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Constraints-Guided Diffusion Reasoner for Neuro-Symbolic Learning

AAAI 2026 · Large language models › Reasoning and chain of thought · approach: Test-time compute scaling · 0 citations (OpenAlex)

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Proposes DDReasoner, a masked DDPM for symbolic puzzles, fine-tuned with a group-based PPO-style RL using a rule-based constraint-consistency reward to improve logical consistency on Sudoku, Maze, path prediction, preference learning, and min-cost path tasks.

Problem

Neural networks struggle to satisfy hard logical constraints in symbolic reasoning tasks; supervised losses can accept outputs that violate constraints with small errors.

Approach

Formulates the masked denoising process of a diffusion model as an MDP and fine-tunes it with a PPO-style clipped objective and group-based dynamic sampling, using a binary reward for logical consistency of the final discretized solution.

Key results

• Sudoku minimal_17 exact accuracy rises from 8.03% (SL) to 18.25% (RL), and big kaggle from 78.19% to 97.79%.
• Maze: DDReasoner-RL reaches 100% on 5x5 through 20x20 mazes versus 43.30% for SL at 20x20.
• Min-cost path finding (k=30) shortest-path rate improves from 70.60% (SL) to 80.10% (RL).

Surprising findings

• Baseline SolverNN gets 0% on minimal_17 Sudoku, which the SL-only diffusion model partially solves.
• Continuing supervised learning on the SL checkpoint overfits and yields no improvement on simple path prediction.

Limitations

• Failure cases are hard to interpret across multi-step denoising.
• RL may be ineffective when SL cannot learn complex constraint relations.
• Evaluated mainly on problems with unique or few deterministic solutions.

Experimental setup

Datasets: big kaggle Sudoku minimal 17 Sudoku multiple solutions Sudoku satnet Sudoku generated Maze datasets (DFS) simple path prediction (NASR benchmark) sushi preference learning min-cost path finding datasets

Benchmarks: Sudoku (big kaggle, minimal 17, multiple sol, satnet) Maze 5x5-20x20 simple path prediction preference learning minimum-cost path finding

Metrics: exact match accuracy hamming accuracy consistency rate shortest path percentage

Baselines: SolverNN (NASR) RNN+PseudoSL MLM-U based Transformer DDReasoner-SL

Builds on: DDPM PPO GRPO DDPO

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