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Nov 12

AsyncOPD: How Stale Can On-Policy Distillation Be?

On-policy distillation (OPD) trains a student on its own rollouts guided by teacher feedback and is becoming increasingly important for large language model (LLM) post-training. Like reinforcement learning (RL), however, OPD faces an on-policy systems bottleneck, as rollouts can dominate training time for reasoning workloads. Asynchronous training pipelines can alleviate this bottleneck by decoupling rollout generation from learner updates, but doing so introduces stale-policy data. While prior work has studied stale data in asynchronous RL, its effects in OPD remain underexplored. We present the first systematic study of staleness in asynchronous OPD, focusing on a practical setting where teacher feedback is implemented through local KL losses and full-vocabulary teacher logits are too expensive to store or transfer, necessitating finite teacher-score caches. We first show that KL direction changes the stale-data problem: teacher-weighted forward KL is more robust to stale rollouts, whereas student-weighted reverse KL is vulnerable. Second, for this vulnerable reverse-KL case, we study whether methods designed to stabilize asynchronous RL can mitigate OPD staleness. In our experiments, they do not improve over a simpler OPD-specific surrogate: recomputing the reverse-KL signal under the current student at learner time. Third, we analyze how finite teacher-score caches create a bias-variance tradeoff for sparse and sampled reverse-KL OPD estimators. This motivates multi-sample Monte Carlo (MC), which preserves MC correctability while reducing one-sample variance. Finally, we present and open-source AsyncOPD, a fully asynchronous OPD training pipeline built from these estimator choices. Experiments show that AsyncOPD improves training throughput by 1.6times to 3.8times over strict synchronous training while reaching comparable accuracy.

furiosa-ai FuriosaAI
·
Jun 22 2

Verify Before You Distill: Prompt-Level Teacher Gating for On-Policy Distillation

On-policy distillation (OPD) accelerates post-training by providing dense token-level supervision from a frozen teacher on the student's own rollouts. Vanilla OPD applies this supervision uniformly across prompts, without checking whether the teacher is reliable for each prompt. Because reverse KL is mode-seeking, a confidently wrong teacher can induce a strong yet misleading update. Distributional proxies, such as entropy or teacher-student likelihood agreement, measure uncertainty or agreement but do not directly verify outcome correctness. We introduce Teacher-Gated On-Policy Distillation (TGOPD), built on the principle that teacher reliability should be verified at the prompt level before dense supervision is admitted. TGOPD estimates reliability from a small set of verifier-scored teacher probes and routes each prompt exclusively to dense OPD when the reliability check passes or to verifier-grounded GRPO otherwise. Across 4B and 35B students in mathematics, code, and instruction following, TGOPD outperforms Vanilla OPD in all six single-domain settings and achieves higher seven-benchmark averages at both scales under multi-domain training. By using otherwise-idle teacher capacity for reliability estimation, TGOPD also reduces teacher-side compute waste in asynchronous OPD, increasing teacher-node GPU utilization from 9.8% to 78.9% in the measured 4B single-domain run.

Coding Agent Memory Post-Training II: Unlocking the Memory Potential of Pre-trained File Operations for Long-Horizon Tasks via On-Policy Distillation

Language-model agents increasingly tackle long-horizon tasks whose interaction histories exceed the model's active context. They must therefore decide what to write down and what to read back, and when to do either. Recent work has begun to use on-policy distillation (OPD) to make memory control part of the policy, relying on memory tools and compaction protocols that lie outside either model's pre-training. However, this weakens the distillation on both sides: the teacher cannot give useful guidance on an interface it has never used, and the student samples too few meaningful memory actions for that guidance to take effect. To study this problem, we introduce Coding Agent Memory Gym II (CAMG-II), a suite of long-horizon agentic-RL environments spanning Shop, Coding, AutoResearch, General, and Visual. Alongside each environment's native task interface, CAMG-II provides ordinary Bash access and an episode-persistent workspace, enabling the policy to create, revise, search, and reuse files as memory across context replacements. We also introduce Coding Agent Memory Post-Training II (CAMP-II), which trains a single policy jointly across all five environments with fully asynchronous OPD to learn this file-based memory behavior directly from a frozen teacher with a prior for file operations. On CAMG-II, CAMP-II obtains 2.97 times the gain of the strongest OPD baseline. The memory behavior CAMP-II learns generalizes to two external benchmarks, Terminal-Bench 2.1 and SWE-Bench Pro V2, with improved success rates.

  • 12 authors
·
Nov 9

DivOPD: Spread Wide, Look Close for Asynchronous On-Policy Distillation of Multi-turn Agents

On-policy distillation (OPD) trains student agents through teacher supervision on their own interactions with an environment. However, in asynchronous multi-turn training, arrival-order batching can allow a few early or long rollouts to dominate learner updates while other valid rollouts become stale before being used, wasting already-generated experience. To address this problem, we introduce DivOPD, a simple learner-side batch-selection method that spreads a fixed turn budget across more rollouts and, within each rollout, prioritizes turns with larger cumulative teacher-student disagreement. Turns without usable teacher feedback are excluded. The per-turn loss and optimizer remain fixed; selection only changes which student-visited turns receive training weight. For no-progress rollouts, an optional extension briefly hands control to the teacher before returning it to the student. Across six teacher-student settings on the simulated ALFWorld, ScienceWorld, and WebShop benchmarks, with 1.5B-7B students, DivOPD raises cross-setting mean peak success rate from 77.4 to 84.4 and mean success over the last five evaluations from 71.5 to 78.6. It reaches all reported setting-specific targets with geometric-mean speedups of 1.84x in training tokens and 1.87x in learner GPU time relative to vanilla OPD. Teacher intervention further raises this last-five mean to 82.4 while retaining about 1.7x learner-GPU speedup over vanilla OPD. Code will be released at https://github.com/HanyangWang0418-oss/DivOPD.

  • 10 authors
·
Sep 27

Act First, Reason Later: Accelerating On-Policy Distillation for Multi-Turn Agents via Reference-Conditioned Inverse Dynamics

On-policy distillation (OPD) trains multi-turn language agents with dense teacher supervision on student-generated responses. However, standard think-then-act rollouts require lengthy reasoning before each short action, delaying environment transitions and experience collection. Generating actions directly reduces this delay but can degrade rollout quality. To address this, we propose ActFirst-OPD, an act-first, reason-later training framework that decouples environment interaction from full-response generation. The student infers and executes actions through reference-conditioned inverse dynamics using its current interaction context and a reference next observation, and switches to autonomous next-action prediction when the resulting transition deviates from the reference trajectory. From the collected interaction contexts, the student asynchronously generates full think-then-act responses for token-level teacher supervision. Experiments across 0.6B-, 1.7B-, and 4B-parameter Qwen3 students show that ActFirst-OPD achieves average wall-clock training speedups of 2.3times on ALFWorld, 1.8times on WebShop, and 4.9times on ScienceWorld over Vanilla OPD. It matches or exceeds all compared OPD baselines in mean task success rate across eight of nine benchmark-model settings. These results demonstrate that reasoning need not block acting during multi-turn agent distillation.

AsyncBEV: Cross-modal Flow Alignment in Asynchronous 3D Object Detection

In autonomous driving, multi-modal perception tasks like 3D object detection typically rely on well-synchronized sensors, both at training and inference. However, despite the use of hardware- or software-based synchronization algorithms, perfect synchrony is rarely guaranteed: Sensors may operate at different frequencies, and real-world factors such as network latency, hardware failures, or processing bottlenecks often introduce time offsets between sensors. Such asynchrony degrades perception performance, especially for dynamic objects. To address this challenge, we propose AsyncBEV, a trainable lightweight and generic module to improve the robustness of 3D Birds' Eye View (BEV) object detection models against sensor asynchrony. Inspired by scene flow estimation, AsyncBEV first estimates the 2D flow from the BEV features of two different sensor modalities, taking into account the known time offset between these sensor measurements. The predicted feature flow is then used to warp and spatially align the feature maps, which we show can easily be integrated into different current BEV detector architectures (e.g., BEV grid-based and token-based). Extensive experiments demonstrate AsyncBEV improves robustness against both small and large asynchrony between LiDAR or camera sensors in both the token-based CMT and grid-based UniBEV, especially for dynamic objects. We significantly outperform the ego motion compensated CMT and UniBEV baselines, notably by 16.6 % and 11.9 % NDS on dynamic objects in the worst-case scenario of a 0.5 s time offset. Code will be released upon acceptance.

  • 4 authors
·
Jan 18

OphBiWSSD: Scaling Temporal Action Localization in Ophthalmic Surgeries with Bidirectional Weight-tied State Space Duality

High-frequency surgical maneuvers in ophthalmology necessitate high-fidelity temporal modeling, yet characterizing long-range procedural dependencies remains computationally prohibitive for attention-based architectures. Existing models often require aggressive temporal downsampling, which compromises the detection of fine-grained action boundaries and instrument-tissue interactions. To address these scalability constraints, we present OphBiWSSD, a framework that reformulates surgical temporal action localization leveraging Bidirectional State Space Duality. By employing a weight-tied selective scan mechanism that incorporates both preceding and succeeding surgical contexts, our approach facilitates the global synthesis of non-causal temporal cues with linear complexity. This streamlined architecture is well-suited to capture the bidirectional dependencies present in ophthalmic workflows, effectively bridging the gap between local boundary precision and long-range procedural context without incurring the quadratic memory overhead of traditional Transformers. Extensive experiments on the OphNet benchmark demonstrate that OphBiWSSD achieves state-of-the-art temporal localization performance, with mean Average Precisions of 44.42% on phases and 43.08% on operations, surpassing the baselines by 6.80% and 6.66%, respectively. Empirical validation indicates that our approach ensures precise temporal localization and offers a computationally viable pathway for deploying surgical intelligence systems in clinical environments. The code is publicly available at https://github.com/yo3nglau/OphBiWSSD.

  • 13 authors
·
Sep 10

Stable Asynchrony: Variance-Controlled Off-Policy RL for LLMs

Asynchronous reinforcement learning has become increasingly central to scaling LLM post-training, delivering major throughput gains by decoupling rollout generation from policy updates. However, widely used policy-gradient objectives such as REINFORCE and GRPO suffer under high asynchrony: stale rollouts produce heavy-tailed importance weights, so a small number of trajectories dominate updates and the policy-gradient estimator becomes markedly higher variance. Through systematic analysis on math, reasoning, and tool-use benchmarks, we find that this increasing variance is reliably predicted by collapsing effective sample size (ESS), which prior stabilization methods largely fail to address. Motivated by this diagnosis, we introduce Variance Controlled Policy Optimization (VCPO), a method that (i) dynamically scales the learning rate with ESS to dampen unreliable updates and (ii) applies a closed-form minimum-variance baseline for off-policy settings, without a critic model and adding minimal overhead. Empirically, across math and general reasoning benchmarks, this enables robustly stable asynchronous training compared to previous stabilization and algorithmic methods, even in highly off-policy regimes (128 steps off-policy). In a long-horizon, tool-use task, VCPO matches synchronous performance while delivering a 2.5times speedup in training time. Code is available at: https://github.com/mit-han-lab/vcpo

  • 5 authors
·
Feb 19

Reactive Real-Time Flow Policies via Asynchronous Distribution Alignment

Generalist robot policies such as vision-language-action models (VLAs) have achieved remarkable generalization, but their inference delays can conflict with the demands of real-time control. Asynchronous execution avoids pauses between action chunks by predicting the next sequence of actions while the robot carries out the previous one. In this paper, we study whether asynchronous execution produces the same action distribution as the original VLA. We find that, for non-Markovian demonstrations, asynchronous execution can produce a fundamentally different action distribution, which can limit the policy's reactivity. In our method, we seek to restore this reactivity by aligning the asynchronously produced action distribution with that of the original VLA through two complementary mechanisms. First, Recursive Flow-Field Distillation trains the asynchronous policy using the VLA's action-generation flow. We characterize the learned distribution theoretically and show experimentally that our asynchronous policy can generate nearly the full range of actions the original VLA would produce, while existing asynchronous methods recover only a fraction of that range. Second, Propose-Resolve prepares multiple action sequences asynchronously and uses the latest observation to select among them based on a lightweight approximation of their likelihood under the VLA's action distribution. Our resulting method matches the original VLA's success on LIBERO and retains about 80% of its success on RoboMimic, about 30 percentage points more than existing asynchronous methods.

  • 4 authors
·
Sep 28

Visual Contrastive Self-Distillation

On-policy self-distillation (OPSD) is promising as it removes the external teacher required by on-policy distillation (OPD), yet it still needs asymmetric information between teacher and student to ensure that the self-teacher provides a stronger learning signal than the student. Existing methods create this asymmetry either through privileged answers or visual evidence. We ask whether both can be removed, yielding a simpler form of OPSD driven purely by input conditioning. For this purpose, we propose Visual Contrastive Self-Distillation, namely VCSD, which converts image-content removal into an on-policy self-distillation signal. At each student-generated response prefix, the EMA teacher produces two next-token distributions under the same prompt and prefix -- one conditioned on the original image and the other on a content-erased control. Their token-wise log-probability difference highlights candidates whose likelihood is specifically increased by the instance-level visual content. We use this contrast to sharpen the teacher's original-image distribution within its plausible support, and distill the resulting full-distribution target into the student. Using ViRL39K dataset, VCSD consistently outperforms matched OPSD across Qwen3-VL and Qwen3.5 models. For example, on Qwen3-VL, it improves the seven-benchmark aggregate from 62.27% rightarrow 67.04% at 2B, 71.30% rightarrow 73.16% at 4B, and 72.51% rightarrow 76.26% at 8B. Furthermore, VCSD requires no external teacher, privileged answers, visual evidence signals, reasoning traces, or additional inference-time cost.

Periodic Asynchrony: An On-Policy Approach for Accelerating LLM Reinforcement Learning

Since the introduction of the GRPO algorithm, reinforcement learning~(RL) has attracted increasing attention for LLM post-training, yet training efficiency remains a critical challenge. In mainstream RL frameworks, inference and training are co-located on the same devices, and their synchronous execution prevents concurrent inference and training. In this work, we revisit the strategy of separating inference and training deployment, and propose a periodically asynchronous framework that transforms synchronous RL training into an asynchronous producer--consumer pipeline. By synchronising model weights at the beginning of each training iteration and generating all rollouts from the same policy, the proposed framework remains inherently on-policy, avoiding the off-policy bias introduced by existing asynchronous approaches without any modification to standard RL algorithms. We further introduce a unified tri-model architecture and a shared-prompt attention mechanism to support efficient asynchronous execution and reduce redundant computation. Experiments on NPU platforms show that the proposed framework achieves around 2times throughput improvement from asynchronous execution, with additional gains from system-level optimisations, substantially outperforming mainstream RL frameworks in end-to-end training throughput while maintaining comparable accuracy. Further validation on GPU platforms confirms that the proposed framework generalises effectively across hardware architectures, indicating its potential for widespread application.

  • 1 authors
·
Apr 27

One-Step Gradient Delay is Not a Barrier for Large-Scale Asynchronous Pipeline Parallel LLM Pretraining

Modern large-scale LLM pretraining benefits from utilizing Pipeline Parallelism; however, synchronous implementations leave GPUs idle during pipeline bubbles, wasting computational resources. Asynchronous Pipeline Parallelism eliminates these bubbles, maximizing throughput at the cost of gradient staleness. Among asynchronous schedules, PipeDream-2BW is particularly appealing: unlike the original PipeDream schedule, it ensures a constant one-step gradient delay regardless of pipeline depth. However, its adoption remains limited due to the common belief that optimizing under staleness is fundamentally unstable. In this work, we challenge this assumption, demonstrating that degradation under one-step delay depends strongly on optimizer choice rather than being an intrinsic limitation. We provide the first comprehensive empirical analysis showing that while AdamW, the predominant optimizer at the time when PipeDream-2BW was introduced, indeed suffers from severe degradation, recent methods like Muon exhibit strong robustness under a one-step delay. We introduce an optimizer-agnostic Error Feedback-inspired correction to further mitigate delay effects. We provide supporting theoretical analysis demonstrating convergence for Muon with and without this correction. Extensive evaluation on models up to 10B parameters confirms that our strategies bridge the performance gap with synchronous training, highlighting the practical potential of asynchronous pipeline parallelism at scale.

ReNIO: Reweighting Negative Trajectory Importance for LLM On-Policy Distillation

On-policy distillation (OPD) improves LLM reasoning by training a student model on its own generated outputs, but standard OPD treats all student-generated outputs (SGOs) equally regardless of their informativeness. We observe a consistent asymmetry in controlled filtering experiments: in both OPD and on-policy self distillation (OPSD), training only on incorrect SGOs outperforms training only on correct ones. Our further analysis suggests that models trained on correct-only SGOs tend to generate shorter reasoning traces and show weaker reflection behavior, while incorrect SGOs better preserve exploratory reasoning near the model's capability boundary. To exploit this signal without requiring full answer-containing rollouts, we introduce ReNIO, which Reweights Negative trajectory Importance for LLM On-policy distillation. By using the student-to-teacher probability ratio, ReNIO identifies pivotal tokens leading to wrong reasoning traces and aggregates their information into a normalized sample weight, inherently assigning larger weights to likely negative trajectories without observing the correctness of final-answer. Since Re-NIO only uses prefix-conditioned token probabilities, it preserves OPD's prefix training advantage over full-rollout reinforcement learning. Across both mathematical reasoning and code generation tasks, ReNIO improves both OPD and OPSD, with representative relative gains of up to 8.90% for Qwen3-1.7B and 10.00% for R1-Distill-Qwen-7B on mathematical reasoning benchmarks. Code repo: https://github.com/BDML-lab/ReNIO.

Learning to Foresee: Unveiling the Unlocking Efficiency of On-Policy Distillation

On-policy distillation (OPD) has emerged as an efficient post-training paradigm for large language models. However, existing studies largely attribute this advantage to denser and more stable supervision, while the parameter-level mechanisms underlying OPD's efficiency remain poorly understood. In this work, we argue that OPD's efficiency stems from a form of ``foresight'': it establishes a stable update trajectory toward the final model early in training. This foresight manifests in two aspects. First, at the Module-Allocation Level, OPD identifies regions with low marginal utility and concentrates updates on modules that are more critical to reasoning. Second, at the Update-Direction Level, OPD exhibits stronger low-rank concentration, with its dominant subspaces aligning closely with the final update subspace early in training. Building on these findings, we propose EffOPD, a plug-and-play acceleration method that speeds up OPD by adaptively selecting an extrapolation step size and moving along the current update direction. EffOPD requires no additional trainable modules or complex hyperparameter tuning, and achieves an average training acceleration of 3times while maintaining comparable final performance. Overall, our findings provide a parameter-dynamics perspective for understanding the efficiency of OPD and offer practical insights for designing more efficient post-training methods for large language models.

Rethinking On-Policy Distillation of Large Language Models II: One Training Example

On-policy distillation (OPD) combines student-generated rollouts with dense token-level supervision from a teacher. Existing work has mainly studied its algorithmic behavior, leaving the role of training data unclear. We examine this role at the data-minimal limit by training on a single query. One-shot OPD keeps improving for hundreds of steps and recovers most of full-data OPD's gain across task domains and model families. We explain this result through the states visited during training and the rate at which the student aligns with the teacher. We measure state coverage, the fraction of the states full-data OPD visits that a query set's rollouts reach. A single query already reaches \(71.5\%\), most of it within the first 100 steps. Adding semantically distinct queries raises coverage and validation accuracy together, until 16 queries reach \(98.9\%\) and match full-data training. Yet alignment slows at a similar pace whether OPD trains on one query or the whole dataset, and even a fixed set of states takes hundreds of steps to absorb. OPD is therefore data-overfed but algorithm-starved. Its rollouts quickly expose broad supervision, while the student absorbs that supervision increasingly slowly. The state-coverage result extends to multi-teacher OPD, where 16 semantically diverse queries per domain match full-data MOPD. As a further stress test, content-light templates and off-domain WildChat queries also approach the real-query baseline. Task content and induced state coverage can therefore come apart. We hope these findings direct future work toward the step efficiency of OPD, and prompt a re-examination of the data and the mechanisms behind its recent successes in frontier post-training.

VLASH: Real-Time VLAs via Future-State-Aware Asynchronous Inference

Vision-Language-Action models (VLAs) are becoming increasingly capable across diverse robotic tasks. However, their real-world deployment remains slow and inefficient: demonstration videos are often sped up by 5-10x to appear smooth, with noticeable action stalls and delayed reactions to environmental changes. Asynchronous inference offers a promising solution to achieve continuous and low-latency control by enabling robots to execute actions and perform inference simultaneously. However, because the robot and environment continue to evolve during inference, a temporal misalignment arises between the prediction and execution intervals. This leads to significant action instability, while existing methods either degrade accuracy or introduce runtime overhead to mitigate it. We propose VLASH, a general asynchronous inference framework for VLAs that delivers smooth, accurate, and fast reaction control without additional overhead or architectural changes. VLASH estimates the future execution-time state by rolling the robot state forward with the previously generated action chunk, thereby bridging the gap between prediction and execution. Experiments show that VLASH achieves up to 2.03x speedup and reduces reaction latency by up to 17.4x compared to synchronous inference while fully preserving the original accuracy. Moreover, it empowers VLAs to handle fast-reaction, high-precision tasks such as playing ping-pong and playing whack-a-mole, where traditional synchronous inference fails. Code is available at https://github.com/mit-han-lab/vlash

  • 10 authors
·
Nov 30, 2025 1

WDL-OPD: Weak-Driven On-Policy Distillation via Mixture-Constrained Co-Training

On-policy distillation (OPD) aligns a student with a teacher on trajectories sampled from the student itself, reducing the train-test state mismatch of offline distillation. The same feedback loop can nevertheless be unstable: each update changes both the policy and the states on which the next update is computed. We introduce WDL-OPD, a mixture-constrained co-training method with two trainable policies. An anchor policy generates every rollout, an auxiliary policy evaluates the same visited states, and a geometric mixture of their token distributions is matched to a frozen teacher by reverse KL. Both policies receive gradient. We show that freezing the auxiliary recovers an anchor-plus-contrast proxy target closely related to OPD^2 and W2S-OPD, whereas joint training creates branch-level degrees of freedom that a static delta cannot express. In recorded Qwen3 experiments at 1.7B and 4B scale, WDL-OPD produces the strongest student checkpoint in each of four scale-domain settings. It raises MATH500 accuracy from 0.630 to 0.685 at 4B and from 0.521 to 0.585 at 1.7B. In code generation, seven single-policy OPD configurations exhibit entropy growth or trajectory degradation, while co-training reaches independently re-evaluated development scores of 0.637 and 0.375. Because several comparisons differ in curriculum or initialization, these results support a stabilization hypothesis rather than a universal causal claim. We provide the exact training algorithm, failure evidence, and the controlled comparison matrix needed to test that hypothesis.

  • 12 authors
·
Sep 2

Single-Rollout Asynchronous Optimization for Agentic Reinforcement Learning

Reinforcement learning (RL) is becoming increasingly important for post-training large language models (LLMs). Previous RL pipelines for LLMs were mostly synchronous and batch-interleaved, which is inefficient for long-horizon agentic tasks. Recently, asynchronous RL has emerged as a more efficient alternative by updating the model as rollouts arrive. However, existing asynchronous RL systems often emphasize throughput, while leaving training stability and task effectiveness largely underexplored. For example, a key challenge is that group-wise sampling in the widely-used GRPO framework does not naturally fit asynchronous agentic training. In this paper, we present Single-rollout Asynchronous Optimization (SAO) to address the stability and off-policy challenges in asynchronous RL. To reduce off-policy effects and improve generalization, we replace group-wise sampling with single-rollout sampling, that is, using one rollout per prompt. We further improve this single-rollout strategy with practical value-model training designs. To improve optimization stability, we introduce a strict double-side token-level clipping strategy. SAO is able to train stably for one thousand steps and consistently outperform GRPO and its variants on agentic coding and reasoning benchmarks, such as SWE-Bench Verified, BeyondAIME, and IMOAnswerBench. We also demonstrate that single-rollout RL is particularly effective in a simulated online learning setting, where the model must adapt to changing evolving environments. To this end, SAO is successfully deployed in the agentic RL pipeline for training the open GLM-5.2 model (750B-A40B).

zai-org Z.ai
·
Jul 7 11

On-Policy Self-Distillation without Any Supervision

On-policy (Self-)Distillation (OPD / OPSD) has shown strong potential for post-training large language models (LLMs). However, existing methods still rely heavily on external supervision, including ground-truth signals, environmental feedback, or guidance from larger models, and therefore fall short of genuine "self"-distillation. In this study, we show that on-policy self-distillation can be achieved using only a model's own generations via internal consistency. We propose unsupervised on-policy self-distillation (U-OPSD). U-OPSD first samples multiple rollouts and constructs a pseudo solution by majority vote under a self-consistency threshold. It then conditions the model's distribution on the pseudo-solution and distills itself on the disagreeing completions, allowing the model to correct itself precisely where it is confidently wrong. Across diverse benchmarks, base models, and training settings, U-OPSD consistently improves over the base models and matches or surpasses supervised methods with ground truth (GT) such as OPSD and GRPO. On five mathematical reasoning benchmarks, i.e., AIME24, AIME25, HMMT25, MATH500, and AMC23, U-OPSD improves over the base model by 8.5% and 10.7% on Qwen3 non-thinking mode at 4B and 8B scales, and outperforms OPSD by 3.2% and 2.3% on average, respectively. In thinking mode, U-OPSD stays on par with OPSD, ahead by 0.9% at 4B and level at 8B and surpassing GRPO by 0.7% and 1.1%, respectively. Code is available at [https://github.com/williamium3000/u-opsd](https://github.com/williamium3000/u-opsd).