# Alternative generation methods

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.

Papers are ordered by first public date. Read the original sources before using a claim.

For example: A diffusion model refines representations of a solution over several rounds, rather than committing to each word in left-to-right order. The final reasoning can still be readable text.

Version 0.9.5; literature checked through 2026-10-18.

[Topic guide](https://latent-implicit-thinking.github.io/topics/alternative-reasoning-schedules/) · [JSON](https://latent-implicit-thinking.github.io/data/topics/alternative-reasoning-schedules.json)

## How the methods connect and differ

**Changing generation order or removing written steps**

Diffusion of Thought changes how a chain of thought is generated: it refines the solution through denoising rather than committing to words strictly from left to right. This changes the generation schedule, not necessarily the visibility of the reasoning. The resulting chain can still be text, unlike methods that only emit the final answer.

Sources: [Diffusion of Thought](https://proceedings.neurips.cc/paper_files/paper/2024/hash/be30024e7fa2c29cac7a6dafcbb8571f-Abstract-Conference.html) · [Deng et al. (2024), §3](https://arxiv.org/html/2405.14838v1#S3)

Paper details: [Diffusion of Thoughts: Chain-of-Thought Reasoning in Diffusion Language Models](https://latent-implicit-thinking.github.io/papers/2402.07754/) · [From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step](https://latent-implicit-thinking.github.io/papers/2405.14838/)

## Papers — oldest first

## Diffusion of Thoughts: Chain-of-Thought Reasoning in Diffusion Language Models

Authors: Jiacheng Ye, Shansan Gong, Liheng Chen, Lin Zheng, Jiahui Gao, Han Shi, Chuan Wu, Xin Jiang, Zhenguo Li, Wei Bi, Lingpeng Kong.

Refines intermediate reasoning representations over several rounds of denoising. A multi-pass version can revisit earlier parts of the reasoning as it refines the solution.

First public: 2024-02-12.
ArXiv initial submission: 2024-02-12.

[Original paper](https://arxiv.org/abs/2402.07754) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2402.07754/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2402.07754/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2402.07754/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2402.07754/record.json)

### Method comparisons

**Changing generation order or removing written steps**

Diffusion of Thought changes how a chain of thought is generated: it refines the solution through denoising rather than committing to words strictly from left to right. This changes the generation schedule, not necessarily the visibility of the reasoning. The resulting chain can still be text, unlike methods that only emit the final answer.

Sources: [Diffusion of Thought](https://proceedings.neurips.cc/paper_files/paper/2024/hash/be30024e7fa2c29cac7a6dafcbb8571f-Abstract-Conference.html) · [Deng et al. (2024), §3](https://arxiv.org/html/2405.14838v1#S3)

Paper details: [Diffusion of Thoughts: Chain-of-Thought Reasoning in Diffusion Language Models](https://latent-implicit-thinking.github.io/papers/2402.07754/) · [From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step](https://latent-implicit-thinking.github.io/papers/2405.14838/)


### Published version

Diffusion of Thought: Chain-of-Thought Reasoning in Diffusion Language Models. Jiacheng Ye, Shansan Gong, Liheng Chen, Lin Zheng, Jiahui Gao, Han Shi, Chuan Wu, Xin Jiang, Zhenguo Li, Wei Bi, Lingpeng Kong. Advances in Neural Information Processing Systems, 2024.
[Publication](https://proceedings.neurips.cc/paper_files/paper/2024/hash/be30024e7fa2c29cac7a6dafcbb8571f-Abstract-Conference.html) · [BibTeX](https://latent-implicit-thinking.github.io/papers/2402.07754/publication.bib) · [CSL-JSON](https://latent-implicit-thinking.github.io/papers/2402.07754/publication.csl.json)
Metadata checked 2026-10-18 against [the publication record](https://proceedings.neurips.cc/paper_files/paper/2024/hash/be30024e7fa2c29cac7a6dafcbb8571f-Abstract-Conference.html).

### Approaches

- [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.


## Multimodal Latent Language Modeling with Next-Token Diffusion

Authors: Yutao Sun, Hangbo Bao, Wenhui Wang, Zhiliang Peng, Li Dong, Shaohan Huang, Jianyong Wang, Furu Wei.

Encodes continuous data such as images as vectors, then generates those vectors with diffusion inside a causal transformer. This is related work on multimodal generation, rather than a method trained directly on reasoning steps.

First public: 2024-12-11.
ArXiv initial submission: 2024-12-11.

[Original paper](https://arxiv.org/abs/2412.08635) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2412.08635/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2412.08635/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2412.08635/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2412.08635/record.json)

### Approaches

- [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.


## Text Generation Beyond Discrete Token Sampling

Authors: Yufan Zhuang, Liyuan Liu, Chandan Singh, Jingbo Shang, Jianfeng Gao.

Feeds posterior expectations back into a language model so intermediate generation can remain continuous instead of sampling discrete tokens.

First public: 2025-05-20.
ArXiv initial submission: 2025-05-20.

[Original paper](https://arxiv.org/abs/2505.14827) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2505.14827/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2505.14827/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2505.14827/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2505.14827/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.


## Parallel Continuous Chain-of-Thought with Jacobi Iteration

Authors: Haoyi Wu, Zhihao Teng, Kewei Tu.

Applies Jacobi-style iteration to update continuous reasoning states in parallel rather than strictly one step at a time.

First public: 2025-06-23.
ArXiv initial submission: 2025-06-23.

[Original paper](https://arxiv.org/abs/2506.18582) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2506.18582/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2506.18582/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2506.18582/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2506.18582/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.


## LaDiR: Latent Diffusion Enhances LLMs for Text Reasoning

Authors: Haoqiang Kang, Yizhe Zhang, Nikki Lijing Kuang, Nicklas Majamaki, Navdeep Jaitly, Yi-An Ma, Lianhui Qin.

Uses a variational autoencoder to compress textual reasoning steps into blocks of continuous states. A diffusion model repeatedly revises each block before generating the next, then produces a textual answer; diversity guidance encourages alternative reasoning trajectories.

First public: 2025-10-06.
ArXiv initial submission: 2025-10-06.

[Original paper](https://arxiv.org/abs/2510.04573) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2510.04573/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2510.04573/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2510.04573/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2510.04573/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.


## Diffusion as a Training Curriculum for Timestep-Free Iterative Reasoning

Authors: Mariia Drozdova, Aidan Sirbu, Pietro Miotti, Robert Obryk, Mayalen Etcheverry, Eyvind Niklasson, Blake Richards.

Turns a diffusion denoiser into a recurrent puzzle solver by adding a persistent hidden state and removing timestep conditioning. Separates the role of denoising during training from the role of repeated updates and noise at inference.

First public: 2026-09-01.
ArXiv initial submission: 2026-09-01.

[Original paper](https://arxiv.org/abs/2609.01449) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.01449/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.01449/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.01449/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.01449/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): Repeat parts of the model or keep intermediate information in memory while working through a problem. Some methods also learn how many passes to run.
- [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.


## Almost Free State Prediction Separation

Authors: John Langford, Nathan Godey, Giovanni Monea, Yoav Artzi, Harry Dong, Ying Fan, Gustavo de Rosa, Zheng Zhan.

Moves pause-token computation into a parallel, weight-shared prediction stream, providing additional internal compute without increasing generated sequence length or key/value-cache length.

First public: 2026-09-03.
ArXiv initial submission: 2026-09-03.

[Original paper](https://arxiv.org/abs/2609.03807) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.03807/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.03807/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.03807/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.03807/record.json)

### Approaches

- [Thinking tokens](https://latent-implicit-thinking.github.io/topics/thinking-tokens/): Give a model extra tokens for computation, such as pauses, filler symbols, or learned planning tokens. These tokens need not spell out the solution.
- [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.


## CanvasAnneal: Curriculum Reinforcement Learning for Diffusion Language Models

Authors: Blake Olson, Yuhang Song, Emmett McQuinn, Yuan Shangguan.

Starts diffusion-model reinforcement learning with teacher-written reasoning partially filled into the output, then gradually removes that guidance. Tests whether this curriculum improves exploration on mathematics and tool-use tasks; inference still produces textual reasoning.

First public: 2026-09-11.
ArXiv initial submission: 2026-09-11.

[Original paper](https://arxiv.org/abs/2609.13060) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.13060/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.13060/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.13060/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.13060/record.json)

### Approaches

- [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.


## Register Tokens for Bounded-State Reasoning in Diffusion Language Models

Authors: Albert Ge, Chandan Singh, Yufan Zhuang, Xiaodong Liu, Jianfeng Gao, Frederic Sala.

Trains a diffusion language model to carry a fixed number of continuous register states between generated chunks. The model still writes text within each chunk, but clears earlier text and continues from the prompt and retained registers.

First public: 2026-09-14.
ArXiv initial submission: 2026-09-14.

[Original paper](https://arxiv.org/abs/2609.16372) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.16372/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.16372/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.16372/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.16372/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.


## LoopSpec: Pipelined Self-Speculative Decoding for Looped Transformers

Authors: SangLyul Cho, Langqing Cui, Sehoon Kim, Dongsu Han, Insu Han.

Drafts future tokens from early loops while later loops verify current tokens, overlapping the work without training an extra model. Final verification preserves the full model's decoding behavior.

First public: 2026-09-15.
ArXiv initial submission: 2026-09-15.

[Original paper](https://arxiv.org/abs/2609.17184) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.17184/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.17184/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.17184/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.17184/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): Repeat parts of the model or keep intermediate information in memory while working through a problem. Some methods also learn how many passes to run.
- [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.


## Uni-LaDiR: Latent Diffusion Unifies Multimodal Reasoning

Authors: Haoqiang Kang, Yizhe Zhang, Nikki Lijing Kuang, Jiatao Gu, Yian Ma, Lianhui Qin.

Encodes teacher reasoning steps from text, images, point clouds, and robot states into a shared continuous representation. A jointly trained diffusion reasoner generates these states at inference, evaluated on visual question answering and robotic manipulation.

First public: 2026-09-17.
ArXiv initial submission: 2026-09-17.

[Original paper](https://arxiv.org/abs/2609.19878) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.19878/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.19878/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.19878/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.19878/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.


## CaLR: Causal Latent Revision for Robust Diffusion Reasoning

Authors: Wei Cai, Jian Zhao, Yuchen Yuan, Xuelong Li.

Uses an expert-derived causal dependency matrix to guide gradient-based revision of diffusion reasoning states. The aim is to preserve logical dependencies while revising several intermediate positions during parallel generation.

First public: 2026-09-17.
ArXiv initial submission: 2026-09-17.

[Original paper](https://arxiv.org/abs/2609.20981) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.20981/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.20981/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.20981/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.20981/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.


## WaveFront Decoding: Parallelized Self-Speculative Decoding for Looped Language Models

Authors: Hyeongju Ha, Jae-Joon Kim.

Uses intermediate loop depths to propose tokens that later loops verify. Arranges speculation across recurrent depths so that more of the draft and verification work can run together.

First public: 2026-09-19.
ArXiv initial submission: 2026-09-19.

[Original paper](https://arxiv.org/abs/2609.23033) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.23033/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.23033/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.23033/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.23033/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): Repeat parts of the model or keep intermediate information in memory while working through a problem. Some methods also learn how many passes to run.
- [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.


## LADDER: Graph-Guided Diffusion Language Models for Efficient Multi-Hop Reasoning

Authors: Senlei Zhang, Linhao Luo, Qian-Wen Zhang, Siyu An, Junnan Dong, Shuhao Zhang, Xing Sun.

Triggers graph retrieval when new entities become identifiable in a partially denoised draft, then uses graph propagation to provide multi-hop evidence for subsequent updates. This combines retrieval with parallel textual reasoning rather than removing the text trace.

First public: 2026-09-21.
ArXiv initial submission: 2026-09-21.

[Original paper](https://arxiv.org/abs/2609.24346) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.24346/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.24346/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.24346/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.24346/record.json)

### Approaches

- [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.


## LOCKR: A Hidden-State Trajectory-Guided Planner for Detecting and Repairing Stable-but-Wrong Lock-In in Diffusion Language Models

Authors: Guoshenghui Zhao, Tan Yu, Weijie Zhao.

Uses the history of diffusion hidden states to detect answers that become stable but remain wrong. A planner selects targeted repair branches and verifies continuations, testing whether these internal trajectories support better repair decisions than confidence or a single snapshot.

First public: 2026-09-23.
ArXiv initial submission: 2026-09-23.

[Original paper](https://arxiv.org/abs/2609.27220) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.27220/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.27220/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.27220/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.27220/record.json)

### Approaches

- [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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

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.


## Towards Efficient Reasoning: Learning Causal Shortcuts for Diffusion Language Models

Authors: Dian Jin, Kairong Han, Baohong Li, Xinpeng Dong, Zijing Hu, Nuanqiao Shan, Fei Wu, Kun Kuang.

Extracts reasoning-guiding token chains and prioritizes them during diffusion-model training to improve denoising speed and accuracy. This is a related text-generating approach, not reasoning without a written trace.

First public: 2026-09-23.
ArXiv initial submission: 2026-09-23.

[Original paper](https://arxiv.org/abs/2609.28272) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.28272/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.28272/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.28272/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.28272/record.json)

### Approaches

- [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.


## 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.


## Next Thoughts Are Distributions: Generative Autoregressive Reasoning in the Latent Space

Authors: Yang Li, Yi Wang, Shiyuan Huang, Yang Liu, Hao Wang, Chengzhi Mao.

Adds a diffusion head that samples the next continuous thought from a distribution rather than predicting one fixed vector. Feeds each sampled thought back into an autoregressive reasoner, supporting variable-length latent traces and multiple reasoning paths.

First public: 2026-09-27.
ArXiv initial submission: 2026-09-27.

[Original paper](https://arxiv.org/abs/2609.33271) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.33271/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.33271/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.33271/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.33271/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.


## Shallow Queries, Mature Values: Depth-Asynchronous Self-Speculation for Looped Transformers

Authors: Guanghao Li, Zihan Su, Hao Yu, Jinyang Jiang, Tao Ren, Zehao Li, Feng Lu, Ming Tang, Chun Yuan.

Uses shallower-loop queries with values from deeper loops to improve draft-token predictions in a looped language model. Studies the different rates at which queries, keys, and values develop, and uses that difference for self-speculative decoding.

First public: 2026-09-28.
ArXiv initial submission: 2026-09-28.

[Original paper](https://arxiv.org/abs/2609.34538) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.34538/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.34538/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.34538/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.34538/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): Repeat parts of the model or keep intermediate information in memory while working through a problem. Some methods also learn how many passes to run.
- [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.


## Why Deterministic PRM Guidance Underperforms in Discrete Diffusion Reasoning

Authors: Yan Zhan, Shaobo Liu, Zhijun Gao.

Compares process-reward guidance with independent sampling and final-answer reranking at matched forward-pass budgets. In the tested diffusion models, early pruning removes promising candidates and intermediate-state scorers can be poor final judges; the generated solutions remain textual.

First public: 2026-09-28.
ArXiv initial submission: 2026-09-28.

[Original paper](https://arxiv.org/abs/2609.35472) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.35472/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.35472/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.35472/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.35472/record.json)

### Approaches

- [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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

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.


## Reasoning with Continuous Latent Diffusion

Authors: Xiang Cheng.

CEDR learns compact representations from several teacher layers, denoises them at different rates, and trains a smaller prompt encoder to replace the teacher at inference. It generates complete mathematical and coding solutions through continuous refinement before text decoding.

First public: 2026-09-28.
ArXiv initial submission: 2026-09-28.

[Original paper](https://arxiv.org/abs/2609.35694) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.35694/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.35694/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.35694/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.35694/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.


## CoDR: Training-Free Confidence-Drift Remasking for Diffusion Language Models

Authors: Yue Wu, Qinghe Zhang, Yu Zhang, Jian Huang.

Checks whether tokens committed earlier in diffusion decoding become less plausible as context fills in. CoDR remasks and regenerates those positions, testing targeted revision against extra-compute controls on reasoning and code tasks.

First public: 2026-09-28.
ArXiv initial submission: 2026-09-28.

[Original paper](https://arxiv.org/abs/2610.08833) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.08833/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.08833/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.08833/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.08833/record.json)

### Approaches

- [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.


## Reliable Parallel Decoding in Masked Diffusion Language Models

Authors: Zhenghao He, Bohan Liu, Guangzhi Xiong, Aidong Zhang.

Studies when simultaneously committing several predicted tokens breaks their reasoning dependencies. RPD combines stability across final layers with confidence and uncertainty in preceding positions to defer unsupported predictions while retaining parallel text generation.

First public: 2026-09-29.
ArXiv initial submission: 2026-09-29.

[Original paper](https://arxiv.org/abs/2609.36452) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.36452/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.36452/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.36452/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.36452/record.json)

### Approaches

- [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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

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.


## Blackboard Intelligence Can Surpass Autoregressive on Globally Constrained Problems

Authors: Woosang Jeon, Jaeyeon Kim, Sham Kakade, Yilun Du, Amrit Singh Bedi, Arun Kumar Chithanar, Chul Lee, Taehyeong Kim, Sitan Chen.

Uses a fixed, revisable output and model confidence to search over candidate solutions with a frozen fine-tuned diffusion checkpoint. Evaluates logic and scheduling problems where global constraints can make irrevocable left-to-right commitments costly.

First public: 2026-09-30.
ArXiv initial submission: 2026-09-30.

[Original paper](https://arxiv.org/abs/2609.38806) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.38806/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.38806/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.38806/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.38806/record.json)

### Approaches

- [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.


## Exploring More, Reasoning Better: Stepwise Risk-Sensitive GRPO for Diffusion Language Models

Authors: Yue Yu, Bowen Zuo, David Crandall, Yinglun Zhu, Dongruo Zhou.

Changes how outcome rewards weight decisions at different denoising states during diffusion-model reinforcement learning. Derives the effect for binary rewards and uses matched-scale controls to test whether the schedule improves mathematical accuracy and reasoning-trace diversity.

First public: 2026-09-30.
ArXiv initial submission: 2026-09-30.

[Original paper](https://arxiv.org/abs/2610.00661) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.00661/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.00661/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.00661/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.00661/record.json)

### Approaches

- [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.


## Temporally-Resolved Token Attribution Reveals the Generation Dynamics of Diffusion Language Models

Authors: Darpan Aswal, Céline Hudelot.

Extends integrated-gradient attribution across layers and denoising steps to examine which inputs influence a diffusion model's developing response. Includes multi-hop graph reasoning; the authors present attribution as a complement to, not a replacement for, causal intervention.

First public: 2026-10-01.
ArXiv initial submission: 2026-10-01.

[Original paper](https://arxiv.org/abs/2610.01177) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.01177/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.01177/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.01177/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.01177/record.json)

### Approaches

- [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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

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.


## Hierarchical Continuous Diffusion Language Models

Authors: Hui Ren, Zihan Li, Chang Liu, Huidong Liu, Alexander Schwing.

Keeps a continuous state throughout denoising while reading out tokens at each step and feeding them back into the next state update. Tests whether this coupling preserves dependencies during parallel generation on Sudoku, Countdown, and language modeling.

First public: 2026-10-01.
ArXiv initial submission: 2026-10-01.

[Original paper](https://arxiv.org/abs/2610.02193) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.02193/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.02193/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.02193/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.02193/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.


## Large Language Continuous Diffusion Models

Authors: Zhihan Yang, Wei Guo, Jean-Marie Lemercier, Simon Welker, Yonggan Fu, Mohammad Mahdi Kamani, Sajad Norouzi, Julius Berner, Tomas Geffner, Karsten Kreis, Yongxin Chen, Molei Tao, John Thickstun, Pavlo Molchanov, Ante Jukić, Arash Vahdat, Morteza Mardani.

Sigma denoises learned continuous token embeddings in blocks, starting from autoregressive pretrained weights. Studies how guidance and temperature affect mathematical reasoning, coding, output diversity, and performance when fewer refinement steps are used.

First public: 2026-10-02.
ArXiv initial submission: 2026-10-02.

[Original paper](https://arxiv.org/abs/2610.02665) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.02665/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.02665/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.02665/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.02665/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.


## Pivot-SD: Efficient Self-Distillation for Masked Diffusion Language Models

Authors: Seo Hyun Kim, Sunwoo Hong, Younwoo Choi, Chen-Hao Chao, Se-Young Yun, Rahul G. Krishnan.

Selects token commitments that most reduce uncertainty over the remaining output. Self-distillation reinforces these pivots from successful diffusion trajectories and discourages selected pivots from failed ones, rather than supervising every token equally.

First public: 2026-10-02.
ArXiv initial submission: 2026-10-02.

[Original paper](https://arxiv.org/abs/2610.03665) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.03665/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.03665/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.03665/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.03665/record.json)

### Approaches

- [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.


## What Matters for Latent Reasoning with Flow Matching

Authors: Yassine Ouali, Adrian Bulat, Georgios Tzimiropoulos.

Compresses symbolic reasoning into latent codes and trains a flow model to refine a block of noise into a thought before decoding the answer. Studies training choices, self-training on verified thoughts, and tests of whether the answer actually uses those thoughts.

First public: 2026-10-05.
ArXiv initial submission: 2026-10-05.

[Original paper](https://arxiv.org/abs/2610.06666) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.06666/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.06666/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.06666/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.06666/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.


## Noise Your Prompt: Noising Conditioning Tokens in Continuous Diffusion Language Models

Authors: Justin Jung.

Adds noise to conditioning tokens during training instead of keeping the prompt clean. Tests improvements in Sudoku and N-Queens generalization and solution diversity, while reporting that the gains do not transfer to every language-generation task.

First public: 2026-10-06.
ArXiv initial submission: 2026-10-06.

[Original paper](https://arxiv.org/abs/2610.09145) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.09145/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.09145/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.09145/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.09145/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.


## Efficient Reasoning with Flow Language Models

Authors: Hanru Bai, Faissal Izermine, Oscar Davis, T. Konstantin Rusch.

Compares continuous flow and discrete diffusion models at matched sizes and denoising steps. A theoretical account and intermediate-state interventions examine whether retaining information about several candidates helps solve mazes and Sudoku before final discretization.

First public: 2026-10-07.
ArXiv initial submission: 2026-10-07.

[Original paper](https://arxiv.org/abs/2610.09416) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.09416/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.09416/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.09416/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.09416/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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

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.


## Think Before You Paint: Recursive Latent Reasoning for Diffusion Models

Authors: Paweł Skierś, Małgorzata Grzanka, Wojciech Masarczyk, Jan-Willem van de Meent, Kamil Deja.

PaTh uses a small recursive network to refine learned image-state tokens inside each denoising step and steer a frozen diffusion model through adapters. It learns visual puzzles from reconstruction targets without symbolic solutions or an external verifier.

First public: 2026-10-07.
ArXiv initial submission: 2026-10-07.

[Original paper](https://arxiv.org/abs/2610.09876) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.09876/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.09876/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.09876/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.09876/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.
- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): Repeat parts of the model or keep intermediate information in memory while working through a problem. Some methods also learn how many passes to run.
- [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.


## Masked Diffusion Language Agents for Tool-Integrated Chemical Reasoning

Authors: Mengdi Liu, Chenghao Jia, Hong Chang, Shiguang Shan.

ChemDiffAgent denoises interleaved textual reasoning and tool-use trajectories, letting tool decisions depend on context across the trajectory. A chemistry benchmark and matched-budget comparisons test this alternative to left-to-right agent generation.

First public: 2026-10-09.
ArXiv initial submission: 2026-10-09.

[Original paper](https://arxiv.org/abs/2610.13330) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.13330/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.13330/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.13330/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.13330/record.json)

### Approaches

- [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.


## Anchors Enhance Controllability and Reasoning of Diffusion Language Models

Authors: Feiyu Qu, Zheng Huang, Andrea Zanette.

Trains an anchor generator to choose a short text fragment and its position in a frozen diffusion model's output. These visible control tokens guide subsequent denoising, with rewards for correct answers and satisfied constraints.

First public: 2026-10-10.
ArXiv initial submission: 2026-10-10.

[Original paper](https://arxiv.org/abs/2610.15097) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.15097/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.15097/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.15097/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.15097/record.json)

### Approaches

- [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.


## Backpropagating Verifier Rewards Through Continuous Flow Language Models

Authors: Xu Han, Jiajing Hu, Li-Ping Liu.

Trains a critic to score intermediate continuous token representations, enabling reward gradients through the denoising trajectory before final discrete decoding. Evaluates this post-training approach on four reasoning tasks.

First public: 2026-10-13.
ArXiv initial submission: 2026-10-13.

[Original paper](https://arxiv.org/abs/2610.19080) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.19080/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.19080/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.19080/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.19080/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.


## ForkGRPO: Efficient Exploration and Fine-Grained Credit Assignment for Diffusion Language Models

Authors: Zhaoyan Jia, Chengwei Zhou, Gourav Datta, Massoud Pedram.

Branches rollouts from uncertain intermediate states and reuses their shared textual prefixes. Local outcome comparisons assign credit to reasoning segments, testing whether more targeted exploration improves diffusion-model reasoning with fewer generated training tokens.

First public: 2026-10-14.
ArXiv initial submission: 2026-10-14.

[Original paper](https://arxiv.org/abs/2610.19408) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.19408/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.19408/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.19408/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.19408/record.json)

### Approaches

- [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.


## Rationale Distribution Distillation via Flow Matching for Distributional Continuous Latent Reasoning

Authors: Mingyeong Kim, Gyusang Cho, Juho Lee, Giung Nam.

Distills multiple written reasoning paths for each question into a flow model over fixed-length latent sequences, including mixtures of complete rationales. Generates all latent slots together, then uses a frozen language model to decode answers from sampled rationale contexts.

First public: 2026-10-14.
ArXiv initial submission: 2026-10-14.

[Original paper](https://arxiv.org/abs/2610.19871) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.19871/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.19871/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.19871/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.19871/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.


## LoopAhead: Speculating Ahead for Faster Decoding in Looped Language Models

Authors: Zixuan Liu, Nan Xue, Rui Bao, Yuhang Xu, Xiaofeng Cao, Jiangchao Yao, Zhiyong Chen.

Trains a small drafter to predict several future tokens from early-loop hidden states. Later loops decide which speculative branches to continue, and full-depth verification determines the final output.

First public: 2026-10-15.
ArXiv initial submission: 2026-10-15.

[Original paper](https://arxiv.org/abs/2610.21594) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.21594/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.21594/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.21594/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.21594/record.json)

### Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): Repeat parts of the model or keep intermediate information in memory while working through a problem. Some methods also learn how many passes to run.
- [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.