# DiBS: Diffusion-Informed Branch Selection

arXiv: https://arxiv.org/abs/2606.06518 · HTML: https://mlsanity.com/paper/2606.06518/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 15 of its 41 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Placed in

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

## Builds on (most cited first, 15 of 15)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Mastering Diverse Domains through World Models](https://mlsanity.com/paper/2301.04104/) (2023)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [Train for the Worst, Plan for the Best: Understanding Token Ordering in Masked Diffusions](https://mlsanity.com/paper/2502.06768/) (2025)
- [Beyond Autoregression: Discrete Diffusion for Complex Reasoning and Planning](https://mlsanity.com/paper/2410.14157/) (2024)
- [Recurrent Relational Networks](https://mlsanity.com/paper/1711.08028/) (2017)
- [Learning to branch with Tree MDPs](https://mlsanity.com/paper/2205.11107/) (2022)
- [Masked Diffusion Models are Secretly Learned-Order Autoregressive Models](https://mlsanity.com/paper/2511.19152/) (2025)

## Abstract (arXiv)

Sudoku is a representative constraint satisfaction problem that requires global structural reasoning under strict discrete constraints. The existing works of solving Sudoku mainly focus on two dominant approaches, i.e., traditional heuristic and deep learning solver. However, they suffer from two complementary limitations: learning-based solvers lack hard correctness guarantees, while complete symbolic solvers are still prone to long-tail search. To address these shortcomings, we propose a novel diffusion model-guided approach, termed as DiBS, for the branch selection search process. Specifically, DiBS keeps the symbolic solver complete and uses the diffusion model as a branch-ordering guide. The core method is ranking candidate values under the current partial assignment and lightweight consistency signal. Furthermore, we provide an in-depth theoretical proof to reveal how it works and why it works. Experiments on the challenging Royle 17-clue Sudoku benchmark show that our DiBS substantially reduces search cost relative to strong heuristic baselines, especially in nodes, backtracks, and long-tail percentiles. Besides, these results confirm that learned global guidance is effective on hard instances where branch-order mistakes are most expensive. All codes are available at https://github.com/shanxierdan/DiBS.