Demystifying MaskGIT Sampler and Beyond: Adaptive Order Selection in Masked Diffusion

Generative models have witnessed remarkable progress in recent years, with diffusion models (Sohl-Dickstein et al., 2015) emerging as a dominant paradigm across various domains including images (Ho et al., 2020; Dhariwal & Nichol, 2021), audio (Kong et al., 2021) and video (Ho et al., 2022). While continuous diffusion models have garnered significant attention, discrete diffusion models (Austin et al., 2021; Campbell et al., 2022; Gu et al., 2022; Lou et al., 2024) offer compelling advantages for inherently discrete data, such as tokenized representations in all the above domains. Among discrete diffusion approaches, masked diffusion models (Sahoo et al., 2024; Shi et al., 2024; Ou et al., 2025) have demonstrated exceptional performance, particularly in generating high-quality samples in language domains. However, their sampling process remains computationally intensive, requiring hundreds of function evaluations. Recent efforts to accelerate sampling in discrete/masked diffusion models have explored various directions, including optimized scheduling (Park et al., 2025), distillation (Deschenaux & Gulcehre, 2025; Hayakawa et al., 2025; Zhu et al., 2025), and adaptive token selection (Kim et al., 2025; Ben-Hamu et al., 2025).