# ρ-textttEOS: Training-free Bidirectional Variable-Length Control for Masked Diffusion LLMs

arXiv: https://arxiv.org/abs/2601.22527 · HTML: https://mlsanity.com/paper/2601.22527/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 29 of its 33 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, 29 of 29)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [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)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [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)
- [DiffuSeq: Sequence to Sequence Text Generation with Diffusion Models](https://mlsanity.com/paper/2210.08933/) (2022)
- [Block Diffusion: Interpolating Between Autoregressive and Diffusion Language Models](https://mlsanity.com/paper/2503.09573/) (2025)
- [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)
- [Masked Diffusion Models are Secretly Time-Agnostic Masked Models and Exploit Inaccurate Categorical Sampling](https://mlsanity.com/paper/2409.02908/) (2024)
- [DiffuCoder: Understanding and Improving Masked Diffusion Models for Code Generation](https://mlsanity.com/paper/2506.20639/) (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)
- [SDAR: A Synergistic Diffusion-AutoRegression Paradigm for Scalable Sequence Generation](https://mlsanity.com/paper/2510.06303/) (2025)
- [LLaDA-MoE: A Sparse MoE Diffusion Language Model](https://mlsanity.com/paper/2509.24389/) (2025)
- [Any-Order Flexible Length Masked Diffusion](https://mlsanity.com/paper/2509.01025/) (2025)
- [SPG: Sandwiched Policy Gradient for Masked Diffusion Language Models](https://mlsanity.com/paper/2510.09541/) (2025)
- [WeDLM: Reconciling Diffusion Language Models with Standard Causal Attention for Fast Inference](https://mlsanity.com/paper/2512.22737/) (2025)
- [Beyond Fixed: Training-Free Variable-Length Denoising for Diffusion Large Language Models](https://mlsanity.com/paper/2508.00819/) (2025)
- [Diffusion LLM with Native Variable Generation Lengths: Let [EOS] Lead the Way](https://mlsanity.com/paper/2510.24605/) (2025)
- [Taming Masked Diffusion Language Models via Consistency Trajectory Reinforcement Learning with Fewer Decoding Step](https://mlsanity.com/paper/2509.23924/) (2025)

## Built on by (most cited first, 7 of 7)

- [DARE: Diffusion Large Language Models Alignment and Reinforcement Executor](https://mlsanity.com/paper/2604.04215/) (2026)
- [Answer First, Reason Later: When Commitment Order Costs Accuracy in Diffusion Language Models](https://mlsanity.com/paper/2608.05687/) (2026)
- [VoidPadding: Let [VOID] Handle Padding in Masked Diffusion Language Models so that [EOS] Can Focus on Semantic Termination](https://mlsanity.com/paper/2606.17999/) (2026)
- [Expanding Flow Maps](https://mlsanity.com/paper/2607.21585/) (2026)
- [A Continuous-Time Markov Chain Framework for Insertion Language Models](https://mlsanity.com/paper/2606.10199/) (2026)
- [Length-Adaptive Decoding for Masked Diffusion Machine Translation](https://mlsanity.com/paper/2608.22274/) (2026)
- [CARVE: Verified Expansion for Variable-Length Generation in Diffusion Language Models](https://mlsanity.com/paper/2608.30922/) (2026)

## Abstract (arXiv)

Beyond parallel generation and global context modeling, current masked diffusion large language models (masked dLLMs, i.e., LLaDA) suffer from a fundamental limitation: they require a predefined, fixed generation length, which lacks flexibility and forces an inevitable trade-off between output quality and computational efficiency. To address this, we study the denoising dynamics and find that the implicit density (ρ) of end-of-sequence (textttEOS) tokens serves as a reliable signal of generation sufficiency. In particular, the evolving implicit textttEOS density during denoising reveals whether the current masked space is excessive or insufficient, thereby guiding the adjustment direction for generation length. Building on this insight, we propose textbfρ-textttEOS, a training-free, single-stage strategy that enables bidirectional variable-length generation for masked dLLMs. Unlike prior two-stage approaches--which require separate length adjustment and iterative mask insertion phases while supporting only unidirectional expansion--textbfρ-textttEOS achieves bidirectional length adjustment within a unified denoising process by continuously estimating the implicit textttEOS density: excessively high density triggers textttMASK token contraction, while insufficient density induces expansion. Extensive experiments on mathematics and code benchmarks demonstrate that textbfρ-textttEOS achieves comparable performance while substantially improving inference efficiency and token utilization. Code is available at https://github.com/yjyddq/rho-EOS.