One-step lowest-variance selection in a Gaussian random-field model motivated by masked diffusion: Total correlation and a square root collision threshold

• URL: http://arxiv.org/abs/2607.17522v1
• Date: Mon, 20 Jul 2026 03:56:34 GMT
• Title: One-step lowest-variance selection in a Gaussian random-field model motivated by masked diffusion: Total correlation and a square root collision threshold
• Abstract summary: Motivated by confidence-guided parallel unmasking in masked discrete diffusion, we study a single selection step in a stylized Gaussian random-field model.<n>Results provide a rigorous confidence-geometry and spatial correlation jointly shape one-step-based selection in masked discrete diffusion.
• Score: 8.230831152671708
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Motivated by confidence-guided parallel unmasking in masked discrete diffusion, we study a single selection step in a stylized Gaussian random-field model. A locally dependent nonnegative score field represents position wise uncertainty, and the scheduler selects the K positions with the smallest scores. Dependence among the selected positions is measured through a distance-dependent Gaussian correlation model. This separation provides a tractable framework for quantifying how the geometry of low-score locations affects the dependence cost of factorized parallel decoding. We establish two complementary results. In a conservative sub-square-root regime, the conditional Gaussian total correlation of the selected block vanishes in probability. At the square-root scale, it remains non-negligible with positive asymptotic probability and admits a strictly positive expectation lower bound. Synthetic experiments support the predicted finite-size behavior. These results provide a rigorous stochastic-geometry baseline for understanding how budget size, score dependence, and spatial correlation jointly shape one-step confidence-based selection in masked discrete diffusion.

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