$\rho$-$\texttt{EOS}$: Training-free Bidirectional Variable-Length Control for Masked Diffusion LLMs

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 ($\rho$) of end-of-sequence ($\texttt{EOS}$) tokens serves as a reliable signal of generation sufficiency. In particular, the evolving implicit $\texttt{EOS}$ 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 $\textbf{$\rho$-$\texttt{EOS}$}$, 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--$\textbf{$\rho$-$\texttt{EOS}$}$ achieves bidirectional length adjustment within a unified denoising process by continuously estimating the implicit $\texttt{EOS}$ density: excessively high density triggers $\texttt{MASK}$ token contraction, while insufficient density induces expansion. Extensive experiments on mathematics and code benchmarks demonstrate that $\textbf{$\rho$-$\texttt{EOS}$}$ achieves comparable performance while substantially improving inference efficiency and token utilization. Code is available at https://github.com/yjyddq/rho-EOS.