# ELF-REG: Scaling Continuous Diffusion Language Models to Reasoning Tasks

Authors: Zeyu Michael Li, William Xingxu Chen, Bingshuo Qian, Jiayin Liu, Xiang Cheng.

Adapts continuous diffusion to mathematics and code using intermediate-feature supervision and a global representation from a frozen autoregressive teacher. It denoises continuous response representations and decodes all response tokens only at the end.

First public: 2026-09-24.
ArXiv initial submission: 2026-09-24.

[Original paper](https://arxiv.org/abs/2609.29102) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.29102/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.29102/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.29102/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.29102/record.json)

## Approaches

- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [Alternative generation methods](https://latent-implicit-thinking.github.io/topics/alternative-reasoning-schedules/): Change how intermediate steps are generated, revised, or searched—for example, by refining several steps in parallel. These are related approaches: some still produce written chains of thought.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.5; literature checked through 2026-10-18.