DiBS: Diffusion-Informed Branch Selection

2026-06-02

AI Summary

This work addresses the limitations of learning-based approaches, which often lack correctness guarantees, and symbolic methods, which suffer from inefficient search on long-tail instances. It proposes the first integration of diffusion models into branch selection for constraint satisfaction problems, embedding them within a complete symbolic solver. The approach leverages the current partial assignment together with lightweight consistency signals to rank candidate values. By doing so, it significantly enhances search efficiency while preserving solution correctness and providing theoretical validity guarantees. Experimental results demonstrate substantial reductions in the number of search nodes, backtracking steps, and solving overhead on long-tail instances, particularly on the Royle 17-clue benchmark.

Abstract

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.

Problem

• Sudoku
• constraint satisfaction problem
• symbolic solver
• learning-based solver
• long-tail search

Innovation

• diffusion model
• branch selection
• constraint satisfaction
• symbolic solver
• global guidance