Diffusion large language models (dLLMs) are a promising alternative to autoregressive generation. However, reasoning-oriented post-training for dLLMs remains challenging. Supervised fine-tuning (SFT) for dLLMs requires dense but often off-policy masked states, while reinforcement learning (RL) relies on sparse rewards or value modeling. This paper proposes \textbf{trace-based on-policy distillation (TOPD)}, a teacher-supervised framework that transfers reasoning ability to a target dLLM without reward estimation. The key idea is to supervise a dLLM on its own denoising trajectory, focusing on the trace-aligned token decisions that form the final response. Specifically, TOPD samples on-policy diffusion trajectories from the target dLLM, obtains teacher token distributions from a teacher model on the corresponding partially denoised states, and updates the target dLLM with a token-level Reverse Kullback-Leibler (Reverse-KL) objective. This design preserves dense teacher supervision while aligning training with the model's own denoising states. On mathematical reasoning benchmarks, TOPD enables SDAR-4B-Chat to match the MATH500 accuracy of its RL-trained counterpart TraDo-4B-Instruct, with gains of +5.7 under static evaluation and +4.5 under dynamic evaluation. Compared with the RL-trained counterpart, TOPD achieves this with 4$\times$ fewer rollout rounds, corresponding to an estimated 96.0$\times$ to-accuracy model-compute speedup.
dOPSD derives the teacher's privilege directly from the student's own denoising trajectory, evaluating masked positions using later, more-decoded steps of that same trajectory rather than an external label, so the teacher's advantage emerges from the model's own decoding process.
Reinforcement learning can align diffusion models with human preferences and task-specific objectives, but endpoint rewards do not specify how an intermediate denoising prediction should change. We introduce DiffusionOPSD as an on-policy self-distillation framework that converts image-level reward guidance into explicit targets for clean-output predictions at sampled queries. At each outer iteration, a frozen behavior policy generates trajectories and supplies query states and anchors. Reward gradients construct bounded positive and negative targets around each anchor. The trainable policy fits these targets as detached supervision through finite fitting before an exponential moving average update refreshes the behavior policy. This setup lets us measure target construction and finite realization separately. Controlled same-query experiments show that larger target-construction gains do not necessarily translate into larger realized gains after a single fitting update. Across SD 3.5-M and the step-distilled Z-Image-Turbo, our approach achieves the best final held-out scores in 19 of 20 reward-matched settings across two backbones and ten evaluators. It outperforms the strongest competing method by up to 44.0% and reduces training GPU-hours relative to DiffusionNFT by 40% on SD 3.5-M and 63% on Z-Image-Turbo. These results support on-policy self-distillation as an efficient and analyzable approach to diffusion post-training by converting image-level reward guidance into explicit and continually refreshed intermediate supervision, thereby opening a path toward more efficient and diagnosable alignment.
Weina Zhou, Xiongwei Zhu, Lingdong Kong et al.· 0 citations
On-policy self-distillation (OPSD) adapts a language model by distilling guidance from a frozen teacher on trajectories sampled from the student. Its effectiveness, however, depends critically on the quality of those trajectories. We show that when student rollouts drift from target trajectories, conditioning the teacher on off-target prefixes substantially weakens its task-relevant supervision. Controlled prefix-corruption experiments expose this failure mode, which we term rollout-conditioned signal degradation. To address this problem, we propose a unified training framework that separates two complementary supervision pathways. The first retains rollout-conditioned distribution matching, providing guidance on states the student actually visits. The second applies supervised cross-entropy on canonical ground-truth contexts, avoiding the incompatibility of imposing target tokens on erroneous rollout prefixes. Token-level rollout-target alignment is used to adapt the strength of the canonical-context anchor, emphasizing it during cold start and relaxing it as rollout quality improves. Experiments across multiple model scales, two task families, and general-reasoning benchmarks show that the proposed approach improves task acquisition over OPSD while preserving general capabilities, resulting in a more favorable empirical plasticity-stability trade-off. These findings identify context quality as a central bottleneck in on-policy self-distillation and demonstrate the value of separating rollout-conditioned guidance from canonical supervision.
Meilin Yang, Zixuan Ding, Jianhao Nie et al.· 0 citations
On-policy distillation (OPD), which leverages a pre-trained, specialized teacher model to provide dense supervisory signals, has achieved significant success in Large Language Models (LLMs) and has recently been adapted to flow matching models. However, this paradigm suffers from two major issues: First, training a separate, task-specific teacher for every new objective incurs high computational costs. Second, the discrepancy between teacher and student distributions often leads to compounding errors along the generation trajectory. In this paper, we introduce \textbf{Self-OPD}, a teacher-free OPD framework for flow matching models that turns the student's own self-exploration into step-wise supervision. At each timestep, Self-OPD branches the deterministic next-state prediction into $K$ stochastic SDE candidates, rolls them out with the ODE sampler, and compares their rewards against a deterministic self-reference baseline to obtain normalized advantages. The velocity field is optimized with an all-branch pull-push objective, where high-advantage branches attract the student and low-advantage branches repel it under direction-aware attenuation and SDE-variance normalization. For multi-objective alignment, Self-OPD fuses normalized scores at the reward level, avoiding direct gradient conflict. Experiments on single and mixed reward benchmarks show that Self-OPD outperforms prior RL and OPD methods without task-specific teachers.
Shiyi Zhang, Mushui Liu, Yunze Tong et al.· 0 citations
Reinforcement learning has proven effective for improving reasoning in large language models, but extending it to Masked Diffusion Language Models (MDLMs) remains challenging due to the intractability of the log-likelihood estimation. Existing approaches approximate this log-likelihood by modeling only the token predictions, ignoring the order in which positions are unmasked during generation. We observe that MDLM generation involves two decisions at each step: what tokens to place at each masked position and which positions to remask. We formalize this as a two-stage action MDP, showing that the policy gradient naturally decomposes into a token term and a masking term. Combining optimization of both terms leads to state-of-the-art outcomes on mathematical reasoning and coding benchmarks, with scores of 87.1% on GSM8K and 53.4% on MBPP.
Haran Raajesh, Kulin Shah, Adam R. Klivans et al.· 1 citation
Reinforcement learning with verifiable rewards (RLVR) improves the reasoning capabilities of large language models using automatically verifiable outcome signals, but these signals are typically sparse and at the sequence-level. On-policy self-distillation (OPSD) mitigates this sparsity by querying a privileged teacher at student-visited prefixes and providing dense token-level distributional supervision. Although this dense supervision alleviates signal sparsity, we find that standard OPSD still underexploits the temporal structure of the rollout. It assigns every local divergence the same coefficient, regardless of its position or the divergence sequence in which it occurs. In on-policy autoregressive generation, the same divergence magnitude can follow different discrepancy histories, reflecting different evolutions of the mismatch between the teacher and student. Since the local scalar alone cannot distinguish these temporal contexts, standard OPSD cannot adapt its token-level weights to the realized discrepancy sequence. To address this limitation, we propose Divergence-Adaptive Supervision Horizons (DASH). DASH maps the gap between each local distillation signal and the sequence-level mean to an adaptive propagation gate and then uses these gates to control backward multi-step aggregation. By doing so, DASH adjusts token-level supervision weights according to how local divergences evolve during generation. Experiments on three mathematical reasoning benchmarks across three model scales show that DASH improves over our matched vanilla OPSD reruns on every benchmark at all three scales. DASH reuses the teacher and student distributions that OPSD already computes, so the gains require no additional teacher or student forward pass. Code: https://github.com/DBtxy/DASH-OPSD
Zhi-Yan Hou, Xinyu Tang, Hongyan An et al.· 1 citation