through the model's own latent rollout over a randomly sampled subinterval of [0, 1], decoding only at the endpoint. On ProsQA, this raises accuracy to 97% and enables performance to improve with additional integration steps. For the longer rollouts required by reasoning tasks such as Sudoku and Maze, retracting the latent state onto a sphere stabilizes the dynamics and yields substantial gains over baselines with more than three times as many parameters. Sampling multiple rollouts further improves performance when paired with a parameter-free selection score, although reliable selection remains challenging for longer answers. Together, these results establish a theoretical basis for reasoning with flows and show how rollout training, stable latent dynamics, and rollout selection help realize this capacity in practice.