VGB for Masked Diffusion Model: Efficient Test-time Scaling for Reward Satisfaction and Sample Editing

• URL: http://arxiv.org/abs/2606.28301v1
• Date: Fri, 26 Jun 2026 17:47:09 GMT
• Title: VGB for Masked Diffusion Model: Efficient Test-time Scaling for Reward Satisfaction and Sample Editing
• Abstract summary: Masked Diffusion Model (MDM-VGB) is a discrete diffusion sampler that augments unmasking generation with principled reward-guided remasking.<n>We prove that MDM-VGB is robust to process-verifier noise and achieves quadratic complexity, while popular test-times such as best-of-$N$ can incur exponential complexity due to error accumulation.
• Score: 20.078996384901966
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Inference-time scaling is a promising paradigm to improve generative models, especially when outputs must satisfy structural constraints or optimize downstream rewards. We consider Masked Diffusion Model (MDM) and introduce MDM-VGB, a discrete diffusion sampler that augments unmasking generation with theoretically principled reward-guided remasking. Inspired by the recent success of the classical Jerrum-Sinclair backtracking Markov chain in reward-tilted generation, MDM-VGB extends the backtracking random walk from a fixed prefix tree to a masked-state graph, allowing tokens to be unmasked and remasked at arbitrary positions. The resulting sampler favors unmasking and remasking moves that lead to higher-value partial configurations, enabling both effective high-reward generation and efficient repair of low-reward samples. We prove that MDM-VGB is robust to process-verifier noise and achieves quadratic complexity, while popular test-time heuristics such as best-of-$N$ can incur exponential complexity due to error accumulation. Our theoretical findings are corroborated by strong empirical performance, particularly on popular constraint-satisfaction and scientific benchmarks such as Sudoku and QM9.

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