| title | Self-Conditioning Enables Deep Sequential Reasoning in Flow Matching |
|---|---|
| authors | Zeyang Zhang, Linxiang Gao, Meiqi Gu, Xingyan Chen, Minrui Luo, Kaifeng Lyu, Tianxing He |
| date | 2026-10-14 |
| venue | arXiv (preprint, not peer reviewed) |
| id | arXiv:2610.19628 |
| affiliation | Shanghai Qizhi Institute |
| upvotes | 13 (Hugging Face Daily Papers, 2026-11-01) |
| links | abs pdf hf code |
| abstract | Recent work has explored visual reasoning through image generation, where models solve visual-reasoning problems by directly generating solution images. Intuitively, iterative samplers such as flow matching are well suited to this task, since each sampling step may resemble one reasoning step. However, in this work, from a circuit complexity perspective, we show that this intuition is misleading. We prove that as long as the model outputs satisfy certain mild regularity conditions, the trajectory of the vanilla flow-matching sampler can be simulated by a constant number of sequential rounds of parallel model evaluations. Consequently, additional sampling steps cannot increase the expressive power of a constant-depth backbone model under the standard complexity-theoretic model of transformers. We then reveal that self-conditioning, which conditions the model on the previous step's estimate of the final image, plays a previously unrecognized role in removing this bottleneck. Controlled experiments on diverse visual-reasoning tasks show that flow matching with self-conditioning achieves higher accuracy and greater reasoning depth than vanilla flow matching, and its performance improves with more sampling steps. Theoretically, we prove that with self-conditioning, a constant-depth backbone can achieve expressive power equivalent to that of space-bounded Turing machines. Our study suggests a design principle for future visual reasoning research: carry more information between sampling steps, so that additional steps translate into deeper reasoning. |
cite
@misc{zhang2026self,
title={Self-Conditioning Enables Deep Sequential Reasoning in Flow Matching},
author={Zeyang Zhang and Linxiang Gao and Meiqi Gu and Xingyan Chen and Minrui Luo and Kaifeng Lyu and Tianxing He},
year={2026},
eprint={2610.19628},
archivePrefix={arXiv},
url={https://arxiv.org/abs/2610.19628}
}