# x-Prediction Flow: Efficient Continuous Decoding for Masked Diffusion Language Models

arXiv: https://arxiv.org/abs/2606.29066 · HTML: https://mlsanity.com/paper/2606.29066/

## 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 10 of its 18 references that are in the map.
- First posted on arXiv 27 Jun 2026.

## Placed in

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

## Builds on (most cited first, 10 of 10)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Data](https://mlsanity.com/paper/2406.03736/) (2024)
- [LLaDA2.0: Scaling Up Diffusion Language Models to 100B](https://mlsanity.com/paper/2512.15745/) (2025)
- [Empowering Diffusion Models on the Embedding Space for Text Generation](https://mlsanity.com/paper/2212.09412/) (2022)

## Abstract (arXiv)

Masked diffusion language models (MDLMs) generate text by iteratively unmasking tokens, but their standard decoder reduces each step to a binary action: a position is either committed to a single token or left fully masked, discarding rich predictive information rather than carrying it forward, and forcing premature, irrevocable commitments that lead to poor performance under a limited decoding budget. In this paper, we reinterpret mask prediction as a clean-state prediction (x-prediction) and show that it can be used to induce a continuous flow in the input embedding space. Building on this view, we propose a continuous decoding framework for MDLMs where tokens can accumulate partial progress at each diffusion step and remain revisable. To match the uneven contextual constraints across positions in language, we replace the globally synchronous schedule in image diffusion with a confidence-based asynchronous update in which the diffusion progress is token-wise accumulated. Additionally, we introduce a lightweight policy network and formulate its training as a reinforcement learning problem. Applied to pretrained LLaDA, our decoder retains 83--97% of full-budget accuracy using under 15% of the diffusion steps, largely outperforming discrete mask-prediction decoding at matched budgets.