DUEL: Exact Likelihood for Masked Diffusion via Deterministic Unmasking

Masked diffusion models (MDMs) generate text by iteratively selecting positions to unmask and then predicting tokens at those positions. Yet MDMs lack proper perplexity evaluation: the ELBO is a loose bound on likelihood under the training distribution, not the test-time distribution, while generative perplexity requires a biased external model and ignores diversity. To address this, we introduce the \textsc{DUEL} framework, which formalizes \emph{deterministic} position selection, unifying leading MDM sampling strategies. We prove \textbf{\textsc{DUEL} admits \emph{exact} likelihood computation} via a simple algorithm, evaluated under the same position selection used at test time. This \textbf{gives MDMs proper perplexity for the first time} -- the natural analogue of autoregressive perplexity. With proper perplexity in hand, we revisit key questions about MDMs. \textbf{MDMs are substantially better than previously thought}: the MDM-autoregressive perplexity gap shrinks by up to 32\% on in-domain data and 82\% on zero-shot benchmarks. \textsc{DUEL} enables the first principled comparison of fast, parallel samplers across compute budgets -- an analysis impossible with the ELBO and unreliable with generative perplexity -- identifying probability margin \citep{kim2025train} as a strong default. Finally, oracle search over position orderings reveals MDMs can far surpass autoregressive models -- achieving 36.47 vs.\ 52.11 perplexity on AG News -- demonstrating the ceiling of MDM performance has not yet been reached.