Continuous diffusion is a natural framework for non-autoregressive generation but has generally lagged behind masked discrete diffusion models (MDMs) on discrete sequence generation. We argue that the bottleneck is not continuity itself, but a representation in which denoising depends on timestep-indexed noise regimes. We introduce \emph{Discrete Stochastic Localization} (DSL), a continuous-state framework with unit-sphere token embeddings whose Bayes-optimal denoiser is invariant to the nominal signal-to-noise ratio (SNR) under the localization channel. One trained network then supports an entire family of per-token SNR paths, with endpoint masked-diffusion paths as a special case. Fine-tuning a pretrained MDLM checkpoint with DSL substantially improves distributional faithfulness (MAUVE) on OpenWebText across all step budgets from T=128 to T=1024, and the same checkpoint supports random-order autoregressive sampling, as well as a hybrid continuous-then-discrete sampler using as few as T=48 total steps -- without distillation or retraining.
@article{arxiv.2602.16169,
title = {Discrete Stochastic Localization for Non-autoregressive Generation},
author = {Yunshu Wu and Jiayi Cheng and Longxuan Yu and Partha Thakuria and Rob Brekelmans and Evangelos E. Papalexakis and Greg Ver Steeg},
journal= {arXiv preprint arXiv:2602.16169},
year = {2026}
}