What Makes a Good Decoding Path? Selecting Parallel-Decodable Trajectories for Diffusion Large Language Models

Diffusion large language models (DLLMs) allow flexible decoding trajectories, but their factorized parallel predictions can produce jointly incompatible tokens even when individual predictions are confident. Existing trajectory-selection methods emphasize marginal predictability or immediate dependency risk, leaving less explored how decoding decisions reshape the dependency structure encountered by subsequent updates. In this paper, we derive an information-theoretic identity linking the current and expected residual factorization costs to the information that revealed tokens provide about remaining positions, and propose Factorization-Aware Candidate Transition Selection (FACTS), a training-free sampler that ranks candidate transitions by combining future uncertainty reduction with a joint-compatibility signal obtained by comparing sequential and factorized scores of the same proposed tokens. Experiments on Dream and LLaDA across mathematical reasoning and code generation show that FACTS is particularly effective under wider parallel decoding.