Path Planning for Masked Diffusion Model Sampling

In this paper, we explore how token unmasking order influences generative quality in masked diffusion models (MDMs). We derive an expanded evidence lower bound (ELBO) that introduces a planner to select which tokens to unmask at each step. Our analysis reveals that alternative unmasking strategies can enhance generation performance. Building on this, we propose Path Planning (P2), a sampling framework that uses a pre-trained BERT model or the denoiser itself to guide unmasking decisions. P2 generalizes all known MDM sampling strategies and significantly improves performance across diverse domains, including language generation (in-context learning, code generation, story infilling, mathematical reasoning, reverse curse correction) and biological sequence generation (protein and RNA sequences).