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

arXiv: https://arxiv.org/abs/2607.17522 · HTML: https://mlsanity.com/paper/2607.17522/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 12 of its 18 references that are in the map.
- First posted on arXiv 20 Jul 2026.

## Placed in

- Diffusion models / [Discrete and text diffusion](https://mlsanity.com/diffusion/discrete-and-text-diffusion/)

## Builds on (most cited first, 12 of 12)

- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Muse: Text-To-Image Generation via Masked Generative Transformers](https://mlsanity.com/paper/2301.00704/) (2023)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [Train for the Worst, Plan for the Best: Understanding Token Ordering in Masked Diffusions](https://mlsanity.com/paper/2502.06768/) (2025)
- [Autoregressive Diffusion Models](https://mlsanity.com/paper/2110.02037/) (2021)
- [Learning Unmasking Policies for Diffusion Language Models](https://mlsanity.com/paper/2512.09106/) (2025)
- [Optimal Inference Schedules for Masked Diffusion Models](https://mlsanity.com/paper/2511.04647/) (2025)
- [Breaking AR's Sampling Bottleneck: Provable Acceleration via Diffusion Language Models](https://mlsanity.com/paper/2505.21400/) (2025)
- [Improving Discrete Diffusion Unmasking Policies Beyond Explicit Reference Policies](https://mlsanity.com/paper/2510.05725/) (2025)

## Abstract (arXiv)

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.