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

arXiv · AI, language, vision and robotics · article · Sep 8, 2026 · UTC

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

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