DUEL: Exact Likelihood for Masked Diffusion via Deterministic Unmasking

• URL: http://arxiv.org/abs/2603.01367v1
• Date: Mon, 02 Mar 2026 01:56:03 GMT
• Title: DUEL: Exact Likelihood for Masked Diffusion via Deterministic Unmasking
• Authors: Gilad Turok, Chris De Sa, Volodymyr Kuleshov,
• Abstract summary: Masked diffusion models (MDMs) generate text by iteratively selecting positions to unmask and then predicting tokens at those positions.<n>Yet MDMs lack proper perplexity evaluation: the ELBO is a loose bound on likelihood under the training distribution, not the test-time distribution.<n>We introduce the textscDUEL framework, which formalizes emphdeterministic position selection, unifying leading MDM sampling strategies.
• Score: 13.905201743303214
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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