# Reconsidering Positional Supervision in Masked Diffusion Language Model Training

arXiv: https://arxiv.org/abs/2601.22947 · HTML: https://mlsanity.com/paper/2601.22947/

## 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 48 of its 60 references that are in the map.
- First posted on arXiv 30 Jan 2026.

## Placed in

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

## Builds on (most cited first, 30 of 48)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (2022)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Speech Recognition with Deep Recurrent Neural Networks](https://mlsanity.com/paper/1303.5778/) (2013)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [Dream 7B: Diffusion Large Language Models](https://mlsanity.com/paper/2508.15487/) (2025)
- [From Crowdsourced Data to High-Quality Benchmarks: Arena-Hard and BenchBuilder Pipeline](https://mlsanity.com/paper/2406.11939/) (2024)
- [Non-Autoregressive Neural Machine Translation](https://mlsanity.com/paper/1711.02281/) (2017)
- [Block Diffusion: Interpolating Between Autoregressive and Diffusion Language Models](https://mlsanity.com/paper/2503.09573/) (2025)
- [Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Data](https://mlsanity.com/paper/2406.03736/) (2024)
- [Magpie: Alignment Data Synthesis from Scratch by Prompting Aligned LLMs with Nothing](https://mlsanity.com/paper/2406.08464/) (2024)
- [LLaDA 1.5: Variance-Reduced Preference Optimization for Large Language Diffusion Models](https://mlsanity.com/paper/2505.19223/) (2025)
- [Soft-DTW: a Differentiable Loss Function for Time-Series](https://mlsanity.com/paper/1703.01541/) (2017)
- [Mercury: Ultra-Fast Language Models Based on Diffusion](https://mlsanity.com/paper/2506.17298/) (2025)
- [WildBench: Benchmarking LLMs with Challenging Tasks from Real Users in the Wild](https://mlsanity.com/paper/2406.04770/) (2024)
- [Remasking Discrete Diffusion Models with Inference-Time Scaling](https://mlsanity.com/paper/2503.00307/) (2025)
- [d1: Scaling Reasoning in Diffusion Large Language Models via Reinforcement Learning](https://mlsanity.com/paper/2504.12216/) (2025)
- [Seed Diffusion: A Large-Scale Diffusion Language Model with High-Speed Inference](https://mlsanity.com/paper/2508.02193/) (2025)
- [Glancing Transformer for Non-Autoregressive Neural Machine Translation](https://mlsanity.com/paper/2008.07905/) (2020)
- [Fully Non-autoregressive Neural Machine Translation: Tricks of the Trade](https://mlsanity.com/paper/2012.15833/) (2020)
- [Non-Autoregressive Machine Translation with Latent Alignments](https://mlsanity.com/paper/2004.07437/) (2020)
- [Path Planning for Masked Diffusion Model Sampling](https://mlsanity.com/paper/2502.03540/) (2025)

## Abstract (arXiv)

Masked diffusion language models (MDLMs) generate text by unmasking tokens in parallel and have recently emerged as alternatives to autoregressive language models. They can be viewed as parallel decoders trained with a position-wise cross-entropy (CE) loss, the same setup as non-autoregressive translation (NAT). In NAT, CE-trained parallel decoders have been argued to be sensitive to small positional shifts, since CE penalizes them harshly. We ask whether CE-trained MDLMs are similarly sensitive to such shifts under iterative decoding. To probe this, we apply a controlled intervention that introduces them during decoding. On LLaDA-8B-Instruct with Arena-Hard, displacing as little as 1% of generated tokens by one position substantially reduces win rates against the unintervened model, showing that MDLMs are sensitive to such small shifts under iterative parallel decoding. Motivated by this, we adapt connectionist temporal classification (CTC), an alignment-flexible objective known to mitigate it there, to MDLM supervised fine-tuning. By relaxing the strict position-wise match that CE imposes, CTC gives the loss room to absorb small positional shifts; concretely, we modified CTC objective to use a special <slack> token that absorbs positional uncertainty between target tokens and output positions, and a updated collapse map that preserves target surface forms. Across four open-ended generation benchmarks, the resulting model consistently improves over both the original model and a matched cross-entropy-trained baseline, with statistically significant gains on all four. These results identify training-side alignment flexibility as a useful design dimension for MDLM SFT, complementary to the inference-time approaches explored in prior work.