# Taming Masked Diffusion Language Models via Consistency Trajectory Reinforcement Learning with Fewer Decoding Step

arXiv: https://arxiv.org/abs/2509.23924 · HTML: https://mlsanity.com/paper/2509.23924/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 37 of its 39 references that are in the map.
- First posted on arXiv 28 Sep 2025.

## Placed in

- Diffusion models / [Discrete and text diffusion](https://mlsanity.com/diffusion/discrete-and-text-diffusion/)
- Efficient LLM inference and serving / [Diffusion LLM and MoE inference](https://mlsanity.com/inference/diffusion-llm-and-moe-inference/)

## Builds on (most cited first, 30 of 37)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (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)
- [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)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [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)
- [LLaDA 1.5: Variance-Reduced Preference Optimization for Large Language Diffusion Models](https://mlsanity.com/paper/2505.19223/) (2025)
- [Scaling Diffusion Language Models via Adaptation from Autoregressive Models](https://mlsanity.com/paper/2410.17891/) (2024)
- [Mercury: Ultra-Fast Language Models Based on Diffusion](https://mlsanity.com/paper/2506.17298/) (2025)

## Built on by (most cited first, 17 of 17)

- [d3LLM: Ultra-Fast Diffusion LLM using Pseudo-Trajectory Distillation](https://mlsanity.com/paper/2601.07568/) (2026)
- [d-TreeRPO: Towards More Reliable Policy Optimization for Diffusion Language Models](https://mlsanity.com/paper/2512.09675/) (2025)
- [Beyond Confidence: Adaptive and Coherent Decoding for Diffusion Language Models](https://mlsanity.com/paper/2512.02044/) (2025)
- [ρ-textttEOS: Training-free Bidirectional Variable-Length Control for Masked Diffusion LLMs](https://mlsanity.com/paper/2601.22527/) (2026)
- [DARE: Diffusion Large Language Models Alignment and Reinforcement Executor](https://mlsanity.com/paper/2604.04215/) (2026)
- [Diffusion-State Policy Optimization for Masked Diffusion Language Models](https://mlsanity.com/paper/2602.06462/) (2026)
- [AdaFlash: Adaptive Speculative Decoding via On-Policy Distilled Diffusion Drafters](https://mlsanity.com/paper/2607.19223/) (2026)
- [Reasoning in Diffusion Large Language Models is Concentrated in Dynamic Confusion Zones](https://mlsanity.com/paper/2511.15208/) (2025)
- [Mask-Aware Policy Gradients for Diffusion Language Models](https://mlsanity.com/paper/2607.15200/) (2026)
- [DOS: Dependency-Oriented Sampler for Masked Diffusion Language Models](https://mlsanity.com/paper/2603.15340/) (2026)
- [TRIMS: Trajectory-Ranked Instruction Masked Supervision for Diffusion Language Models](https://mlsanity.com/paper/2604.00666/) (2026)
- [CAGenMol: Condition-Aware Diffusion Language Model for Goal-Directed Molecular Generation](https://mlsanity.com/paper/2604.11483/) (2026)
- [Self-Distilled Trajectory-Aware Boltzmann Modeling: Bridging the Training-Inference Discrepancy in Diffusion Language Models](https://mlsanity.com/paper/2605.11854/) (2026)
- [Sketch Then Paint: Hierarchical Reinforcement Learning for Diffusion Multi-Modal Large Language Models](https://mlsanity.com/paper/2605.16842/) (2026)
- [Progressive Refinement Regulation for Accelerating Diffusion Language Model Decoding](https://mlsanity.com/paper/2603.04514/) (2026)
- [What Gets Unmasked First? Trajectory Analysis of Diffusion Models for Graph-to-Text Generation](https://mlsanity.com/paper/2605.31564/) (2026)
- [Read the Trace, Steer the Path: Trajectory-Aware Reinforcement Learning for Diffusion Language Models](https://mlsanity.com/paper/2606.04396/) (2026)

## Abstract (arXiv)

Masked diffusion language models (MDLMs) have recently emerged as a promising alternative to autoregressive (AR) language models, offering properties such as parallel decoding, flexible generation orders, and the potential for fewer inference steps. Despite these advantages, decoding strategies and reinforcement learning (RL) algorithms tailored for MDLMs remain underexplored. A naive approach is to directly transfer techniques well-established for AR models to MDLMs. However, this raises an immediate question: Is such a naive transfer truly optimal? For example, 1) Block-wise and semi-AR decoding strategies are not employed during the training of MDLMs, so why do they outperform full diffusion-style decoding during inference? 2) Applying RL algorithms designed for AR models directly to MDLMs exhibits a training-inference inconsistency, since MDLM decoding are non-causal (parallel). This results in inconsistencies between the rollout trajectory and the optimization trajectory. To address these challenges, we propose EOS Early Rejection (EOSER) and Ascending Step-Size (ASS) decoding scheduler, which unlock the potential of MDLMs to perform full diffusion-style decoding, achieving competitive performance with fewer decoding steps. Additionally, we introduce Consistency Trajectory Group Relative Policy Optimization (CJ-GRPO) for taming MDLMs, which emphasizes the consistency between rollout trajectory and optimization trajectory, and reduces the optimization errors caused by skip-step optimization. We conduct extensive experiments on reasoning tasks, such as mathematical and planning benchmarks, using LLaDA-8B-Instruct. The results demonstrate that the proposed EOSER and ASS mechanisms, together with CJ-GRPO, hold significant promise for effectively and efficiently taming MDLMs. Code: https://github.com/yjyddq/EOSER-ASS-RL.