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Life sciences · Preprint
arXiv · September 8, 2026
Early or partial results. Treat as a signal, not a conclusion.
This preprint proposes two modifications to diffusion model sampling for discrete constraint satisfaction: using direct clean predictions instead of iterative denoising, and self-correction training to reduce inference-time errors. The approach improves Sudoku validity substantially and shows consistent gains on related combinatorial tasks, but the work is unrefereed and does not address scalability, generalization to unseen constraints, or real-world applicability.
Preprint. Denoising Diffusion Probabilistic Models evaluated on globally constrained discrete tasks: Sudoku, graph connectivity, Latin squares, and N-queens problems.. Intervention: Direct sampling from model clean predictions (without retraining); self-correction training exposing the model to its own predictions.. Compared with: Standard diffusion sampling (iterative denoising while staying close to current noisy state)..
Standard diffusion sampling achieved 31% Sudoku validity; direct clean prediction sampling improved this to 95% Self-correction training substantially improved performance of standard samplers on discrete tasks Consistent improvements observed across Sudoku, graph connectivity, Latin squares, and N-queens without task-specific retraining
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This is a preprint presenting an algorithmic improvement to diffusion models on discrete constraint satisfaction tasks, supported by empirical results but lacking peer review and clinical or validated-domain applicability.
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Denoising Diffusion Probabilistic Models (DDPMs) generate samples by starting from noise and repeatedly denoising while keeping each update close to the current noisy state. This behavior is effective in many continuous domains, but its role is less clear for globally constrained discrete tasks, such as Sudoku, graph connectivity, Latin squares, and N-queens. In such settings, early discrete errors can be difficult to undo. As a result, standard diffusion sampling may preserve early mistakes, even when the model's clean predictions are informative. We compare standard samplers to sampling directly from the model's clean prediction. Without retraining, this single change improves Sudoku validity from 31% to 95%, with consistent gains across the other discrete tasks. We hypothesize that staying close to the current noisy state is harmful because the reverse trajectory can drift off the forward noising distribution the model was trained on. To reduce this train-test mismatch, we further introduce self-correction training, which exposes the model to its own predictions, improving robustness to errors that arise during inference. This substantially improves the performance of standard samplers. Our results suggest that continuous diffusion models can learn nontrivial global constraints, but discrete reasoning tasks require better alignment between training and inference: either through samplers that reduce commitment to early decisions, or through training that teaches the model to correct its own inference-time errors.
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