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Let It Go or Learn to Self-Correct: Continuous Diffusion for Constrained Discrete Tasks

ArXiv|Tuesday, September 8, 2026|about 12 hours ago|Mariia Drozdova

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Why It Matters

Denoising Diffusion Probabilistic Models (DDPMs) generate samples by starting from noise and repeatedly denoising while keeping each update close to the current noisy state.

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Key Claims

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.

Original description

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 dire...

arxiv cs.LG cs.AI publisher:arxiv tier:research

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Publisher: arxiv.org

ID: http://arxiv.org/abs/2609.09009v1 · Indexed about 1 hour ago