# Binary Discrete Diffusion: Candidate-Set Diffusion for Logic and Planning Tasks

Authors: Rodrigo Casado Noguerales, Dimitri von Rütte, Bernhard Schölkopf, Thomas Hofmann, Aran Raoufi.

Represents each unfinished output position as a set of possible tokens. Denoising removes or restores candidates before choosing a final token, testing how this intermediate representation affects Sudoku, Boxoban, graph coloring and language modeling.

First public: 2026-10-20.
ArXiv initial submission: 2026-10-20.

[Original paper](https://arxiv.org/abs/2610.28543) · [PDF](https://arxiv.org/pdf/2610.28543) · [HTML](https://arxiv.org/html/2610.28543v1) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.28543/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.28543/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.28543/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.28543/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. Some produce written chains of thought.

Reading-list version 0.11.0; literature checked through 2026-10-26.