Coupling Matters: Finite-Horizon Transport Analysis for Quantized Masked Diffusion Language Models

Abstract

Preprint / technical report; not peer reviewed. This record presents Coupling Matters: Finite-Horizon Transport Analysis for Quantized Masked Diffusion Language Models, together with the public source and a compact research artifact. Post-training quantization of masked diffusion language models can change token choices, commit sets, and subsequent generation states. We develop a finite-horizon transport framework in which the coupling used to synchronize full-precision and quantized generation is part of the measured upper bound. The main structural result controls terminal distortion through the first divergence time and the residual unresolved mask mass. The empirical study includes fixed-suite and declared prompt-population analyses, finite-bit scaling, validation on a second model, and an official sample-then-select sampler. The record also preserves preregistered negative investigations: additive token metrics did not materially resolve Hamming saturation, held-out transport lower-bound witnesses were vacuous at the preregistered confidence level, and survival–residual transport-weighted calibration did not improve the primary held-out W4 GSM8K accuracy endpoint over the strongest calibration baseline. The accompanying artifact contains the technical report, LaTeX source, compact result tables and figures, audit material, selected model-free analysis code, reproducibility documentation, and SHA-256 ledgers for larger omitted work packages. Model checkpoints and datasets are not redistributed. Status: preprint / technical report; not peer reviewed.