# Guided Discrete Diffusion for Constraint Satisfaction Problems

arXiv: https://arxiv.org/abs/2512.14765 · HTML: https://mlsanity.com/paper/2512.14765/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 9 of its 9 references that are in the map.
- First posted on arXiv 16 Dec 2025.

## Placed in

- Diffusion models / [Discrete and text diffusion](https://mlsanity.com/diffusion/discrete-and-text-diffusion/)

## Builds on (most cited first, 9 of 9)

- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Plug and Play Language Models: A Simple Approach to Controlled Text Generation](https://mlsanity.com/paper/1912.02164/) (2019)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [Protein Design with Guided Discrete Diffusion](https://mlsanity.com/paper/2305.20009/) (2023)
- [Recurrent Relational Networks](https://mlsanity.com/paper/1711.08028/) (2017)
- [Learning to Solve Constraint Satisfaction Problems with Recurrent Transformer](https://mlsanity.com/paper/2307.04895/) (2023)

## Built on by (most cited first, 1 of 1)

- [Constraints Are Graphs, Not Chains: Exact Decoding for Diffusion Language Models](https://mlsanity.com/paper/2609.32900/) (2026)

## Abstract (arXiv)

We propose discrete diffusion guidance for constraint satisfaction problems (CSPs) and demonstrate its ability to solve Sudoku puzzles without supervision.