d-OPD: Future-Aware On-Policy Distillation for Block Diffusion Language Models

Ruitao Liu, Qinghao Hu, Song Han

Large language models (LLMs) typically generate text autoregressively (AR), predicting one token at a time. Block diffusion language models (dLLMs) instead generate blocks sequentially while denoising multiple tokens in parallel within each block, offering a promising way to accelerate generation. Rather than training such models from scratch, recent work adapts strong pretrained AR models into block dLLMs through distillation. On-policy distillation (OPD) has been widely used for LLM training because it supervises the student on states generated by its current policy, rather than only on fixed offline trajectories. By training on the states the student actually visits, it reduces the mismatch between training and generation and can provide more relevant supervision as the student evolves. Recent work has extended this idea to AR-to-block-diffusion conversion. However, this setting introduces a fundamental mismatch in supervision: the block-diffusion student and the causal AR teacher condition on different information at the same training state. The student predicts from the entire partially denoised block, including visible future context, whereas the standard AR teacher target…