Towards Unbiased On-Policy Distillation for Block Diffusion Language Models

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 is defined only from the causal prefix. As a result, the teacher distribution used for distillation is not fully aligned with the information available to the student. We therefore introduce d-OPD, a future-aware on-policy distillation method that corrects the AR teacher distribution to better align with the student-visible state by incorporating visible future information within each block, providing supervision that better matches the information used by the student. Across Qwen3 models from 0.6B to 8B, d-OPD improves the six-benchmark average by up to $4.0$ points over OPDLM and reduces training time by $1.35$-$1.58\times$. The code is available at https://github.com/mit-han-lab/d-OPD.

On-policy distillation (OPD) has recently emerged as an effective post-training paradigm for consolidating the capabilities of specialized expert models into a single student model. Despite its empirical success, the conditions under which OPD yields reliable improvement remain poorly understood. In this work, we identify two fundamental bottlenecks that limit effective OPD: insufficient exploration of informative states and unreliable teacher supervision for student rollouts. Building on this insight, we propose Uni-OPD, a unified OPD framework that generalizes across Large Language Models (LLMs) and Multimodal Large Language Models (MLLMs), centered on a dual-perspective optimization strategy. Specifically, from the student's perspective, we adopt two data balancing strategies to promote exploration of informative student-generated states during training. From the teacher's perspective, we show that reliable supervision hinges on whether aggregated token-level guidance remains order-consistent with the outcome reward. To this end, we develop an outcome-guided margin calibration mechanism to restore order consistency between correct and incorrect trajectories. We conduct extensive experiments on 5 domains and 16 benchmarks covering diverse settings, including single-teacher and multi-teacher distillation across LLMs and MLLMs, strong-to-weak distillation, and cross-modal distillation. Our results verify the effectiveness and versatility of Uni-OPD and provide practical insights into reliable OPD.

On-policy distillation (OPD) and on-policy self-distillation (OPSD) have emerged as promising post-training methods for large language models, offering dense token-level supervision on trajectories sampled from the model's own policy. However, existing results on their effectiveness remain mixed: while OP(S)D has shown promise in system prompt and knowledge internalization, recent studies also report instability and degradation. In this work, we present a comprehensive empirical study of when OPD and OPSD work, when they fail, and why. We find that OPD on mathematical reasoning is highly sensitive to teacher choice and loss formulation, whereas OPSD fails in our tested settings due to test-time absence of instance-specific privileged information (PI). In contrast, OPSD is effective when PI represents a shared latent rule, such as a system prompt or alignment preference. We identify three failure mechanisms: (1) distribution mismatch between teacher and student caused by conditioning on student-generated prefixes, (2) optimization instability from biased TopK reverse-KL gradients, and (3) an OPSD-specific limitation where the student learns a PI-free policy that aggregates PI-conditioned teachers, which is insufficient when PI is instance-specific. We further show that stop-gradient TopK objectives, RLVR-adapted teachers, and SFT-stabilized students mitigate these failures.