Daily Papers

Large language model agents are commonly trained through reinforcement learning with sparse trajectory-level rewards, which offer limited guidance on how strongly individual tokens should be updated. On-Policy Self-Distillation (OPSD) addresses this by re-scoring generated tokens under a privileged replay view to obtain dense, token-level supervision. However, we identify a confounding issue: the resulting support may reflect both the privileged information contained in the replay view and score shifts induced by the replay scaffold, making it difficult to attribute the support specifically to that information. This issue is especially pronounced when future environment observations serve as privileged information, since replaying them requires reconstructing an extended scaffold that itself perturbs token scores. To resolve this confounding, we propose Observation-Calibrated Self-Distillation (OCSD), which contrasts two structurally matched replay views, Full and Observation-Ablated, differing only in whether the actual future observation is present, to derive an observation residual that discounts score changes shared by the replay scaffold. OCSD then applies this residual to modulate token-level GRPO updates at high-uncertainty steps, while preserving the trajectory-level update direction. Experiments on ALFWorld, WebShop, and Search-QA across three Qwen3 model scales show that OCSD consistently outperforms strong baselines. Diagnostic analyses further confirm that the calibrated residual aligns better with local environment feedback. Our code is publicly available at https://github.com/yiy1x/OCSD.

Self-distillation (SD) is the process of retraining a student on a mixture of ground-truth labels and the teacher's own predictions using the same architecture and training data. Although SD has been empirically shown to often improve generalization, its formal guarantees remain limited. We study SD for ridge regression in unconstrained setting in which the mixing weight ξ may be outside the unit interval. Conditioned on the training data and without any distributional assumptions, we prove that for any squared prediction risk (including out-of-distribution), the optimally mixed student strictly improves upon the ridge teacher for every regularization level λ> 0 at which the teacher ridge risk R(λ) is nonstationary (i.e., R'(λ) neq 0). We obtain a closed-form expression for the optimal mixing weight ξ^star(λ) for any value of λ and show that it obeys the sign rule: sign(ξ^star(λ))=-sign(R'(λ)). In particular, ξ^star(λ) can be negative, which is the case in over-regularized regimes. To quantify the risk improvement due to SD, we derive exact deterministic equivalents for the optimal SD risk in the proportional asymptotics regime (where the sample and feature sizes n and p both diverge but their aspect ratio p/n converges) under general anisotropic covariance and deterministic signals. Our asymptotic analysis extends standard second-order ridge deterministic equivalents to their fourth-order analogs using block linearization, which may be of independent interest. From a practical standpoint, we propose a consistent one-shot tuning method to estimate ξ^star without grid search, sample splitting, or refitting. Experiments on real-world datasets and pretrained neural network features support our theory and the one-shot tuning method.

On-policy self-distillation (OPSD) combines student generated trajectories with dense supervision from a privileged teacher of the same model. Its pointwise clipping protects the student from locally incompatible teacher directions, but the fixed teacher receives no feedback about the supervision the student rejects, which limits effective learning from the teacher. We introduce DualOPSD, which alternates updates in a coupled teacher-student system. The student retains OPSD's clipped forward KL objective. The privileged teacher adapts to the updated student after each student step. A residual target based on the frozen initial model preserves the effect of privileged context during teacher adaptation. Across Qwen3-8B/4B/1.7B and three math benchmarks, DualOPSD improves avg@12 accuracy over OPSD by 9.83 percentage points. Further diagnostic analyses show lower bidirectional KL, less persistent mismatch, and retained sensitivity to privileged reference. Together, these results demonstrate that DualOPSD can be a more effective form of privileged self-distillation. Code is available at: https://github.com/on1262/DualOPSD.

Self-distillation enables language models to learn on-policy from their own trajectories by using the same model as both student and teacher, with the teacher being conditioned on privileged information unavailable to the student. Such information can come in different types or views, such as solutions, demonstrations, feedback, or final answers. This setup provides dense token-level feedback without relying on a separate external model, but creates a fundamental asymmetry: the teacher may rely on view-specific information that the student cannot access at inference time. Moreover, the best type of privileged information is often task-dependent, making it difficult to choose a single teacher view. In this work, we address both these challenges jointly by introducing AVSD (Adaptive-View Self-Distillation), a novel method of self-distillation with multiple privileged-information views, which reconstructs token-level supervision by separating stable cross-view consensus from view-specific residual signals. AVSD identifies the consensus signal shared across views, which provides a reliable update direction, and then selectively adds the view-specific residual signal to adjust the update magnitude when it both aligns with the consensus direction and remains proportionate to the consensus signal. Experiments on math competition benchmarks (AIME24, AIME25, and HMMT25) show that AVSD consistently outperforms both single-view self-distillation baselines and GRPO, achieving average Avg@8 gains of 3.1% and 2.2% over the strongest baselines on Qwen3-8B and Qwen3-4B, respectively. Moreover, on code-generation benchmarks (Codeforces, LiveCodeBench v6) using Qwen3-8B, AVSD outperforms the single-view self-distillation baseline by 2.4% on average.

On-policy self-distillation (OPSD) is an emerging LLM post-training paradigm in which the model serves as its own teacher: conditioned on privileged information such as a reference trace or hint, the same policy provides dense token-level supervision on its own rollouts. However, recent studies show that OPSD degrades complex reasoning by suppressing predictive uncertainty, which supports exploration and hypothesis revision. Our token-level analysis shows that this failure arises from applying a uniform direction of teacher supervision across tokens with different uncertainty levels: conformity to the privileged self-teacher suppresses exploration at high entropy, while deviation from the teacher degrades step accuracy at low entropy. Accordingly, we propose Direction-Adaptive Self-Distillation (DASD), which reframes privileged self-distillation from uniform teacher imitation into entropy-routed directional supervision: high-entropy tokens are pushed away from the privileged teacher to preserve exploration, while low-entropy tokens are pulled toward the teacher to stabilize step-level execution. Across six mathematical reasoning benchmarks, DASD achieves the best macro Avg@16 over strong RLVR and self-distillation baselines. Pass@k, reasoning-health, and generalization analyses show that these average gains come from preserving exploration without sacrificing step-level execution.

Self-Distillation is a special type of knowledge distillation where the student model has the same architecture as the teacher model. Despite using the same architecture and the same training data, self-distillation has been empirically observed to improve performance, especially when applied repeatedly. For such a process, there is a fundamental question of interest: How much gain is possible by applying multiple steps of self-distillation? To investigate this relative gain, we propose studying the simple but canonical task of linear regression. Our analysis shows that the excess risk achieved by multi-step self-distillation can significantly improve upon a single step of self-distillation, reducing the excess risk by a factor as large as d, where d is the input dimension. Empirical results on regression tasks from the UCI repository show a reduction in the learnt model's risk (MSE) by up to 47%.

On-policy distillation (OPD) has become a popular training paradigm in the LLM community. This paradigm selects a larger model as the teacher to provide dense, fine-grained signals for each sampled trajectory, in contrast to reinforcement learning with verifiable rewards (RLVR), which only obtains sparse signals from verifiable outcomes in the environment. Recently, the community has explored on-policy self-distillation (OPSD), where the same model serves as both teacher and student, with the teacher receiving additional privileged information such as reference answers to enable self-evolution. This paper demonstrates that learning signals solely derived from the privileged teacher result in severe information leakage and unstable long-term training. Accordingly, we identify the optimal niche for self-distillation and propose RLSD (RLVR with Self-Distillation). Specifically, we leverage self-distillation to obtain token-level policy differences for determining fine-grained update magnitudes, while continuing to use RLVR to derive reliable update directions from environmental feedback (e.g., response correctness). This enables RLSD to simultaneously harness the strengths of both RLVR and OPSD, achieving a higher convergence ceiling and superior training stability.

On-policy distillation (OPD) improves reasoning models by learning the token-level discrepancy between a stronger teacher and an on-policy student. However, this discrepancy does not purely reflect the capability gap between the teacher and the student: it also contains deviations arising from the teacher itself, which are consequently mixed into the observed teacher--student discrepancy and indiscriminately learned by standard OPD during training. This issue is further exacerbated by privileged OPD, where privileged information induces larger teacher-side likelihood shifts, thereby encouraging the student to learn more of the teacher's own deviation. We introduce Calibrated On-Policy Distillation (Cal-OPD), which estimates the teacher's self-deviation region through positive and negative privileged interventions and calibrates the original teacher--student discrepancy by retaining only the component that lies beyond this region. Experiments on mathematical reasoning benchmarks show that, while retaining only about 52--65\% of the original teacher--student discrepancy as the optimization signal, Cal-OPD consistently outperforms standard OPD and its variants across model scales.

Current post-training methods in verifiable settings fall into two categories. Reinforcement learning (RLVR) relies on binary rewards, which are broadly applicable and powerful, but provide only sparse supervision during training. Distillation provides dense token-level supervision, typically obtained from an external teacher or using high-quality demonstrations. Collecting such supervision can be costly or unavailable. We propose Self-Distillation Zero (SD-Zero), a method that is substantially more training sample-efficient than RL and does not require an external teacher or high-quality demonstrations. SD-Zero trains a single model to play two roles: a Generator, which produces an initial response, and a Reviser, which conditions on that response and its binary reward to produce an improved response. We then perform on-policy self-distillation to distill the reviser into the generator, using the reviser's token distributions conditioned on the generator's response and its reward as supervision. In effect, SD-Zero trains the model to transform binary rewards into dense token-level self-supervision. On math and code reasoning benchmarks with Qwen3-4B-Instruct and Olmo-3-7B-Instruct, SD-Zero improves performance by at least 10% over the base models and outperforms strong baselines, including Rejection Fine-Tuning (RFT), GRPO, and Self-Distillation Fine-Tuning (SDFT), under the same question set and training sample budget. Extensive ablation studies show two novel characteristics of our proposed algorithm: (a) token-level self-localization, where the reviser can identify the key tokens that need to be revised in the generator's response based on reward, and (b) iterative self-evolution, where the improving ability to revise answers can be distilled back into generation performance with regular teacher synchronization.

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).

Knowledge distillation is classically a procedure where a neural network is trained on the output of another network along with the original targets in order to transfer knowledge between the architectures. The special case of self-distillation, where the network architectures are identical, has been observed to improve generalization accuracy. In this paper, we consider an iterative variant of self-distillation in a kernel regression setting, in which successive steps incorporate both model outputs and the ground-truth targets. This allows us to provide the first theoretical results on the importance of using the weighted ground-truth targets in self-distillation. Our focus is on fitting nonlinear functions to training data with a weighted mean square error objective function suitable for distillation, subject to ell_2 regularization of the model parameters. We show that any such function obtained with self-distillation can be calculated directly as a function of the initial fit, and that infinite distillation steps yields the same optimization problem as the original with amplified regularization. Furthermore, we provide a closed form solution for the optimal choice of weighting parameter at each step, and show how to efficiently estimate this weighting parameter for deep learning and significantly reduce the computational requirements compared to a grid search.

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.

We study multi-domain LLM training in which two models, each stronger in a different domain, co-evolve by tutoring each other through on-policy feedback. Unlike one-way distillation or single-model fine-tuning, our goal is mutual Pareto improvement: each model improves across domains without losing its original strength. To this end, we propose On-Policy Co-Distillation (OPCoD), where each student's self-distillation is conditioned on its own correct rollout and feedback from its peer. To make feedback exchange effective, OPCoD uses cognizance-based gating to decide when to give feedback and feedback anchoring to ground feedback in the problem. On Science Q\&A tasks, OPCoD consistently outperforms baselines and achieves Pareto improvement across all evaluated domain pairs and students.

Text-Image-to-Video (TI2V) models are an emerging unified architecture, where a single model simultaneously supports text-to-video (T2V) and image-to-video (I2V) generation. Given a high-quality first frame or a detailed textual prompt, TI2V models unlock substantially better visual quality than their T2V mode, raising a natural question: can the capability elicited by such privileged conditions be internalized into the model's own base generation ability? A common approach toward this goal is model self-distillation. However, the most straightforward solution, supervised fine-tuning, follows an off-policy strategy: its supervision is confined to teacher-generated endpoints from a fixed offline distribution rather than student-visited states, lacking precise correction tailored to the evolving policy. Recent on-policy distillation methods instead suffer from condition-state mismatch, where supervision is steered toward the given first frame instead of the student's actual content, misleading the correction. To achieve self-distillation that absorbs the teacher's privileged prior while retaining precise policy correction, in this work, we propose Hybrid-Policy Self-Distillation (HPSD), a novel self-distillation framework where a single TI2V model acts as both teacher and student under different conditions: the teacher operates in TI2V mode with a high-quality first frame and an enhanced prompt, while the student runs in the base T2V mode with only the vanilla prompt. Specifically, the student inherits off-policy teacher trajectory points as anchors, locally refines them toward its own policy, and finally receives velocity-level supervision on these self-generated roll-outs. Extensive experiments demonstrate that HPSD significantly improves T2V performance while also delivering notable TI2V gains, effectively strengthening the model's base generation ability.

Self-Distillation Fine-Tuning (SDFT) enables a language model to act as its own teacher: by conditioning on a demonstration, the model produces an implicit reward via pointwise mutual information, which guides on-policy learning without external supervision. However, SDFT operates at training time: it requires gradient updates and access to expert demonstrations, making it inapplicable at inference. We propose test-time self-distillation, a decoding-time method that extracts a steering signal from the self-distillation framework without any parameter updates, reward models, or training data. Our key insight is that counterfactual contexts, i.e. fixed textual templates that hypothetically prime the model for excellent versus poor reasoning, can substitute for the demonstration. The log-odds ratio of a candidate answer under these two counterfactual conditions defines a new reward signal. We derive the optimal KL-regularized policy under this reward, which takes the form of a Gibbs reweighting of the base distribution. Crucially, this reweighting is global: it cannot be decomposed into independent per-token operations without ignoring future trajectory quality. We therefore approximate the target distribution via beam search. Experiments on mathematical reasoning (MATH500), code generation (HumanEval), and graduate-level science QA (GPQA) across multiple model scales show that test-time self-distillation improves over standard sampling, low temperature, beam search and power sampling baselines on average, demonstrating that the self-distillation principle can be operationalized at inference time.

On-policy self-distillation (OPSD) trains a student to match a privileged teacher distribution along its own sampled trajectory. Standard OPSD applies this supervision to unverified student rollouts while conditioning the teacher on privileged context, typically a reference solution. We separate these roles in a factorial analysis and find that scaffold correctness has a stronger effect on downstream accuracy than context correctness. Unverified scaffolds create an imitation gap because the teacher can use information unavailable to the student. This gap shrinks with model scale, yet OPSD continues to supervise mostly unverified trajectories. In contrast, verified scaffolds remain effective even when the teacher is conditioned on the student's own unsuccessful rollout. Based on this finding, we introduce OASIS, which retains the OPSD objective but supervises mostly verified by label on-policy trajectories and replaces written solutions with unverified model-generated attempts as the teacher context. OASIS therefore requires only final-answer labels. Across Qwen3-1.7B, 4B, and 8B on AIME 2024, AIME 2025, and HMMT 2025, OASIS improves over the base model by 3.2--3.8 points on average, while OPSD's gain falls from 3.05 points at 1.7B to 0.14 at 8B. At 8B, OASIS improves over OPSD by 3.05 points, showing that verified on-policy scaffolds preserve the effectiveness of self-distillation as models scale.

Self-distillation (SD) is the process of first training a teacher model and then using its predictions to train a student model with the same architecture. Specifically, the student's objective function is big(xi*ell(teacher's predictions, student's predictions) + (1-xi)*ell(given labels, student's predictions)big), where ell is some loss function and xi is some parameter in [0,1]. Empirically, SD has been observed to provide performance gains in several settings. In this paper, we theoretically characterize the effect of SD in two supervised learning problems with noisy labels. We first analyze SD for regularized linear regression and show that in the high label noise regime, the optimal value of xi that minimizes the expected error in estimating the ground truth parameter is surprisingly greater than 1. Empirically, we show that xi > 1 works better than xi leq 1 even with the cross-entropy loss for several classification datasets when 50\% or 30\% of the labels are corrupted. Further, we quantify when optimal SD is better than optimal regularization. Next, we analyze SD in the case of logistic regression for binary classification with random label corruption and quantify the range of label corruption in which the student outperforms the teacher in terms of accuracy. To our knowledge, this is the first result of its kind for the cross-entropy loss.

On-policy distillation (OPD) is an increasingly important paradigm for post-training language models. However, we identify a pervasive Scaling Law of Miscalibration: while OPD effectively improves task accuracy, it systematically traps models in severe overconfidence. We trace this failure to an information mismatch: teacher supervision is formed under privileged context available during training, whereas the deployed model must report confidence using only deployment-time information. We formalize this perspective theoretically, showing that teacher-conditioned success is generally not a valid target for deployment-time confidence and that helpful privileged context induces entropy collapse and a systematic optimism bias. To address this, we propose a calibration-aware OPD framework, CaOPD, that estimates empirical confidence from model rollouts, replaces self-reported confidence with this student-grounded target, and distills the revised response through the same self-distillation pipeline. Experiments across various models and domains show that CaOPD achieves Pareto-optimal calibration while maintaining competitive capability, generalizing robustly under out-of-distribution and continual learning. Our findings highlight that capability distillation does not imply calibrated confidence, and that confidence should be treated as an essential objective in post-training. Code: https://github.com/SalesforceAIResearch/CaOPD

Large-scale multi-view reconstruction models have made remarkable progress, but most existing approaches still rely on fully supervised training with ground-truth 3D/4D annotations. Such annotations are expensive and particularly scarce for dynamic scenes, limiting scalability. We propose SelfEvo, a self-improving framework that continually improves pretrained multi-view reconstruction models using unlabeled videos. SelfEvo introduces a self-distillation scheme using spatiotemporal context asymmetry, enabling self-improvement for learning-based 4D perception without external annotations. We systematically study design choices that make self-improvement effective, including loss signals, forms of asymmetry, and other training strategies. Across eight benchmarks spanning diverse datasets and domains, SelfEvo consistently improves pretrained baselines and generalizes across base models (e.g. VGGT and π^3), with significant gains on dynamic scenes. Overall, SelfEvo achieves up to 36.5% relative improvement in video depth estimation and 20.1% in camera estimation, without using any labeled data. Project Page: https://self-evo.github.io/.

Self-distillation (SD) offers a promising path for adapting large language models (LLMs) without relying on stronger external teachers. However, SD in autoregressive LLMs remains challenging because self-generated trajectories are free-form, correctness is task-dependent, and plausible rationales can still provide unstable or unreliable supervision. Existing methods mainly examine isolated design choices, leaving their effectiveness, roles, and interactions unclear. In this paper, we propose UniSD, a unified framework to systematically study self-distillation. UniSD integrates complementary mechanisms that address supervision reliability, representation alignment, and training stability, including multi-teacher agreement, EMA teacher stabilization, token-level contrastive learning, feature matching, and divergence clipping. Across six benchmarks and six models from three model families, UniSD reveals when self-distillation improves over static imitation, which components drive the gains, and how these components interact across tasks. Guided by these insights, we construct UniSDfull, an integrated pipeline that combines complementary components and achieves the strongest overall performance, improving over the base model by +5.4 points and the strongest baseline by +2.8 points. Extensive evaluation highlights self-distillation as a practical and steerable approach for efficient LLM adaptation without stronger external teachers.

Iterative self-training (self-distillation) repeatedly refits a model on pseudo-labels generated by its own predictions. We study this procedure in overparameterized linear regression: an initial estimator is trained on noisy labels, and each subsequent iterate is trained on fresh covariates with noiseless pseudo-labels from the previous model. In the high-dimensional regime, we derive deterministic-equivalent recursions for the prediction risk and effective noise across iterations, and prove that the empirical quantities concentrate sharply around these limits. The recursion separates two competing forces: a systematic component that grows with iteration due to progressive signal forgetting, and a stochastic component that decays due to denoising via repeated data-dependent projections. Their interaction yields a U-shaped test-risk curve and an optimal early-stopping time. In spiked covariance models, iteration further acts as an iteration-dependent spectral filter that preserves strong eigendirections while suppressing weaker ones, inducing an implicit form of soft feature selection distinct from ridge regression. Finally, we propose an iterated generalized cross-validation criterion and prove its uniform consistency for estimating the risk along the self-training trajectory, enabling fully data-driven selection of the stopping time and regularization. Experiments on synthetic covariances validate the theory and illustrate the predicted denoising-forgetting trade-off.

Continual post-training enables foundation models to acquire new knowledge while preserving existing capabilities. Recent work suggests that on-policy learning can mitigate forgetting, with on-policy self-distillation emerging as a particularly attractive approach. In this work, we revisit this optimistic view through self-distillation policy optimization (SDPO). Our experiments show that SDPO can accelerate in-domain specialization when teacher signals are stable and well aligned, but it struggles to generalize to out-of-distribution scenarios. In continual post-training, SDPO exhibits stronger forgetting and can even collapse, whereas on-policy reinforcement learning methods such as GRPO adapt more conservatively and better preserve prior capabilities. Further analyses reveal that denser self-distillation induces larger drift in both parameter space and response space, and can amplify high-frequency formatting artifacts through a self-reinforcing teacher--student loop. These findings suggest that on-policy data alone is insufficient for continual learning. Dense self-distillation can accelerate specialization when teacher targets are stable and token-level supervision is reliable, but it should not be treated as a default stabilizer for continual post-training. Our code is available at https://github.com/Moenupa/SDPO-CL.

Training multi-turn LLM agents with reinforcement learning typically relies on trajectory-level rewards, which assign a uniform advantage to every step and cannot identify which decisions led to success or failure. Self-distillation methods can provide finer-grained supervision by augmenting RL with privileged information. However, existing approaches usually apply the same type of privileged information to every step in an indistinguishable manner, ignoring a key asymmetry: routine steps need little additional guidance, while critical error steps require corrective direction that environment feedback alone cannot provide. We propose AHEAD, a step-aware framework that matches different supervision sources to different step types. The teacher receives environment feedback on all steps as a grounded dense signal, and additionally receives LLM-generated corrective hints on error steps to supply the direction that environment feedback lacks. The method introduces minimal changes to the standard GRPO algorithm. Across ALFWorld, WebShop, and Search-based QA, and across three model scales, AHEAD raises task success (+13.3 points on ALFWorld and +11.0 on WebShop at 7B over GRPO), reaches a given success rate in fewer training steps, and solves tasks within tighter interaction budgets than outcome-only RL and prior self-distillation baselines.

On-policy self-distillation (OPSD) trains mathematical reasoning models using a privileged teacher that sees a reference solution and supervises student-sampled prefixes. Standard OPSD uses one fixed parameter setting at every state, but nearby settings may offer additional supervision. We find that local parameter perturbations reveal complementary reference-aligned corrections under the same reference context. Different experts supply these corrections at different reference positions. Their pool covers more such positions than the unperturbed privileged teacher. We introduce Neighborhood OPSD (N-OPSD) to turn these corrections into supervision at student-visited states. Offline, greedy selection builds a compact pool of frozen experts by rewarding filtered reference-token gains beyond the pool's current best at each position. The highest-peak expert need not provide the best training target. Online routing therefore separates the anchor direction from its level of support. MaxPeak selects the anchor token, and quantile selection chooses among experts whose top token matches it. The student learns from the chosen expert's full next-token distribution through the clipped forward-KL objective inherited from OPSD. We evaluate on AIME 2024, AIME 2025, and HMMT February 2025. Across three independent runs per method, Neighborhood OPSD improves the three-benchmark Average@12 over OPSD by 2.75, 1.67, and 1.94 points on Qwen3-1.7B, 4B, and 8B, respectively. Student-prefix continuations support using the pool beyond the reference trajectories used for selection. Matched ablations support filtered reference-token gains as a selection criterion. Accounting for overlap within the pool and routing by state further improve student accuracy. Inference uses only the distilled student.

Reinforcement learning with verifiable rewards (RLVR) has substantially improved the reasoning capabilities of large language models on tasks such as mathematical reasoning and code generation. However, most RLVR methods assign a scalar outcome reward to an entire trajectory, resulting in sparse supervision and limited token-level credit assignment. On-policy distillation (OPD) provides denser supervision by distilling token-level distributions from a stronger teacher model, but requires an additional teacher and typically assumes a shared vocabulary. On-policy self-distillation (OPSD) removes this dependency by conditioning the same model on privileged information to construct a teacher policy. However, directly matching the teacher distribution may cause information leakage and unstable optimization. RLSD avoids direct matching by using the teacher signal only to modulate update magnitudes, but it cannot provide an explicit correction direction when the sampled reasoning fails. To address this tradeoff, we introduce H^{2}SD, a hybrid hindsight self distillation framework that uses the teacher differently according to trajectory correctness. For successful trajectories, the teacher receives the student response confirmed as correct together with a rephrasing instruction, and its probabilities on the original response tokens are used to modulate update magnitudes without changing the direction determined by the reward. For failed trajectories, we condition the teacher on a reference hint containing key reasoning steps and a verified answer, and minimize the reverse KL divergence from the student to the teacher. Experiments on multiple challenging reasoning benchmarks show that H^2SD consistently outperforms representative RLVR, OPSD, and RLSD baselines while maintaining stable optimization and favorable generation efficiency.

On-policy self-distillation (OPSD) trains a large language model using supervision from a teacher instantiated from the same model as the student. The teacher is conditioned on privileged information (PI), such as verified solutions. The student, which does not observe PI, learns from the teacher's next-token distributions along its own sampled responses. However, PI can bias supervision toward shortcut reasoning with limited verification or reconsideration, accompanied by a sharp drop in the entropy of the output distribution. To address this challenge, we introduce self-distillation with verbal regularization (VRSD), which uses system prompts to regulate how the teacher uses PI, thereby encouraging rethinking and exploration to counteract premature commitment. Theoretically, we model prompting as attenuating the influence of PI on the teacher distribution and derive conditions for entropy preservation. Across three models and four tasks, VRSD improves Pass@1 over OPSD in 11 of 12 model-task settings, by 3.9 percentage points on average, while generally maintaining higher token entropy.

Reinforcement learning (RL) has been widely used to train LLM agents for multi-turn interactive tasks, but its sample efficiency is severely limited by sparse rewards and long horizons. On-policy self-distillation (OPSD) alleviates this by providing dense token-level supervision from a privileged teacher that has access to ground-truth answers. However, such fixed privileged information cannot capture the diverse valid strategies in agent tasks, and naively combining OPSD with RL often leads to training collapse. To address these limitations, we introduce Skill-SD, a framework that turns the agent's own trajectories into dynamic training-only supervision. Completed trajectories are summarized into compact natural language skills that describe successful behaviors, mistakes, and workflows. These skills serve as dynamic privileged information conditioning only the teacher, while the student always acts under the plain task prompt and learns to internalize the guidance through distillation. To stabilize the training, we derive an importance-weighted reverse-KL loss to provide gradient-correct token-level distillation, and dynamically synchronize the teacher with the improving student. Experimental results on agentic benchmarks demonstrate that Skill-SD substantially outperforms the standard RL baseline, improving both vanilla GRPO (+14.0%/+10.9% on AppWorld/Sokoban) and vanilla OPD (+42.1%/+40.6%). Project page: https://k1xe.github.io/skill-sd/

Majorities of distillation methods on pre-trained diffusion models or on pre-trained rectified flow, focus on either the distillation outputs or the trajectories between random noises and clean images to speed up sample generations from pre-trained models. In those trajectory-based distillation methods, consistency distillation requires the self-consistent trajectory projection to regulate the trajectory, which might avoid the common ODE approximation error {while still be concerning about sampling efficiencies}. At the same time, rectified flow distillations enforce straight trajectory for fast sampling, although an ODE solver is still required. In this work, we propose a trajectory distillation method, \modelname, that enjoys the benefits of both and enables few-step generations. TraFlow adopts the settings of consistency trajectory models, and further enforces the properties of self-consistency and straightness throughout the entire trajectory. These two properties are pursued by reaching a balance with following three targets: (1) reconstruct the output from pre-trained models; (2) learn the amount of changes by pre-trained models; (3) satisfy the self-consistency over its trajectory. Extensive experimental results have shown the effectiveness of our proposed method.

Recent work on LLM agents is shifting from external capability elicitation to capability internalization, enabling agents to retain useful skills without retrieval at inference time. On-policy self-distillation (OPSD) offers a promising direction, but many existing methods typically supervise students by scoring actions along student-generated trajectories. Such supervision has two limitations: teacher preferences are not validated by environment outcomes, and action-level scores underuse information from student rollouts, teacher rollouts, and their behavioral relationship. We therefore advocate outcome-verified teacher supervision and comparative learning over teacher-student trajectories. Based on this view, we propose Outcome-Verified Comparative Self-Distillation (OVCSD). OVCSD organizes failed student rollouts into a prefix tree, adaptively invokes a skill-conditioned teacher from student-reached states, and retains only outcome-verified successful continuations. It then applies localized comparative learning at the first state-aligned divergence and distills the post-divergence teacher suffix to transfer completion behavior. Experiments on ALFWorld and WebShop across three model scales show that OVCSD consistently outperforms skill-free RL and existing self-distillation baselines, achieving up to 29.7 and 5.4 absolute success-rate gains over the strongest baselines on ALFWorld and WebShop, respectively, while adding less than 3% privileged interaction during training.

On-policy self-distillation (OPSD) trains a student on its own rollouts using a privileged teacher, but its standard objective weights all generated tokens equally, implicitly treating the privileged teacher target as equally reliable at every student-visited prefix. Existing entropy-based OPD methods relax this uniformity by modulating token-level supervision with teacher entropy, but high teacher entropy in reasoning has an ambiguous reliability meaning: it can reflect either non-viable uncertainty or benign solution diversity. To identify this phenomenon, we introduce a branch-viability diagnostic. Specifically, we record next-token alternatives from the privileged-answer teacher prompt, force each alternative after the student prompt plus its on-policy spine prefix, and test whether the resulting student-template continuation recovers the correct answer. On Qwen3-4B, we find that an oriented within-sequence position score is the strongest tested predictor of teacher-token reliability, reaching an area-under-ROC-curve (AUROC) of 0.83; local uncertainty scores are at most 0.57. Motivated by this trajectory-level structure, we propose Position-Weighted On-Policy Self-Distillation (PW-OPSD), which applies an increasing position weight while keeping the same student rollout, privileged teacher pass, and clipped forward-KL target as OPSD. In our comprehensive evaluations with different random seeds, the diagnostic-derived PW-OPSD improves AIME 2024 and AIME 2025 Avg@12 by +1.0 and +1.1 points, and a generalization evaluation on two larger-scale models from different families, DeepSeek-R1-Distill-Llama-8B and Olmo-3-7B-Think, also demonstrates consistent aggregate Avg@12 improvements. These results show that teacher-token reliability in reasoning distillation is trajectory-structured and can be utilized without additional teacher computation.

Self-distillation has emerged as a powerful framework for post-training LLMs, where a teacher conditioned on extra information guides a student without it, both from the same model. While this guidance is useful when the student has failed, on successful rollouts, the same mechanism instead overwrites the student's choices and suppresses it's own reasoning. Therefore, we propose reading the original self-distillation signal in reverse: when the student succeeds along a path the teacher would not have predicted, these tokens reflect its self-driven reasoning. Building on this, we propose RLRT (RLVR with Reversed Teacher), which augments GRPO by reinforcing these tokens on correct rollouts. We interpret this as a new form of exploration in RLVR: not uniform diversity, but valuable exploration grounded in the student's own success. Across base, instruction-tuned, and thinking-tuned Qwen3 checkpoints, RLRT substantially outperforms self-distillation and exploration-based baselines, establishing information asymmetry as a new, principled design axis for RLVR.

Online training enables computer-use agents (CUAs) to improve through interaction with executable environments. However, existing methods primarily rely on sparse outcome rewards, which provide no supervision for intermediate actions. On-policy self-distillation (OPSD) offers token-level learning signals through privileged rescoring, but directly applying it to CUA online training presents two challenges: fixed guidance may become misaligned with the student's current state, and guidance-induced probability shifts may conflict with step-level correctness. We introduce ComputerSD, an online self-distillation method for CUAs that converts real-time feedback from executed GUI transitions into guidance for policy learning. A fine-tuned GUI analyzer produces guidance and a step-level value score after each action; the guidance provides privileged context, while the score regulates the resulting OPSD signals. ComputerSD jointly optimizes token-level OPSD and trajectory-level GRPO in a fully asynchronous training framework. On OSWorld-Verified, ComputerSD outperforms outcome-only GRPO by 1.9 and 4.1 percentage points on the general-purpose Qwen3-VL-8B-Thinking and specialized EvoCUA-8B backbones, respectively. Evaluation in out-of-distribution settings further supports the generalizability of ComputerSD. These results demonstrate the effectiveness of learning from real-time feedback through online self-distillation for CUAs.

Large language model agents have shown strong potential in complex interactive tasks, yet their reinforcement learning (RL) is often hindered by sparse rewards, as a long multi-turn trajectory may receive only a single outcome-level signal. On-policy self-distillation (OPSD) provides dense token-level supervision from a privileged teacher, but the teacher may not be reliable at every position. Existing methods commonly rely on isolated token-level discrepancies, which can be sensitive to noise, or assign a shared step-level weight that may overlook positional variation. We propose Persistent Consistency Self-Distillation (PCSD), which derives token-level distillation weights from the local persistence of teacher-favoring signals. PCSD combines adaptive windows with exponentially decayed aggregation to capture persistent relative teacher support, applies trend-aware modulation to attenuate locally declining support, and produces continuous weights through sigmoid gating. The resulting objective is jointly optimized with GRPO, combining dense teacher guidance with sparse environmental feedback. Without inference-time skills, PCSD achieves the best ALFWorld Overall results among all baselines on both backbones, exceeding GRPO by 15.6 and 13.3 points and SDAR by 6.2 and 5.5 points, while remaining competitive on WebShop and gaining 15.8 points over GRPO on unseen ALFWorld split.

Tool-Integrated Reasoning (TIR) enables LLMs to solve complex tasks through iterative tool interactions. However, existing reinforcement learning methods often rely on trajectory-level supervision, limiting fine-grained credit assignment in long-horizon TIR scenarios. On-policy self-distillation offers denser signals through teacher branches with privileged context, but existing approaches typically derive such context from ground-truth answers or retrieved skills, which may not reflect the states actually visited by the agent. Moreover, token-level supervision fails to capture the turn-level structure of tool interactions. To address this, we propose TurnSight, a turn-level hindsight self-distillation framework that derives supervision directly from execution-conditioned hindsight. It then constructs multiple hindsight views with different lookahead horizons and selects reliable supervision through cross-horizon directional agreement. Finally, the selected hindsight signal is normalized across sibling rollouts and used to adaptively modulate RL advantages while preserving their original optimization direction. Extensive experiments on three benchmarks demonstrate the effectiveness of TurnSight. Our codes are available at https://github.com/quchangle1/TurnSight.

Graphical user interface (GUI) grounding requires vision-language models (VLMs) to identify small target elements in high-resolution screenshots and predict precise screen coordinates. On-policy self-distillation (OPSD) is a promising post-training approach for this coordinate-sensitive task, since it provides dense token-level teacher signals beyond hard coordinate labels. However, naive OPSD is not well suited to GUI grounding: OPSD evaluates the teacher on student-generated prefixes, the quality of coordinate-token teacher signals can degrade when the prefix has already deviated from the target coordinate, leading to unreliable teacher signal. To mitigate this, We propose quality-aware self-distillation for VLM-based GUI grounding, which improves coordinate-token teacher-signal quality through soft correctness-aware gating and teacher-probability scaling. The soft correctness-aware gate checks whether the teacher's current coordinate-token prediction can still be completed into the ground-truth box under the student-generated prefix. If not, the corresponding teacher signal is down-weighted. Teacher-probability scaling then uses the teacher's confidence as a lightweight factor to further calibrate the strength of the gated supervision. A key empirical finding is that neither component alone improves overall performance, whereas combining them consistently improves performance. This suggests that the two mechanisms play complementary roles: correctness-aware gating suppresses unreliable coordinate-token supervision, while teacher-probability scaling calibrates the strength of the remaining signals. Experiments across six GUI grounding benchmarks show that our method consistently improves the base model and outperforms strong baselines.

Diffusion large language models (dLLMs) generate text by iteratively denoising a masked sequence, offering a parallel alternative to autoregressive models, but eliciting strong reasoning through post-training remains difficult: supervised fine-tuning is off-policy and suffers from exposure bias, while reinforcement learning gives only sparse, sequence-level rewards and is hard to apply without tractable sequence likelihoods. On-policy self-distillation (OPSD) offers a promising alternative, using one model as both student and teacher to provide dense, token-level, on-policy supervision, but its effectiveness hinges on giving the teacher privileged information (PI) - typically an instance-specific ground-truth reference unavailable at inference - so the student ends up distilling a weak PI-free consensus policy that yields little improvement on dLLM reasoning. We introduce dOPSD, which instead 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; on Dream and LLaDA, dOPSD improves both in-domain math reasoning and out-of-domain code generation, outperforming supervised and on-policy baselines.

Knowledge distillation has become a primary mechanism for transferring reasoning and domain expertise from frontier Large Language Models (LLMs) to smaller, deployable students. However, the dominant paradigm remains off-policy: students train on static teacher-generated data and never encounter their own errors during learning. This train--test mismatch, an instance of exposure bias, causes prediction errors to compound autoregressively at inference time. On-Policy Distillation (OPD) addresses this by letting the student generate its own trajectories and receive teacher feedback on these self-generated outputs, grounding distillation in the theory of interactive imitation learning. Despite rapid growth spanning divergence minimization, reward-guided learning, and self-play, the OPD literature remains fragmented with no unified treatment. This survey provides the first comprehensive overview of OPD for LLMs. We introduce a unified f-divergence framework over on-policy samples and organize the landscape along three orthogonal dimensions: feedback signal (logit-based, outcome-based, or self-play), teacher access (white-box, black-box, or teacher-free), and loss granularity (token-level, sequence-level, or hybrid). We systematically analyze representative methods, examine industrial deployments, and identify open problems including distillation scaling laws, uncertainty-aware feedback, and agent-level distillation.

On-policy self-distillation (OPSD) is a promising approach to improve reasoning language models, but it remains brittle in practice: making it work reliably often requires substantial engineering effort. We identify a structural source of this difficulty: vanilla OPSD is precisely the β=1 member of a broader policy-optimization family, where β weights the KL penalty anchoring the student to a reference policy. This equivalence turns β from an implicit value fixed at one into a controllable regularization parameter, yielding a more general formulation that trades off proximity to a reference policy against privileged teacher guidance. We introduce β-OPSD and derive its optimal policy as a geometric interpolation between the reference policy and the privileged teacher. Directly optimizing this objective with reinforcement learning, however, would be costly and high-variance. Rather than optimize the RL objective directly, we turn its closed-form solution into a distillation target. Each value of β selects a target along the reference-to-teacher path, which we implement efficiently by mixing their token-level logits. In this way, inexpensive distillation approximates the solution of expensive policy optimization. Return-to-go credit assignment further aligns token updates with the sequence-level objective while retaining the simplicity of OPSD. Experiments on mathematical reasoning benchmarks show that β-OPSD consistently outperforms vanilla OPSD, improving optimization stability and downstream reasoning performance. Our results provide a principled route from self-distillation to policy optimization and back without sacrificing the efficiency that makes OPSD practical.

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.

On-policy self-distillation (OPSD) has proven effective for post-training large language models (LLMs), yet its application to diffusion LLMs (dLLMs) remains unexplored. Existing OPSD methods are inherently autoregressive-centric. They inject privileged information via left-to-right prefix conditioning with token-level divergence supervision, a design that fundamentally conflicts with the arbitraryorder generation of dLLMs. We introduce d-OPSD, the first OPSD framework tailored for dLLMs. Our approach makes two core contributions. First, we reframe self-teacher construction by using self-generated answers as suffix conditioning, enabling the student model to learn from "self future-experience" rather than privileged prefixes. Second, we shift supervision from token-level to step-level, aligning training with the iterative denoising process of dLLMs. Experiments across four reasoning benchmarks show that d-OPSD consistently outperforms RLVR and SFT baselines with superior sample efficiency, requiring only around 10% of the optimization steps by RLVR and opening a promising pathway for dLLM posttraining. The code is available at https://github.com/xingzhejun/d-OPSD.

Conditioning a language model on additional context, such as feedback on a previous attempt, typically improves its response. Self-distillation trains the model to retain this improvement when the context is not present. The method works by matching the model's output distribution under two settings: a student that sees only the question, and a self-teacher that also sees the context. What the model learns therefore depends on what context the self-teacher receives, yet the design of this context remains largely unexplored. We study context design for self-distillation by training a solver on feedback from a frozen critic. We compare three conditions: (i) a binary reward (GRPO), (ii) the reference solution, and (iii) a step-by-step critique aligned to the solver's reasoning trace. Step-aligned critique yields the largest gains, outperforming GRPO by 16.11 points and reference-solution-conditioned self-distillation by 5.27 points (Avg@12). Per-token advantage analysis reveals why: step-aligned feedback targets only the tokens where reasoning fails, leaving correct behavior intact. Conditioning on the reference solution, by contrast, pressures the model to change its behavior at every token (even correct steps) because an alternative derivation inevitably differs in phrasing and approach. This suggests that structural alignment between feedback and the solver's reasoning is a key driver of self-distillation effectiveness.

In this work, we investigate the implicit regularization induced by teacher-student learning dynamics in self-distillation. To isolate its effect, we describe a simple experiment where we consider teachers at random initialization instead of trained teachers. Surprisingly, when distilling a student into such a random teacher, we observe that the resulting model and its representations already possess very interesting characteristics; (1) we observe a strong improvement of the distilled student over its teacher in terms of probing accuracy. (2) The learned representations are data-dependent and transferable between different tasks but deteriorate strongly if trained on random inputs. (3) The student checkpoint contains sparse subnetworks, so-called lottery tickets, and lies on the border of linear basins in the supervised loss landscape. These observations have interesting consequences for several important areas in machine learning: (1) Self-distillation can work solely based on the implicit regularization present in the gradient dynamics without relying on any dark knowledge, (2) self-supervised learning can learn features even in the absence of data augmentation and (3) training dynamics during the early phase of supervised training do not necessarily require label information. Finally, we shed light on an intriguing local property of the loss landscape: the process of feature learning is strongly amplified if the student is initialized closely to the teacher. These results raise interesting questions about the nature of the landscape that have remained unexplored so far. Code is available at https://github.com/safelix/dinopl.

Knowledge distillation is one of the most effective methods for model compression. Previous studies have focused on the student model effectively training the predictive distribution of the teacher model. However, during training, the student model may inherit the shortcomings of the teacher model, which can lead to a decline in generalization capacity. To mitigate this issue, we propose adaptive self-knowledge distillation (ASKD), which dynamically reduces the dependence of the teacher model to improve the self-training capacity, and performs the self-knowledge distillation method to improve the generalization capacity of the student model. We further distill the Whisper model into a smaller variant, called FastWhisper. In our post-training setting, FastWhisper achieved a word error rate of 1.07% lower than the teacher model Whisper, and its relative inference time was 5 times faster.

Self-distillation in agentic reinforcement learning has produced a growing number of methods. However, existing evaluations often reuse published baseline scores under differing experimental conditions, provide few direct comparisons among contemporaneous methods, and give limited attention to training stability and computational cost. These limitations obscure the source of reported gains and the practical strengths and weaknesses of competing methods. Costly agent training further motivates a common basis for comparison. To address these gaps, we compare ten representative methods against GRPO on ALFWorld, ScienceWorld, Search-QA, and WebShop across three model sizes. Our study comprises 132 training runs totaling 12,124.4 recorded H800 GPU-hours, with repeated evaluations over eight rollout seeds for the pretrained backbones and all eleven trained methods. Beyond final task performance, we examine training progress, stability, and measured computational cost. Our evaluation yields three key findings. First, gains over GRPO remain limited in scope, with no method consistently outperforming it across settings. Second, strong final performance can mask unstable training. Third, additional training cost does not consistently translate into better performance. We establish this benchmark to support fair, comprehensive comparison and guide future research toward reliable and cost-effective improvements in agent training. Project page: https://aim-uofa.github.io/Self-Distillation-AgentRL/

On-policy self-distillation has emerged as a promising paradigm for post-training language models, in which the model conditions on environment feedback to serve as its own teacher, providing dense token-level rewards without external teacher models or step-level annotations. Despite its empirical success, what this reward actually measures and what kind of credit it assigns remain unclear. Under a posterior-compatibility interpretation of feedback conditioning, standard in the implicit-reward literature, we show that the self-distillation token reward is a Bayesian filtering increment whose trajectory sum is exactly the pointwise mutual information between the response and the feedback given the input. This pMI can be raised by input-specific reasoning or by input-generic shortcuts, so we further decompose the teacher log-probability along the input axis. Based on this analysis, we propose CREDIT (Contrastive REward from DIsTillation), which isolates the input-specific component with a batch-contrastive baseline. At the sequence level, CREDIT is a teacher-side surrogate for a contrastive pMI objective that also penalizes responses remaining likely under unrelated inputs. Across coding, scientific reasoning, and tool-use benchmarks on two model families, CREDIT delivers the strongest aggregate performance at negligible additional compute.

On-policy self-distillation (OPSD) uses a privileged teacher to supervise a reasoning model on prefixes sampled from its own rollouts. Yet each rollout also reveals how the student's response unfolds and whether it succeeds, student-specific hindsight that standard OPSD does not use to form the teacher. We introduce Privileged Adaptation from Student Trajectories (PAST), which treats each completed student trajectory as additional privileged information for the OPSD teacher while leaving the student's distillation prefixes unchanged. PAST preserves the student's next-token distribution on correct trajectories and uses failed trajectories to adapt the teacher toward verified success under student-proximity regularization. We characterize what such a trajectory-conditioned teacher can transfer to a prefix-only student. Forward-KL distillation projects the teacher distributions to their conditional arithmetic mean given the prefix. This projection separates trajectory-specific variation that remains privileged from the mean policy shift available to the student. For correct trajectories, the unclipped population objective also has the frozen student as an ideal distributional fixed point. Across three mathematical reasoning benchmarks, PAST improves the Avg@12 macro average over Vanilla OPSD by 5.6 percentage points. A 2times2 factorial study shows gains from both complete-trajectory access and teacher adaptation, while trajectory removal and shuffling confirm that the adapted teacher uses the matching hindsight context.

Post-training for reasoning models typically combines supervised fine-tuning with reinforcement learning from verifiable rewards, most commonly with GRPO. However, this algorithm suffers from sparse rewards, limited exploration, and mode collapse. Building upon recent works on self-distillation, we propose Feedback Distillation, a training method where the model is trained to match, at the token level, its own distribution conditioned on privileged feedback produced by a language model. Feedback Distillation offers token-level supervision and can inject external knowledge. Evaluating our method for Lean4 theorem-proving, we find that Feedback Distillation maintains greater diversity in generated trajectories than GRPO, yielding higher policy entropy and better pass@k scaling. The two methods are complementary: initializing GRPO from a Feedback Distillation checkpoint outperforms either method alone. All in all, our results suggest a promising avenue to improve post-training for complex reasoning.

Bayesian optimization (BO) has contributed greatly to improving model performance by suggesting promising hyperparameter configurations iteratively based on observations from multiple training trials. However, only partial knowledge (i.e., the measured performances of trained models and their hyperparameter configurations) from previous trials is transferred. On the other hand, Self-Distillation (SD) only transfers partial knowledge learned by the task model itself. To fully leverage the various knowledge gained from all training trials, we propose the BOSS framework, which combines BO and SD. BOSS suggests promising hyperparameter configurations through BO and carefully selects pre-trained models from previous trials for SD, which are otherwise abandoned in the conventional BO process. BOSS achieves significantly better performance than both BO and SD in a wide range of tasks including general image classification, learning with noisy labels, semi-supervised learning, and medical image analysis tasks.

On-policy self-distillation (self-OPD) densifies reinforcement learning with verifiable rewards (RLVR) by letting a policy teach itself under privileged context. We find that when this guidance spans the full response, all-token KL spends gradients on mostly redundant positions and amplifies privileged-information leakage, causing entropy rise, shortened reasoning, and out-of-distribution degradation in long-horizon math training. We propose Token-Routed Alignment for Critical rEasoning (TRACE), which distills only on annotator-marked critical spans: forward KL on key spans of correct rollouts, optional reverse KL on localized error spans, and GRPO on all remaining tokens, with the KL channel annealed away after a short warm-up. Our analysis explains TRACE through two effects: forward KL provides non-vanishing lift to teacher-supported tokens that the student under-allocates, while span masking and decay keep cumulative privileged-gradient exposure finite. On four held-out math benchmarks plus GPQA-Diamond, TRACE improves over GRPO by 2.76 percentage points on average and preserves the Qwen3-8B base OOD score on GPQA-Diamond, where GRPO and all-token self-OPD baselines degrade. Gains persist under online self-annotation (+1.90 percentage points, about 69% of the strong-API gain), reducing the concern that TRACE merely imports external annotator capability. Across scales, the best routed action is base-dependent: on Qwen3-8B it is forward KL on key spans, while on Qwen3-1.7B it shifts to reverse KL on error spans.

The generalization capability of deep neural networks has been substantially improved by applying a wide spectrum of regularization methods, e.g., restricting function space, injecting randomness during training, augmenting data, etc. In this work, we propose a simple yet effective regularization method named progressive self-knowledge distillation (PS-KD), which progressively distills a model's own knowledge to soften hard targets (i.e., one-hot vectors) during training. Hence, it can be interpreted within a framework of knowledge distillation as a student becomes a teacher itself. Specifically, targets are adjusted adaptively by combining the ground-truth and past predictions from the model itself. We show that PS-KD provides an effect of hard example mining by rescaling gradients according to difficulty in classifying examples. The proposed method is applicable to any supervised learning tasks with hard targets and can be easily combined with existing regularization methods to further enhance the generalization performance. Furthermore, it is confirmed that PS-KD achieves not only better accuracy, but also provides high quality of confidence estimates in terms of calibration as well as ordinal ranking. Extensive experimental results on three different tasks, image classification, object detection, and machine translation, demonstrate that our method consistently improves the performance of the state-of-the-art baselines. The code is available at https://github.com/lgcnsai/PS-KD-Pytorch.

On-policy distillation (OPD) provides dense, per-token supervision for language model post-training, but its effectiveness is bottlenecked by teacher quality: external teachers suffer from distribution mismatch, while self-distillation with privileged conditioning is limited by in-context learning capacity. We propose RISE (Recursive Improvement via Self-Extrapolating Policy Distillation), which constructs a synthetic teacher directly from the model's own RLVR training trajectory. By extrapolating the displacement between the current checkpoint and a trailing anchor---in parameter space or output logit space---RISE converts a sparse outcome-induced parameter update into a dense token-level target, without any external model or privileged conditioning. RISE combines RLVR and OPD in a complementary loop: outcome rewards ground the extrapolation toward correct reasoning, while the extrapolated teacher refines token-level decisions. Moreover, since the teacher is refreshed every iteration as the student improves, distillation becomes a recursive improvement mechanism rather than a one-shot compression step. Experiments spanning mathematical reasoning, multi-domain STEM, code generation, and multi-turn agentic tasks show that RISE outperforms RLVR-only training and on-policy self-distillation across all settings.

On-Policy Self-Distillation (OPSD) uses privileged information available only to the teacher to provide dense token-level supervision on trajectories generated by the student. However, existing methods often rely on verified solution traces, explanations generated by external models, or manually localized visual evidence, which limits their scalable application to multimodal large language models. To address this issue, we exploit the information gap between high- and low-resolution views of the same image and propose RP-OPSD (Resolution-Privileged On-Policy Self-Distillation for Multimodal Large Language Models). During training, the student policy generates on-policy trajectories from images at one-quarter of the original resolution, while the teacher policy provides supervision using the original-resolution images. By minimizing the divergence between their output distributions along the student trajectories, the student learns the predictive behavior of the teacher under high-resolution inputs, thereby strengthening its low-resolution capability and transferring the learned improvement to original-resolution inference. RP-OPSD requires neither additional human annotations nor external models to generate solution traces but only image--question pairs. Experiments on Qwen3.5-9B show that RP-OPSD achieves a 5.45\% relative improvement in average performance at the original resolution and a 1.78times training speedup over OPSD. These results demonstrate that resolution differences can serve as a simple and scalable source of privileged information, providing an effective and efficient approach to on-policy self-distillation for multimodal large language models.

Long-horizon tool-use reinforcement learning learns from outcome verification, but trajectory-level advantages are broadcast over reasoning, API, and answer tokens. Direct self-distillation can supply a denser signal, but in our experiments it can also destroy tool use by rehearsing teacher behavior without identifying which actions the verifier rewards. We introduce Sibling-Guided Credit Distillation (SGCD), which uses distillation for bounded credit weighting rather than as a competing actor loss. Dynamic sampling produces mixed successful and failed sibling rollouts; an external LLM summarizes their contrast into a training-only credit reference; and detached teacher/student divergence reshapes GRPO token advantages. The deployed student receives only the clean task prompt. Across AppWorld and tau^3-airline, SGCD reports higher held-out point estimates than GRPO-family comparators: AppWorld TGC improves from 42.9 to 45.6 on test_normal and from 24.7 to 27.0 on test_challenge, and tau^3-airline held-out evaluator score improves from 0.583 to 0.602. These results support a narrow design rule for long-horizon tool-use agents: use distillation to guide credit assignment while keeping policy gradient in charge of the actor update.

On-policy self-distillation has become a strong recipe for LLM reasoning, where a privileged teacher supervises the student's own rollouts while conditioning on the reference solution. A design choice shared by nearly all such methods, however, has gone unquestioned: the teacher always sees the full reference reasoning. We argue that this default itself is part of the problem and identify a teacher-side exposure mismatch: when the teacher conditions on reasoning far beyond the student's current competence, the resulting token targets become too strong to absorb. A controlled fixed-exposure sweep makes this concrete on two fronts: 1) full exposure is not reliably the best choice, and 2) student-teacher mismatch grows monotonically as the teacher sees more privileged reasoning. This motivates treating teacher exposure not as a fixed hyperparameter but as a learnable training-time control variable. We therefore propose Adaptive Teacher Exposure for Self-Distillation (ATESD). ATESD models the reveal ratio with a lightweight Beta-policy controller conditioned on compact training-state statistics, and uses one sampled exposure for a short hold window of student updates. To make this exposure controller learnable, we optimize it with a discounted learning-progress reward that scores each held decision by its effect on the student's future improvement rather than its immediate loss change, addressing the delayed credit assignment induced by on-policy distillation. Experiments on AIME 24, AIME 25, and HMMT 25 across Qwen3-{1.7B, 4B, 8B} show that ATESD consistently outperforms competitive self-distillation and RL baselines, improving over OPSD by +0.95, +2.05, and +2.33 Average@12 points respectively, and establishing adaptive teacher exposure as an effective new axis for reasoning self-distillation.

On-policy distillation trains a language model on its own generations while a teacher scores them token by token. It combines the dense supervision of imitation learning with the on-policy sampling of reinforcement learning. But it requires a second, larger model to act as teacher. On-Policy Self-Distillation (OPSD) removes that cost. The teacher is the model itself, conditioned on privileged information the student will not have at test time, such as a reference solution, a plan, or environment feedback. The teacher is no stronger than the student, only better informed. Early results were promising, with accuracy comparable to reinforcement learning at a fraction of the generated tokens. But the same asymmetry that produces the signal also biases it. One failure mode now dominates the field: collapse, the progressive narrowing of the set of reasoning paths the model can produce. Collapse is not specific to OPSD, though privileged information aggravates it. This review treats collapse as a symptom governed by three levers: (i) where the signal is applied, that is, how tokens are weighted; (ii) what the teacher is shown, that is, the nature of the privileged information; and (iii) when the signal changes, that is, the teacher's dynamics and the decay of guidance. We restrict our scope to mathematical reasoning, where the method originated and where its failure modes are best documented. We report no new experiments. The contribution is structural: a shared vocabulary for phenomena named differently across papers, and a clear line between what is settled and what is still disputed.

This paper proposes an interpretation of RLAIF as Bayesian inference by introducing distilled Self-Critique (dSC), which refines the outputs of a LLM through a Gibbs sampler that is later distilled into a fine-tuned model. Only requiring synthetic data, dSC is exercised in experiments regarding safety, sentiment, and privacy control, showing it can be a viable and cheap alternative to align LLMs. Code released at https://github.com/vicgalle/distilled-self-critique.

Large language models are increasingly evaluated by other models, raising a natural question: can a model predict how a judge will score its own output? We find that the ability is largely present before any targeted training: prompted few-shot, a base model already predicts an external judge's multi-attribute quality scores on open-ended responses well above chance across three benchmarks. We introduce Self-Evaluation Elicitation (SEE), a method that surfaces this latent ability through a short cycle comprising a calibration-coupled reinforcement learning phase that improves the answer and predicts the judge, followed by a masked distillation phase that sharpens the prediction while leaving the answer untouched. From 160 unique examples, roughly 31x fewer than a reinforcement learning baseline, SEE improves held-out calibration across three benchmarks while preserving answer quality. The elicited self-evaluation is sharply localized within the model's own token distribution and stable across judges it was never trained against, indicating a transferable notion of quality rather than a single judge's preference. These results reframe judge-aligned self-evaluation as a problem of elicitation rather than acquisition.

Diffusion distillation models effectively accelerate reverse sampling by compressing the process into fewer steps. However, these models still exhibit a performance gap compared to their pre-trained diffusion model counterparts, exacerbated by distribution shifts and accumulated errors during multi-step sampling. To address this, we introduce Distillation++, a novel inference-time distillation framework that reduces this gap by incorporating teacher-guided refinement during sampling. Inspired by recent advances in conditional sampling, our approach recasts student model sampling as a proximal optimization problem with a score distillation sampling loss (SDS). To this end, we integrate distillation optimization during reverse sampling, which can be viewed as teacher guidance that drives student sampling trajectory towards the clean manifold using pre-trained diffusion models. Thus, Distillation++ improves the denoising process in real-time without additional source data or fine-tuning. Distillation++ demonstrates substantial improvements over state-of-the-art distillation baselines, particularly in early sampling stages, positioning itself as a robust guided sampling process crafted for diffusion distillation models. Code: https://github.com/geonyeong-park/inference_distillation.

On-policy self-distillation, where a language model conditions on privileged context to supervise its own generations, is a promising source of dense supervision for sparse-reward reinforcement learning. Actually, it can be instantiated as an auxiliary full-vocabulary student-to-teacher reverse Kullback-Leibler divergence loss. We therefore propose SDPG, a self-distilled policy-gradient framework that combines group-relative verifier advantages with normalized standard deviation, exact full-vocabulary on-policy self-distillation, as well as reference-policy KL regularization. Empirically, SDPG improves stability and performance over RLVR and self-distillation baselines. The code is available at https://github.com/lauyikfung/SDPG.

On-Policy Self-Distillation (OPSD) is commonly interpreted as the transfer of privileged information: a teacher observes the verified solution to the target problem and supervises the student's trajectory. However, this interpretation conflates two effects. The reference solution not only reveals the answer to the current instance but also changes the context under which the teacher provides token-level supervision. We investigate the role of target-specific privilege with OP^{2}SD (On-Policy Self-Distillation from Other Problems), which replaces the paired reference with a problem and solution from a different example, while preserving the student rollout, teacher, and distillation objective. Across three models and three mathematics benchmarks, OP^{2}SD improves over the base model, remains competitive with OPSD. The success of OP^{2}SD implies that OPSD gains do not necessarily come from access to the reference solution, and that the teacher's context-induced behavior is an important factor.

Diffusion language models (DLMs) alleviate the inherent latency bottleneck of autoregressive (AR) large language models (LLMs), but their degraded generation quality limits practical applicability. Although knowledge distillation (KD) can be a promising direction for improving performance, we empirically find that naively applying conventional KD yields only marginal gains, or even degrades generation quality. Based on these observations, we propose a novel self-distillation framework for DLMs, namely SelFusion. To enable effective KD without an external teacher model, SelFusion performs two forward passes with different masking levels, defining the hard mode with a larger masking probability and the easy mode with a smaller masking probability. However, the easy mode is not always more accurate than the hard mode and can be overconfident on incorrect tokens. Thus, we introduce bidirectional KD between the two modes, which can dynamically determine the distillation direction based on token-level correctness. Experimental results on instruction-following tasks show that the proposed self-distillation substantially outperforms other KD methods with external LLM and DLM teachers. In many configurations, the student trained with SelFusion even surpasses the performance of the LLM teacher, providing a practical path toward improving DLM generation quality. Source code can be found at https://github.com/scai-research/SelFusion_official

Training-time privileged information (PI) can enable language models to succeed on tasks they would otherwise fail, making it a powerful tool for reinforcement learning in hard, long-horizon settings. However, transferring capabilities learned with PI to policies that must act without it at inference time remains a fundamental challenge. We study this problem in the context of distilling frontier models for multi-turn agentic environments, where closed-source systems typically hide their internal reasoning and expose only action trajectories. This breaks standard distillation pipelines, since successful behavior is observable but the reasoning process is not. For this, we introduce π-Distill, a joint teacher-student objective that trains a PI-conditioned teacher and an unconditioned student simultaneously using the same model. Additionally, we also introduce On-Policy Self-Distillation (OPSD), an alternative approach that trains using Reinforcement Learning (RL) with a reverse KL-penalty between the student and the PI-conditioned teacher. We show that both of these algorithms effectively distill frontier agents using action-only PI. Specifically we find that π-Distill and in some cases OPSD, outperform industry standard practices (Supervised finetuning followed by RL) that assume access to full Chain-of-Thought supervision across multiple agentic benchmarks, models, and forms of PI. We complement our results with extensive analysis that characterizes the factors enabling effective learning with PI, focusing primarily on π-Distill and characterizing when OPSD is competitive.

Knowledge distillation (KD) has gained a lot of attention in the field of model compression for edge devices thanks to its effectiveness in compressing large powerful networks into smaller lower-capacity models. Online distillation, in which both the teacher and the student are learning collaboratively, has also gained much interest due to its ability to improve on the performance of the networks involved. The Kullback-Leibler (KL) divergence ensures the proper knowledge transfer between the teacher and student. However, most online KD techniques present some bottlenecks under the network capacity gap. By cooperatively and simultaneously training, the models the KL distance becomes incapable of properly minimizing the teacher's and student's distributions. Alongside accuracy, critical edge device applications are in need of well-calibrated compact networks. Confidence calibration provides a sensible way of getting trustworthy predictions. We propose BD-KD: Balancing of Divergences for online Knowledge Distillation. We show that adaptively balancing between the reverse and forward divergences shifts the focus of the training strategy to the compact student network without limiting the teacher network's learning process. We demonstrate that, by performing this balancing design at the level of the student distillation loss, we improve upon both performance accuracy and calibration of the compact student network. We conducted extensive experiments using a variety of network architectures and show improvements on multiple datasets including CIFAR-10, CIFAR-100, Tiny-ImageNet, and ImageNet. We illustrate the effectiveness of our approach through comprehensive comparisons and ablations with current state-of-the-art online and offline KD techniques.

Reinforcement learning with verifiable rewards (RLVR) has become a standard paradigm for post-training large language models. While Group Relative Policy Optimization (GRPO) is widely adopted, its coarse credit assignment uniformly penalizes failed rollouts, lacking the token-level focus needed to efficiently address specific deviations. Self-Distillation Policy Optimization (SDPO) addresses this by providing denser, more targeted logit-level supervision that facilitates rapid early improvement, yet it frequently collapses during prolonged training. We trace this late-stage instability to two intrinsic flaws: self-distillation on already-correct samples introduces optimization ambiguity, and the self-teacher's signal reliability progressively degrades. To resolve these issues, we propose Sample-Routed Policy Optimization (SRPO), a unified on-policy framework that routes correct samples to GRPO's reward-aligned reinforcement and failed samples to SDPO's targeted logit-level correction. SRPO further incorporates an entropy-aware dynamic weighting mechanism to suppress high-entropy, unreliable distillation targets while emphasizing confident ones. Evaluated across five benchmarks and two model scales, SRPO achieves both the rapid early improvement of SDPO and the long-horizon stability of GRPO. It consistently surpasses the peak performance of both baselines, raising the five-benchmark average on Qwen3-8B by 3.4% over GRPO and 6.3% over SDPO, while simultaneously yielding moderate response lengths and lowering per-step compute cost by up to 17.2%.

Visual on-policy distillation relies heavily on an informative teacher-student asymmetry, through either a larger, stronger teacher or privileged supervision, such as reference answers or ground-truth regions of interest. This raises a fundamental question: where can informative asymmetry come from when nothing privileged is available? We answer this by inverting where the asymmetry comes from. Rather than adding privileged information to the teacher, we subtract information from the student. This asymmetry creates the same effective learning signal for free as a teacher with access to information unavailable to the student, without ground-truth annotations, rewards, or a separate stronger teacher model. Building on this principle, we introduce Self-Supervised Visual On-Policy Distillation (S^2VOPD), a simple yet effective method that constructs on-policy learning signals from asymmetric augmented views. S^2VOPD distills the teacher's distribution conditioned on the original image on-policy into the student distribution conditioned on a strongly augmented view of the same image. We systematically explore a broad design space of visual augmentations and uncover that (1) asymmetry matters: all four augmentation families improve performance, while symmetric self-distillation degrades it; (2) strength matters: performance peaks at a moderate strength; and (3) the gap must remain task-consistent: augmentations that completely remove the question-relevant evidence can induce large but uninformative discrepancies. Across six fine-grained perception benchmarks, S^2VOPD improves Qwen3.5-4B from 70.7% to 77.4%, above all open-source models compared, up to Qwen3-VL at 235B, and surpasses GPT-5.4. While holding training data the same, it recovers 96% of the improvement achieved by methods with privileged information. Website is at https://williamium3000.github.io/s2vopd

Self-supervised learning, which learns by constructing artificial labels given only the input signals, has recently gained considerable attention for learning representations with unlabeled datasets, i.e., learning without any human-annotated supervision. In this paper, we show that such a technique can be used to significantly improve the model accuracy even under fully-labeled datasets. Our scheme trains the model to learn both original and self-supervised tasks, but is different from conventional multi-task learning frameworks that optimize the summation of their corresponding losses. Our main idea is to learn a single unified task with respect to the joint distribution of the original and self-supervised labels, i.e., we augment original labels via self-supervision of input transformation. This simple, yet effective approach allows to train models easier by relaxing a certain invariant constraint during learning the original and self-supervised tasks simultaneously. It also enables an aggregated inference which combines the predictions from different augmentations to improve the prediction accuracy. Furthermore, we propose a novel knowledge transfer technique, which we refer to as self-distillation, that has the effect of the aggregated inference in a single (faster) inference. We demonstrate the large accuracy improvement and wide applicability of our framework on various fully-supervised settings, e.g., the few-shot and imbalanced classification scenarios.

Modern large language models (LLMs) can translate natural-language descriptions into operations research (OR) formulations. Post-training techniques including reinforcement learning and on-policy self-distillation have further improved this capability. However, three limitations remain in training LLMs for OR formulations. First, training commonly relies on synthetic formulations validated by human experts or stronger models, constraining scalable supervision. Second, credit assignment is either coarse or costly: outcome rewards score an entire trajectory without locating the responsible modeling decision, whereas process-level supervision requires an additional evaluator. Third, privileged self-distillation can induce style mismatch by using solver context unavailable at deployment. We find that a model can improve from solver-artifact feedback generated by its own rollouts, making self-distillation a practical, evaluator-free source of dense supervision. Therefore, we propose SOLID: Solver-Informed On-Policy LearnIng through Self-Distillation, a novel framework for self-improving OR language models without verified answers or external evaluators. SOLID executes candidate programs from multiple rollouts, clusters their objectives, and selects a majority-group artifact as a pseudo-reference. The model then performs updates using group-relative advantages and dense self-supervision signals. Across multiple OR benchmarks, SOLID improves solution accuracy for both general-purpose and OR-tuned models over outcome-only group-relative training. These results show that solver artifacts can support scalable self-improvement without trusted answers.

On-Policy Self-Distillation (OPSD) has recently emerged as an alternative to Reinforcement Learning with Verifiable Rewards (RLVR), promising higher accuracy and shorter responses through token-level credit assignment from a self-teacher conditioned on privileged context. However, this promise does not carry over to thinking-enabled mathematical reasoning, where reported accuracy gains shrink and sometimes turn negative. We hypothesize that hindsight supervision can specify better token-level alternatives in short thinking-disabled outputs, but in long thinking-enabled traces it more readily identifies redundancy than supplies better replacements. To test this, we applied OPSD separately to correct and incorrect rollout groups, so that compression and correction can be observed in isolation. Our results show that in thinking-enabled mathematical reasoning, OPSD behaves most reliably as a compression mechanism rather than a correction mechanism: training only on correct rollouts preserves accuracy while substantially shortening responses, whereas training only on incorrect rollouts damages accuracy. In light of these findings, we propose a revised post-training pipeline for thinking-enabled mathematical reasoning: SFT then RLVR then OPSD.

We present a simple but effective pixel-level self-supervised distillation framework friendly to dense prediction tasks. Our method, called Pixel-Wise Contrastive Distillation (PCD), distills knowledge by attracting the corresponding pixels from student's and teacher's output feature maps. PCD includes a novel design called SpatialAdaptor which ``reshapes'' a part of the teacher network while preserving the distribution of its output features. Our ablation experiments suggest that this reshaping behavior enables more informative pixel-to-pixel distillation. Moreover, we utilize a plug-in multi-head self-attention module that explicitly relates the pixels of student's feature maps to enhance the effective receptive field, leading to a more competitive student. PCD outperforms previous self-supervised distillation methods on various dense prediction tasks. A backbone of ResNet-18-FPN distilled by PCD achieves 37.4 AP^bbox and 34.0 AP^mask on COCO dataset using the detector of Mask R-CNN. We hope our study will inspire future research on how to pre-train a small model friendly to dense prediction tasks in a self-supervised fashion.

Recent language models have shown remarkable performance on natural language understanding (NLU) tasks. However, they are often sub-optimal when faced with ambiguous samples that can be interpreted in multiple ways, over-confidently predicting a single label without consideration for its correctness. To address this issue, we propose a novel self-knowledge distillation method that enables models to learn label distributions more accurately by leveraging knowledge distilled from their lower layers. This approach also includes a learning phase that re-calibrates the unnecessarily strengthened confidence for training samples judged as extremely ambiguous based on the distilled distribution knowledge. We validate our method on diverse NLU benchmark datasets and the experimental results demonstrate its effectiveness in producing better label distributions. Particularly, through the process of re-calibrating the confidence for highly ambiguous samples, the issue of over-confidence when predictions for unseen samples do not match with their ground-truth labels has been significantly alleviated. This has been shown to contribute to generating better distributions than the existing state-of-the-art method. Moreover, our method is more efficient in training the models compared to the existing method, as it does not involve additional training processes to refine label distributions.

On-policy self-distillation (OPSD) has become a popular recipe for post-training LLM agents. It supervises the agent model at the token level with a stronger teacher view of the same model, obtained by conditioning on privileged information (PI). In this work, we show that in multi-turn agents, this paradigm teaches the student to act with confidence but without the information behind it. The trained agent behaves as if it had privileged information it never observed, and its performance falls well short of plain RL, in the worst case below the untrained base model. Therefore, we propose Privileged Self-Practice (PSP), which keeps the PI and moves it from the loss to the sampler. When the student's rollouts on a task mostly fail, we inject a short per-task instruction written by an analyzer model, sample the task again with the instruction in context, and train on the result with an unchanged GRPO objective. The privileged information stays in the prompt and never enters the loss. Across AppWorld and SWE-bench Verified, with three different student models, PSP obtains the best average score in every setting and is the only method that consistently outperforms plain GRPO, improving task-goal completion by up to 65% on AppWorld and the resolved rate by up to 61% on SWE-bench Verified.

Iterative self-distillation enables LLM agents to learn from successive deployments, offering a path toward recursive self-improvement (RSI). Yet our experiments with existing methods reveal a collapse in deployment performance across cycles, while task performance with privileged information (PI) also declines. We address this collapse by prioritizing informative interaction steps for distillation and preserving PI-conditioned behavior as the student becomes the next teacher. We introduce Retentive and Selective Augmentation for Iterative Self-Distillation (ReSAIL), a plug-in augmentation for iterative PI-based self-distillation. ReSAIL selects interaction steps where PI most strongly changes the teacher's predictions and balances the resulting distillation losses across trajectories. It also regularizes the student's PI-conditioned output distributions toward those of the frozen teacher at selected and unselected steps to preserve PI-conditioned behavior for supervision in the next cycle. On ALFWorld and TextCraft, ReSAIL sustains substantial gains across model scales over three cycles, with an average absolute gain of 22.5% in final-cycle success rates when added to self-distillation baselines. Sensitivity-guided selection of offline data also improves action prediction accuracy for multimodal GUI agents on AITZ. These findings provide the first evidence that a more robust learning mechanism can effectively mitigate performance collapse in iterative agent self-distillation over deployment trajectories.

Reinforcement learning (RL) can be used to improve the policy (denoiser) of diffusion large language models (dLLMs), while being hindered by the intractability of the policy likelihood. A dominant and efficient family of methods replaces the likelihood in standard RL with its evidence lower bound (ELBO), estimated from randomly masked sequences. Despite being well aligned with pre-training, these approaches introduce bias through training--inference mismatch by using the ELBO as a likelihood surrogate, which can degrade performance. In this work, we propose Guided Denoiser Self-Distillation (GDSD) to directly distill the denoiser of dLLMs from an advantage-guided self-teacher, derived from the closed-form optimum of reverse-KL regularized RL. GDSD matches the dLLM's denoiser logits to the teacher's via a normalization-free objective, which reduces RL to likelihood-free self-distillation and thus bypasses the TIM biases. Recent ELBO-based methods emerge as instances of applying different distillation divergences, but with diagnosable pathologies that GDSD avoids. On planning, math, and coding benchmarks with LLaDA-8B and Dream-7B, GDSD consistently outperforms prior state-of-the-art ELBO-based methods with a more stable training reward dynamics, achieving test-accuracy improvements of up to +19.6%. These results suggest that direct denoiser self-distillation, without relying on an ELBO likelihood surrogate, can provide a more stable and effective RL procedure for dLLMs. Code is available at https://github.com/GaryBall/GDSD.

Reinforcement learning (RL) has emerged as a central paradigm for post-training LLM agents, yet its trajectory-level reward signal provides only coarse supervision for long-horizon interaction. On-Policy Self-Distillation (OPSD) complements RL by introducing dense token-level guidance from a teacher branch augmented with privileged context. However, transferring OPSD to multi-turn agents proves problematic: compounding multi-turn instability destabilizes supervision, while skill-conditioned privileged guidance requires asymmetric treatment for negative teacher rejections may arise from imperfect skills retrieval or utilization. We introduce SDAR (Self-Distilled Agentic Reinforcement Learning), which treats OPSD as a gated auxiliary objective while keeping RL as the primary optimization backbone. SDAR maps detached token-level signals into a sigmoid gate, strengthening distillation on teacher-endorsed positive-gap tokens and softly attenuating negative teacher rejections. Across the Qwen2.5 and Qwen3 families on ALFWorld, WebShop, and Search-QA, SDAR substantially improves over GRPO (+9.4% on ALFWorld, +7.0% on Search-QA, +10.2% on WebShop-Acc), avoids the instability of naive GRPO+OPSD, and consistently outperforms hybrid RL--OPSD baselines across model scales.

Whether a language model has improved itself is increasingly judged not by mean accuracy but by which individual problems it gains and loses. Tracking these transitions means differencing two noisy estimates, leaving them vulnerable to measurement artifacts. Auditing three rounds of rank-32 LoRA self-training on Qwen3-8B against a frozen control pushed through the identical pipeline, we identify seven measurement failures, each of which inverts a reported finding when its control is absent. Several are standard practice. A ledger built on a single greedy decode manufactures capability changes on an untrained model, largely an artifact of inference batching; the expansion statistic separating acquisition from sharpening assigns that same model a rate of 0.280. The natural threshold repair does not survive replication: estimated across the frozen comparisons such a design already contains, its null stays non-zero. We replace it with a per-problem exact test against a pooled baseline under false-discovery-rate control, which detects nothing on any held-out replicate and is unchanged under the multiple-testing rule, error rate and pool size. Applied to a ladder of arms matched in stream, volume and evaluation, the audit finds that external distillation improves problems the base model rarely reaches while three forms of self-training do not; a regression rejects this asymmetry as a by-product of distillation's larger overall gain (p < 10^{-8}). On the far smaller set of problems the base model never reaches, the evidence is inconclusive, while self-training corrupts problems solved at baseline at rates well above the measured floor. Transition-level auditing therefore requires a separately measured null for every statistic it reports: nulls that cost no new experiments, built from baseline replicates a multi-arm study already owns, though not from as few as most possess.

On-policy distillation (OPD), which samples trajectories from the student model and supervises them with a teacher at the token level, avoids relying solely on verifiable terminal rewards and can yield better generalization than off-policy distillation. However, OPD requires expensive on-the-fly sampling of the student policy during training, which substantially increases training cost, especially for long responses. Our initial analysis shows that, during OPD, training signals are often concentrated in the prefix of each output, and that even a short teacher-generated prefix can significantly help the student produce the correct answer. Motivated by these observations, we propose a simple yet effective modification of OPD: we apply the distillation objective only to prefixes of student-generated outputs and terminate each sampling early during distillation. Experiments on a suite of AI-for-Math and out-of-domain benchmarks show that on-policy prefix distillation matches the performance of full OPD while reducing training FLOP by 2x-47x.

Standard LLM distillation wastes compute on two fronts: problems the student has already mastered (near-zero gradients) and problems far beyond its reach (incoherent gradients that erode existing capabilities). We show that this waste is not merely intuitive but structurally inevitable: the gradient signal-to-noise ratio in distillation provably vanishes at both pass-rate extremes. This theoretical observation leads to Paced, a framework that concentrates distillation on the zone of proximal development -- the frontier of a student model's competence -- via a principled pass-rate weight w(p) = p^α(1 - p)^β derived from the boundary-vanishing structure of distillation gradients. Key results: (1) Theory: We prove that the Beta kernel w(p) = p^α(1-p)^β is a leading-order weight family arising from the SNR structure of distillation, and that it is minimax-robust -- under bounded multiplicative misspecification, worst-case efficiency loss is only O(δ^2). (2)Distillation: On distillation from a larger teacher to a smaller student model with forward KL, Paced achieves significant gain over the base model, while keeping benchmark forgetting at a low level. (3)Self-distillation: On instruction-tuned models with reverse KL, gains are exceeding baselines as well. (4)Two-stage synergy: A forward-KL-then-reverse-KL schedule yields the strongest results in our setting, reaching substantial improvements on standard reasoning benchmarks -- supporting a mode-coverage-then-consolidation interpretation of the distillation process. All configurations require only student rollouts to estimate pass rates, need no architectural changes, and are compatible with any KL direction.

We study training LLM judges from natural language feedback, especially for subjective tasks where the verdict depends strongly on which evaluation criteria the judge invokes and how it weighs them. The dominant approach, outcome-supervised RL (e.g., GRPO), credits every token in the rollout with a single scalar determined only by the accuracy of the final verdict, providing no separate credit at the criterion-choice tokens and ignoring the rich language feedback (e.g., preference rationales) that naturally accompanies preference labels. Self-Distillation (SD) is one natural way to use this language feedback: the same model, conditioned on this feedback, acts as a teacher providing dense, position-level supervision. However, not all positions carry equally useful signal. Using the per-position entropy shift between teacher and student, we identify two regimes: context sharpening, where the teacher concentrates probability on a particular feedback-aligned criterion expression, and context spreading, where the teacher distributes probability across multiple feedback-aligned alternatives. We interpret these patterns as follows: sharpening encourages memorization of a particular criterion expression, whereas spreading promotes semantic understanding by preserving these alternatives. Motivated by this asymmetry, we introduce position masking based on the entropy shift that retains the lower tail of the entropy-shift distribution. Experiments show that masking higher-entropy-shift positions improves out-of-distribution generalization over naive SD. The resulting self-distilled judges outperform judges trained with outcome-supervised RL by 2-9 percentage points on the evaluated subjective subcategories, while remaining competitive on objective ones.

Recent hybrid video generation models combine autoregressive temporal dynamics with diffusion-based spatial denoising, but their sequential, iterative nature leads to error accumulation and long inference times. In this work, we propose a distillation-based framework for efficient causal video generation that enables high-quality synthesis with extremely limited denoising steps. Our approach builds upon the Distribution Matching Distillation (DMD) framework and proposes a novel Adversarial Self-Distillation (ASD) strategy, which aligns the outputs of the student model's n-step denoising process with its (n+1)-step version at the distribution level. This design provides smoother supervision by bridging small intra-student gaps and more informative guidance by combining teacher knowledge with locally consistent student behavior, substantially improving training stability and generation quality in extremely few-step scenarios (e.g., 1-2 steps). In addition, we present a First-Frame Enhancement (FFE) strategy, which allocates more denoising steps to the initial frames to mitigate error propagation while applying larger skipping steps to later frames. Extensive experiments on VBench demonstrate that our method surpasses state-of-the-art approaches in both one-step and two-step video generation. Notably, our framework produces a single distilled model that flexibly supports multiple inference-step settings, eliminating the need for repeated re-distillation and enabling efficient, high-quality video synthesis.

On-policy self-distillation, where a student is pulled toward a copy of itself conditioned on privileged context (e.g., a verified solution or feedback), offers a promising direction for advancing reasoning capability without a stronger external teacher. Yet in math reasoning the gains are inconsistent, even when the same approach succeeds elsewhere. A pointwise mutual information analysis traces the failure to the privileged context itself: it inflates the teacher's confidence on tokens already implied by the solution (structural connectives, verifiable claims) and deflates it on deliberation tokens ("Wait", "Let", "Maybe") that drive multi-step search. We propose Anti-Self-Distillation (AntiSD), which ascends a divergence between student and teacher rather than descending it: this reverses the per-token sign and yields a naturally bounded advantage in one step. An entropy-triggered gate disables the term once the teacher entropy collapses, completing a drop-in replacement for default self-distillation. Across five models from 4B to 30B parameters on math reasoning benchmarks, AntiSD reaches the GRPO baseline's accuracy in 2 to 10x fewer training steps and improves final accuracy by up to 11.5 points. AntiSD opens a path to scalable self-improvement, where a language model bootstraps its own reasoning through its training signal.

Increasing test-time computation is a straightforward approach to enhancing the quality of responses in Large Language Models (LLMs). While Best-of-N sampling and Self-Consistency with majority voting are simple and effective, they require a fixed number of sampling responses for each query, regardless of its complexity. This could result in wasted computation for simpler questions and insufficient exploration for more challenging ones. In this work, we argue that model confidence of responses can be used for improving the efficiency of test-time scaling. Unfortunately, LLMs are known to be overconfident and provide unreliable confidence estimation. To address this limitation, we introduce Self-Calibration by distilling Self-Consistency-derived confidence into the model itself. This enables reliable confidence estimation at test time with one forward pass. We then design confidence-based efficient test-time scaling methods to handle queries of various difficulty, such as Early-Stopping for Best-of-N and Self-Consistency with calibrated confidence. Experiments on three LLMs across six datasets demonstrate the effectiveness of our approach. Specifically, applying confidence-based Early Stopping to Best-of-N improves MathQA accuracy from 81.0 to 83.6 with a sample budget of 16 responses, indicating the efficacy of confidence-based sampling strategy at inference time.

On-policy distillation (OPD) provides dense teacher supervision on student-generated trajectories, but standard reverse-KL training can assign insufficient probability to other plausible continuations. Teacher entropy alone does not reveal whether uncertainty is concentrated among a few plausible next tokens or dispersed over a long probability tail, nor whether the student already represents those candidates well. Moreover, local teacher probabilities may not predict downstream success. We introduce Sparse Probing and Outcome-calibrated Targets OPD (SPOT), which addresses two coupled decisions, where to probe and what to distill, through an acquisition--exploration--exploitation procedure. During acquisition, a position-level score combines normalized teacher entropy, the probability mass captured by a small top-k candidate set, and student--teacher mismatch to allocate a limited probing budget. During exploration, SPOT evaluates teacher-proposed candidates through verifier-scored student continuations. During exploitation, these outcomes produce a closed-form, KL-regularized target that favors candidates with better downstream outcomes while remaining anchored to the teacher distribution. Extensive experiments across multiple student models and reasoning benchmarks demonstrate the effectiveness of SPOT in improving reasoning performance while balancing solution quality and coverage.

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.

Blind super-resolution methods based on stable diffusion showcase formidable generative capabilities in reconstructing clear high-resolution images with intricate details from low-resolution inputs. However, their practical applicability is often hampered by poor efficiency, stemming from the requirement of thousands or hundreds of sampling steps. Inspired by the efficient adversarial diffusion distillation (ADD), we design~\name~to address this issue by incorporating the ideas of both distillation and ControlNet. Specifically, we first propose a prediction-based self-refinement strategy to provide high-frequency information in the student model output with marginal additional time cost. Furthermore, we refine the training process by employing HR images, rather than LR images, to regulate the teacher model, providing a more robust constraint for distillation. Second, we introduce a timestep-adaptive ADD to address the perception-distortion imbalance problem introduced by original ADD. Extensive experiments demonstrate our~\name~generates better restoration results, while achieving faster speed than previous SD-based state-of-the-art models (e.g., 7times faster than SeeSR).

Rubrics have emerged as an alternative to RLVR in open-ended domains where a single ground-truth final answer is not available. Existing rubric-based training methods rely on an LLM verifier that scores each rollout against rubrics. This introduces substantial training-time overhead, exposes optimization to verifier-specific biases, and reduces rubric feedback to a sparse end-of-trajectory signal. We propose Rubric-Guided Self-Distillation (RGSD), a verifier-free training method in which the base policy, conditioned on the rubric, serves as the teacher for the unconditioned student. RGSD distills the rubric-conditioned teacher distribution into the student token-by-token, replacing sparse trajectory-level rewards with dense per-token learning signals and removing the LLM judge from the training loop entirely. Across Qwen-2.5 (3B, 7B) and Qwen3-Thinking (4B, 8B) models on medical and science domains, RGSD achieves rubric satisfaction comparable to judge-based GRPO while using one on-policy rollout per prompt and no training-time verifier calls. Ablations show that raw rubrics provide a stronger teacher enrichment signal than self-generated reference responses, while a stronger GRPO judge can outperform RGSD in some settings, positioning RGSD as a complementary verifier-free alternative when verifier cost or reliability is the bottleneck.

On-policy distillation offers dense, per-token supervision for training reasoning models; however, it remains unclear under which conditions this signal is beneficial and under which it is detrimental. Which teacher model should be used, and in the case of self-distillation, which specific context should serve as the supervisory signal? Does the optimal choice vary from one token to the next? At present, addressing these questions typically requires costly training runs whose aggregate performance metrics obscure the dynamics at the level of individual tokens. We introduce a training-free diagnostic framework that operates at the highest resolution: per token, per question, and per teacher. We derive an ideal per-node gradient defined as the parameter update that maximally increases the student's probability of success. We then develop a scalable targeted-rollout algorithm to estimate this gradient efficiently, even for long chains of intermediate thoughts. The gradient alignment score, defined as the cosine similarity between this ideal gradient and any given distillation gradient, quantifies the extent to which a particular configuration approximates the ideal signal. Across a range of self-distillation settings and external teacher models, we observe that distillation guidance exhibits substantially higher alignment with the ideal on incorrect rollouts than on correct ones, where the student already performs well and the teacher's signal tends to become noisy. Furthermore, we find that the optimal distillation context depends jointly on the student model's capacity and the target task, and that no single universally effective configuration emerges. These findings motivate the use of per-task, per-token diagnostic analyses for distillation.

Few-step streaming audio--video generation requires both causal modeling and step distillation, yet standard training recipes face two context-related challenges. Teacher forcing pairs clean history with a noisy target, but supervises predictive contextual representations only indirectly through velocity prediction. Meanwhile, directly reusing bidirectional score models in causal Distribution Matching Distillation (DMD) creates a mismatch between generation and scoring contexts. We address these challenges with Salt++, a two-stage post-training framework comprising Causal Self-Flow (CSF) and context-aligned autoregressive DMD. CSF exploits contextual information asymmetry by varying the history while keeping the noisy target fixed: a noise-mixed-history student aligns its intermediate representations with those of a clean-history exponential-moving-average teacher. This self-supervised signal encourages the student to extract semantic information and improves cross-modal alignment. Context-aligned AR DMD shares the causal mask and prefix across generator sampling, fake-score training, and real-score evaluation to match generated and reference distributions under a block-conditional KL objective. With calibrated teacher guidance, it performs clean-prefix few-step distillation and then adapts to generated histories without switching objectives or requiring separate consistency distillation. At 480p, Salt++ improves visual and motion quality by 57% and 45% over OmniForcing on JavisBench under the same 4-step causal setting. A separate scale-wise post-training stage extends Salt++ to 4-step 1664times960 generation, outperforming bidirectional LTX-2 on six of seven reported metrics. Project page: https://xingtongge.github.io/Saltpp

While diffusion distillation has enabled one-step generation through methods like Variational Score Distillation, adapting distilled models to emerging new controls -- such as novel structural constraints or latest user preferences -- remains challenging. Conventional approaches typically requires modifying the base diffusion model and redistilling it -- a process that is both computationally intensive and time-consuming. To address these challenges, we introduce Joint Distribution Matching (JDM), a novel approach that minimizes the reverse KL divergence between image-condition joint distributions. By deriving a tractable upper bound, JDM decouples fidelity learning from condition learning. This asymmetric distillation scheme enables our one-step student to handle controls unknown to the teacher model and facilitates improved classifier-free guidance (CFG) usage and seamless integration of human feedback learning (HFL). Experimental results demonstrate that JDM surpasses baseline methods such as multi-step ControlNet by mere one-step in most cases, while achieving state-of-the-art performance in one-step text-to-image synthesis through improved usage of CFG or HFL integration.

Recent work on distilling Whisper's knowledge into small models using pseudo-labels shows promising performance while reducing the size by up to 50\%. This results in small, efficient, and dedicated models. However, a critical step of distillation from pseudo-labels involves filtering high-quality predictions and using only those during training. This step requires ground truth labels to compare and filter low-quality examples making the whole process supervised. In addition to that, the distillation process requires a large amount of data thereby limiting the ability to distill models in low-resource settings. To address this challenge, we propose a distillation framework that does not require any labeled data. Through experimentation, we show that our best distilled models outperform the teacher model by 5-7 points in terms of WER compared to those without filtering and are on par with or perform better than similar supervised data filtering setups. When we scale the data, our models significantly outperform all zero-shot and supervised models. We demonstrate that it is possible to distill large Whisper models into relatively small ones without using any labeled data. Our distilled models are also 25-50\% more compute- and memory-efficient while maintaining performance equal to or better than that of the teacher model.

On-policy distillation (OPD) trains a student on its own trajectories under token-level teacher supervision, but existing methods are capped by a single-teacher capability ceiling: when the teacher errs, the student inherits the error. OPD also remains largely unexplored in agentic tasks, where per-step errors compound across long trajectories and destabilize training. We propose MAD-OPD (Multi-Agent Debate-driven On-Policy Distillation), which breaks this ceiling by recasting the distillation teacher as a deliberative collective of teachers that debate over the student's on-policy state; the debate produces an emergent collective intelligence that supplies token-level supervision, with each teacher's contribution weighted by its post-debate confidence. To extend OPD to agentic tasks, we also introduce On-Policy Agentic Distillation (OPAD), which adds step-level sampling to stabilize training under multi-step error compounding. We additionally derive a task-adaptive divergence principle, selecting JSD (Jensen-Shannon divergence) for agentic stability and reverse KL (Kullback-Leibler) divergence for code generation, and verify it both theoretically and empirically. Across six teacher-student configurations (Qwen3 and Qwen3.5; 1.7B-14B students, 8B-32B teachers) and five agentic and code benchmarks, MAD-OPD ranks first across all six configurations; on the 14B+8Bto4B setting it lifts the agentic average by +2.4% and the code average by +3.7% over the stronger single-teacher OPD.

RLVR provides reliable trajectory-level credit, while OPSD offers dense supervision for token-level credit. This exposes a fundamental coupling when updating step-level credit direction and magnitude with teacher supervision, preventing steps from receiving reliable credit directions and contribution magnitudes, while making both vulnerable to teacher judgment errors and preference variance, as supported by our theoretical analysis. To separate credit direction from its contribution magnitude, we introduce Decoupled Credit Self-Distillation (DCSD), which theoretically decouples credit direction and magnitude into two reliable signals and uses them to calibrate privileged teacher supervision. Specifically, we design belief-margin probing to determine credit direction and marginal information gain to quantify credit magnitude, enabling step-to-token credit assignment for policy optimization. Across 11 benchmarks, DCSD achieves the best overall scores against GRPO, OPSD, RLSD, and RLCSD. Compared with base models, DCSD improves the overall score by 8.45 points on mathematical reasoning and 7.01 points on multimodal reasoning, while correcting the credit direction for 6\% of tokens and yielding a 1.5times reduction in token credit magnitude.

Mixture-of-Experts (MoE) scales language models efficiently through sparse expert activation, and its dynamic variant further reduces computation by adjusting the activated experts in an input-dependent manner. Existing dynamic MoE methods usually rely on pre-training from scratch or task-specific adaptation, leaving the practical conversion of fully trained MoE underexplored. Enabling such adaptation would directly alleviate the inference costs by allowing easy tokens to bypass unnecessary expert during serving. This paper introduces Zero-Expert Self-Distillation Adaptation (ZEDA), a low-cost framework that transforms post-trained static MoE models into efficient dynamic ones. To stabilize this architectural conversion, ZEDA injects parameter-free zero-output experts into each MoE layer and adapts the augmented model through two-stage self-distillation, utilizing the original MoE as a frozen teacher and applying a group-level balancing loss. On Qwen3-30B-A3B and GLM-4.7-Flash across 11 benchmarks spanning math, code, and instruction following, ZEDA eliminates over 50% of expert FLOPs at marginal accuracy loss. It outperforms the strongest dynamic MoE baseline by 6.1 and 4.0 points on the two models, and delivers ~1.20times end-to-end inference speedup.

Consistency models have been proposed for fast generative modeling, achieving results competitive with diffusion and flow models. However, these methods exhibit inherent instability and limited reproducibility when training from scratch, motivating subsequent work to explain and stabilize these issues. While these efforts have provided valuable insights, the explanations remain fragmented, and the theoretical relationships remain unclear. In this work, we provide a theoretical examination of consistency models by analyzing them from a flow map-based perspective. This joint analysis clarifies how training stability and convergence behavior can give rise to degenerate solutions. Building on these insights, we revisit self-distillation as a practical remedy for certain forms of suboptimal convergence and reformulate it to avoid excessive gradient norms for stable optimization. We further demonstrate that our strategy extends beyond image generation to diffusion-based policy learning, without reliance on a pretrained diffusion model for initialization, thereby illustrating its broader applicability.

Diffusion Models (DMs) have achieved great success in image generation and other fields. By fine sampling through the trajectory defined by the SDE/ODE solver based on a well-trained score model, DMs can generate remarkable high-quality results. However, this precise sampling often requires multiple steps and is computationally demanding. To address this problem, instance-based distillation methods have been proposed to distill a one-step generator from a DM by having a simpler student model mimic a more complex teacher model. Yet, our research reveals an inherent limitations in these methods: the teacher model, with more steps and more parameters, occupies different local minima compared to the student model, leading to suboptimal performance when the student model attempts to replicate the teacher. To avoid this problem, we introduce a novel distributional distillation method, which uses an exclusive distributional loss. This method exceeds state-of-the-art (SOTA) results while requiring significantly fewer training images. Additionally, we show that DMs' layers are differentially activated at different time steps, leading to an inherent capability to generate images in a single step. Freezing most of the convolutional layers in a DM during distributional distillation enables this innate capability and leads to further performance improvements. Our method achieves the SOTA results on CIFAR-10 (FID 1.54), AFHQv2 64x64 (FID 1.23), FFHQ 64x64 (FID 0.85) and ImageNet 64x64 (FID 1.16) with great efficiency. Most of those results are obtained with only 5 million training images within 6 hours on 8 A100 GPUs.

Reasoning models have advanced rapidly, but the dominant reinforcement learning from verifiable rewards (RLVR) recipe remains surprisingly narrow: sample many responses and reward each with a single bit indicating whether the final answer is correct. Yet many settings provide rich feedback, including execution traces, tool outputs, expert corrections, and model self-evaluations. We study how to use such feedback through a distributional variant of the classic imitation learning algorithm DAgger, where the learner has local access to an expert distribution on states visited by the current policy. This yields a simple forward cross-entropy objective that admits a blackbox expert and whose sequence-level gradient {conduct rich credit assignment by propagating} future expert-student disagreement back to earlier decisions. We show that prior RL with self-distillation objectives based on reverse KL or Jensen-Shannon fail to guarantee monotonic policy improvement: even when the expert has higher reward, their updates may increase probability on worse actions. In contrast, we show that forward cross-entropy admits monotonic policy improvement and enjoys guarantees on regret. We further show that our objective optimizes a lower bound on teacher-weighted likelihood of success, leading to improved Pass@N. Empirically, our approach, DistIL, improves over RLVR and RL with self-distillation baselines across a variety of domains: scientific reasoning, coding, and solving hard mathematical problems.

On-policy Distillation (OPD) supervises a student model on trajectories sampled from its own policy by minimizing the divergence between the output distributions of the teacher and student at each token position, thereby providing dense token-level supervision. Although existing OPD methods have demonstrated strong performance in improving the reasoning ability of student models, their objectives fundamentally rely on token-level distribution matching. Consequently, they lack an explicit signal for comparing a token's relative compatibility across reasoning modes and thus do not directly model preferences between these modes. To address this limitation, we propose COPD, a contrastive OPD framework. Specifically, for each token generated by the student model, a frozen teacher model scores the same student state under two contrasting instructions that elicit light and heavy reasoning. The difference between the resulting log probabilities serves as a token-level advantage signal to guide the OPD update. Rather than merely imitating a single teacher distribution, COPD directly encourages the student model to learn more concise and efficient reasoning strategies. We conduct experiments on nine multimodal benchmarks covering both reasoning and understanding tasks. The results show that COPD substantially reduces reasoning length without compromising model performance and consistently improves efficiency across different tasks and model scales. Furthermore, the contrastive formulation can be seamlessly integrated into the On-policy Self-distillation (OPSD) framework, where self-contrastive supervision is constructed without an additional teacher model, thereby enabling the model to distill itself toward lightweight reasoning.

In standard adversarial training, models are optimized to fit one-hot labels within allowable adversarial perturbation budgets. However, the ignorance of underlying distribution shifts brought by perturbations causes the problem of robust overfitting. To address this issue and enhance adversarial robustness, we analyze the characteristics of robust models and identify that robust models tend to produce smoother and well-calibrated outputs. Based on the observation, we propose a simple yet effective method, Annealing Self-Distillation Rectification (ADR), which generates soft labels as a better guidance mechanism that accurately reflects the distribution shift under attack during adversarial training. By utilizing ADR, we can obtain rectified distributions that significantly improve model robustness without the need for pre-trained models or extensive extra computation. Moreover, our method facilitates seamless plug-and-play integration with other adversarial training techniques by replacing the hard labels in their objectives. We demonstrate the efficacy of ADR through extensive experiments and strong performances across datasets.

On-policy self-distillation (OPSD) lets a language model learn from a frozen copy of itself that sees an answer or a worked solution. Giving the teacher this extra information seems to offer the student more to learn, but how much does it add beyond distillation itself? To isolate that contribution, we construct AMPLE-Math, a reusable suite of 5,319 mathematical problems with six reasoning views that share the same answer, and compare each view with matched reference-free distillation. With a thinking-enabled teacher supervising direct-response rollouts, reference-free distillation accounts for much of Qwen3-1.7B's improvement under thinking-enabled evaluation, both in domain and on external benchmarks. Evidence for an additional reference benefit is modest in Qwen, strongest for a polished solution, whereas complete traces add two percentage points in SmolLM3-3B at step 50. These benefits depend on the student being trained. At the same checkpoint, replacing short direct-response rollouts with long thinking-enabled rollouts turns gains into losses in both families while the problems, references, and evaluation stay fixed. Teacher profiles and matched loss interventions in Qwen further show that changing token-level supervision can leave student behavior largely unchanged. Together, these findings suggest that OPSD can improve access to existing reasoning capabilities through parameters shared by direct-response and thinking-enabled inference. The value of a privileged reference is what it adds to this cross-mode transfer, not how much of the solution it reveals.

On-policy self-distillation (OPSD) provides dense, token-level supervision for reasoning models by aligning a model's own distribution with the distribution it produces under privileged context, typically a verified solution. However, we show that the learning signal drawn from this distributional gap concentrates on style tokens rather than task-bearing ones, as the hinted model tends to produce more direct, shorter outputs. We term this pathology privilege-induced style drift, which destabilizes training or causes response length to shrink. To address this, we propose RLCSD (Reinforcement Learning with Contrastive on-policy Self-Distillation), which mitigates this drift by contrasting the teacher-student gap under a correct hint against that under a wrong hint, suppressing the style shift that conditioning on a hint tends to induce regardless of correctness, and yielding a signal that is more concentrated on task-bearing tokens. Experiments on Qwen3 (1.7B/4B/8B) and Olmo-3-7B-Think across mathematical and logical reasoning show that RLCSD consistently outperforms GRPO and prior OPSD methods. We further show that the contrastive principle is general: it plugs into existing OPSD methods to improve them, and its underlying insight extends to the broader cross-model on-policy distillation setting.

On-policy distillation (OPD) trains a student on its own trajectories with dense per-token supervision from a stronger teacher, and often outperforms off-policy distillation and standard reinforcement learning. However, we find that its effectiveness implicitly relies on two assumptions that frequently break in practice: trajectory-level alignment between the student and the teacher, and uniform token-level reliability of the teacher's preferences. We therefore propose Sign-Gated On-Policy Distillation (SG-OPD), which uses a binary verifier as a trust signal for the teacher at two complementary granularities: phased teacher sampling mixes in verifier-endorsed teacher rollouts at cold-start, and a sign-consistency gate extrapolates the distillation update on tokens where the teacher agrees with the verifier-correct direction and interpolates it where it disagrees. Experiments on competition-level mathematical reasoning benchmarks show that SG-OPD consistently outperforms standard OPD, with average gains of 1.98 and 7.50 at the per-sample and per-question levels, respectively.

On-policy self-distillation provides dense supervision for reasoning models via a privileged self-teacher. However, this supervision reflects local token preferences rather than the expected return of an unguided student continuation. Recent methods combine this signal with GRPO. They use GRPO for update directions and the teacher for signal scaling. However, we demonstrate a more effective integration within PPO. Specifically, we identify complementary positional dynamics: privileged information enhances a critic's value-prediction accuracy toward the response's end, whereas self-teacher guidance is strong initially, drops mid-generation, and rebounds finally. These insights motivate Value-Augmented Self-Distillation Policy Optimization (VASPO), wherein a self-teacher and critic evaluate identical privileged information at student-generated prefixes. The critic computes token-level PPO advantages from predicted continuation returns, while the self-teacher modulates selected positive advantages via bounded probability ratios. Across six mathematical reasoning benchmarks, VASPO improves mean accuracy over PPO by 2.59 and 1.81 percentage points on Qwen3-4B and OLMo3-7B variants, respectively, and achieves the highest mean accuracy among evaluated methods on Knights and Knaves. Our code is available at https://github.com/cii030/VASPO.

Enabling large language models to achieve stable self-improvement without external expert supervision remains a central challenge in complex reasoning tasks. Existing self-distillation and reinforcement learning methods lack explicit mechanisms for tracking problem-level learning progress and adapting optimization strategies accordingly. Consequently, training may over-optimize easy problems, receive weak supervision from hard problems, and fail to sufficiently explore borderline cases. To resolve these issues, we propose DRIFT, an online self-evolution policy optimization framework for large language models. DRIFT regulates the model's self-improvement process through the joint use of Difficulty Routing and Rhythm Gating. The former identifies the model's learning state at the problem level and dynamically allocates self-distillation and reinforcement learning signals, while the latter refines policy updates at the token level, concentrating exploration on critical reasoning positions. By further incorporating a success buffer and a two-stage curriculum learning strategy, DRIFT preserves high-quality historical experience while progressively guiding the model from reliable behavior acquisition toward stable policy evolution. Evaluated across five benchmarks and three model scales, DRIFT surpasses the peak performance of both GRPO and SDPO across all evaluated metrics. On the average score over the five benchmarks, DRIFT achieves 79.5%, outperforming GRPO by 9.5% and SDPO by 7.5%, establishing a new state-of-the-art result. Notably, on ToolUse, DRIFT reaches an accuracy of 79.2%, improving over GRPO by 13.5% and SDPO by 10.7%, setting a new state-of-the-art and substantially outperforming all concurrent methods.

On-policy distillation (OPD) trains a student on its own trajectories with token-level teacher feedback and often outperforms off-policy distillation and standard reinforcement learning. However, we find that its standard advantage weighted policy gradient suffers from three structural weaknesses, including high variance updates, vanishing gradients in zero-advantage regions, and exploration bottlenecks when corrective signals are insufficient. We therefore propose Asymmetric On-Policy Distillation (AOPD), which replaces ineffective negative reinforcement with localized divergence minimization in non-positive advantage regions while preserving positive reinforcement learning. Experiments on mathematical reasoning benchmarks show that AOPD consistently outperforms standard OPD, with average gains of 4.09 / 8.34 under strong / weak initialization, respectively. AOPD also maintains higher policy entropy during training and better capability retention during sequential tool-use adaptation.

Large reasoning models often solve problems through long chain-of-thought (CoT) traces, yet much of this computation is spent on redundant derivations, repeated self-verification, and detours that do not improve the final answer. Existing on-policy self-distillation methods reduce this cost by matching a student model to a concise copy of itself on prefixes sampled from the student's own rollouts. We show that this objective has an initialization bottleneck. Since supervision is applied only to visited prefixes, training from a verbose base model places the KL loss on contexts that are often noisy, redundant, or already off track. In such regions, a concise teacher can provide only local corrections, while the student continues to explore trajectories that an efficient reasoner should avoid. In this paper, we propose BIRD(Bootstrapped Iterative Self-Reasoning Distillation), a two-stage self-reasoning distillation method that improves the rollout distribution before on-policy training. BIRD first samples concise solutions from the base model under a brevity instruction, keeps only answer-correct traces, and performs a lightweight prompt-switch SFT step. The traces are generated with the brevity instruction but learned under the original task prompt, turning instruction-induced conciseness into a default reasoning behavior. Starting from this warm model, BIRD then applies on-policy reverse-KL distillation with a concise self-teacher, now on cleaner and more informative prefixes. Across Qwen3 series models, BIRD achieves a stronger accuracy-efficiency trade-off than prompting and cold-start on-policy distillation on MATH-500 and AIME benchmarks. On Qwen3-8B, it improves MATH-500 accuracy from 86.2% to 92.0% while reducing the average response length from 3,099 to 1,115 tokens. These results highlight prefix support as a central factor in efficient reasoning distillation.

Text-to-image diffusion models produce impressive results but are frustrating tools for artists who desire fine-grained control. For example, a common use case is to create images of a specific instance in novel contexts, i.e., "identity-preserving generation". This setting, along with many other tasks (e.g., relighting), is a natural fit for image+text-conditional generative models. However, there is insufficient high-quality paired data to train such a model directly. We propose Diffusion Self-Distillation, a method for using a pre-trained text-to-image model to generate its own dataset for text-conditioned image-to-image tasks. We first leverage a text-to-image diffusion model's in-context generation ability to create grids of images and curate a large paired dataset with the help of a Visual-Language Model. We then fine-tune the text-to-image model into a text+image-to-image model using the curated paired dataset. We demonstrate that Diffusion Self-Distillation outperforms existing zero-shot methods and is competitive with per-instance tuning techniques on a wide range of identity-preservation generation tasks, without requiring test-time optimization.

On-policy self-distillation fine-tuning (SDFT) learns new skills from demonstrations while reducing forgetting, but it always distils toward the full demonstration-conditioned teacher. This fixes teacher influence at the full-teacher endpoint, providing no control over how much demonstration information should be transferred at each prediction state. We introduce Information-Proximal SDFT (iSDFT), which instead treats the teacher as a budgeted source of information. At each token, iSDFT selects the distribution closest to the current student that satisfies a prescribed teacher-information constraint, yielding a closed-form exponential target with a locally determined tilt. To control cumulative drift, we further anchor the student to its frozen base policy. Across four heterogeneous LLM backbones and two specialisation tasks, iSDFT improves vanilla SDFT in 7 of 8 model-task settings and matches it in the remaining one. It also provides tighter retention on the original SDFT benchmark suite, with 73% of evaluations remaining within 0.5 points of the base model versus 52% for the strongest baseline, while achieving the largest mean improvement on all ten additional mathematics, coding, and competition-mathematics benchmarks. These results show that controlling how much and when teacher information is introduced improves specialisation while preserving broader capability.

We present an ultra-efficient post-training method for shortcutting large-scale pre-trained flow matching diffusion models into efficient few-step samplers, enabled by novel velocity field self-distillation. While shortcutting in flow matching, originally introduced by shortcut models, offers flexible trajectory-skipping capabilities, it requires a specialized step-size embedding incompatible with existing models unless retraining from scratchx2013a process nearly as costly as pretraining itself. Our key contribution is thus imparting a more aggressive shortcut mechanism to standard flow matching models (e.g., Flux), leveraging a unique distillation principle that obviates the need for step-size embedding. Working on the velocity field rather than sample space and learning rapidly from self-guided distillation in an online manner, our approach trains efficiently, e.g., producing a 3-step Flux less than one A100 day. Beyond distillation, our method can be incorporated into the pretraining stage itself, yielding models that inherently learn efficient, few-step flows without compromising quality. This capability also enables, to our knowledge, the first few-shot distillation method (e.g., 10 text-image pairs) for dozen-billion-parameter diffusion models, delivering state-of-the-art performance at almost free cost.

The ability to generate virtual environments is crucial for applications ranging from gaming to physical AI domains such as robotics, autonomous driving, and industrial AI. Current learning-based 3D reconstruction methods rely on the availability of captured real-world multi-view data, which is not always readily available. Recent advancements in video diffusion models have shown remarkable imagination capabilities, yet their 2D nature limits the applications to simulation where a robot needs to navigate and interact with the environment. In this paper, we propose a self-distillation framework that aims to distill the implicit 3D knowledge in the video diffusion models into an explicit 3D Gaussian Splatting (3DGS) representation, eliminating the need for multi-view training data. Specifically, we augment the typical RGB decoder with a 3DGS decoder, which is supervised by the output of the RGB decoder. In this approach, the 3DGS decoder can be purely trained with synthetic data generated by video diffusion models. At inference time, our model can synthesize 3D scenes from either a text prompt or a single image for real-time rendering. Our framework further extends to dynamic 3D scene generation from a monocular input video. Experimental results show that our framework achieves state-of-the-art performance in static and dynamic 3D scene generation.

Enabling agents to learn from experience and internalize it into their policy has become a central problem in self-evolving AI. On-policy self-distillation (OPSD) offers an effective pathway by using a privileged self-teacher to provide dense supervision on the student's own trajectories; however, existing methods still rely heavily on designer-specified privileged artifacts (e.g., answers, feedback, skills, or trajectories), limiting the end-to-end learnability and scalability required for continual self-improvement. In this work, we introduce Latent On-Policy Self-Distillation (LOPD), which, rather than proposing another hand-crafted OPSD variant with a newly prescribed form of privileged context, makes the teacher's privileged context itself learnable end-to-end from experience. Technically, LOPD retrieves relevant experiences and composes them into continuous latent tokens that condition a self-teacher, while the student generates trajectories from the task and interaction history and receives dense token-level supervision at every visited prefix. We further introduce a privileged-margin objective to stabilize and regulate the learning of latent context. Empirically, LOPD demonstrates (I) strong performance, outperforming RLVR and representative OPSD methods including OPSD, SDPO, and Skill-SD across both agentic tool use and code generation; and (II) high learning efficiency, surpassing GRPO and Skill-SD with less than 30% of their rollout budget. Ablation studies further provide direct evidence that making privileged context learnable is necessary for realizing these gains. Together, these results position LOPD as a step toward a more scalable and self-directed paradigm for agent evolution.

Continual learning, enabling models to acquire new skills and knowledge without degrading existing capabilities, remains a fundamental challenge for foundation models. While on-policy reinforcement learning can reduce forgetting, it requires explicit reward functions that are often unavailable. Learning from expert demonstrations, the primary alternative, is dominated by supervised fine-tuning (SFT), which is inherently off-policy. We introduce Self-Distillation Fine-Tuning (SDFT), a simple method that enables on-policy learning directly from demonstrations. SDFT leverages in-context learning by using a demonstration-conditioned model as its own teacher, generating on-policy training signals that preserve prior capabilities while acquiring new skills. Across skill learning and knowledge acquisition tasks, SDFT consistently outperforms SFT, achieving higher new-task accuracy while substantially reducing catastrophic forgetting. In sequential learning experiments, SDFT enables a single model to accumulate multiple skills over time without performance regression, establishing on-policy distillation as a practical path to continual learning from demonstrations.

Consistency distillation methods have demonstrated significant success in accelerating generative tasks of diffusion models. However, since previous consistency distillation methods use simple and straightforward strategies in selecting target timesteps, they usually struggle with blurs and detail losses in generated images. To address these limitations, we introduce Target-Driven Distillation (TDD), which (1) adopts a delicate selection strategy of target timesteps, increasing the training efficiency; (2) utilizes decoupled guidances during training, making TDD open to post-tuning on guidance scale during inference periods; (3) can be optionally equipped with non-equidistant sampling and x0 clipping, enabling a more flexible and accurate way for image sampling. Experiments verify that TDD achieves state-of-the-art performance in few-step generation, offering a better choice among consistency distillation models.

On-Policy Self-Distillation (OPSD) has emerged as a popular paradigm for large language model (LLM) self-improvement, allowing models to act as their own teachers by leveraging privileged information such as ground-truth solutions. However, recent findings indicate that OPSD can severely degrade the performance of LLMs on complex reasoning tasks: By forcing the student to imitate an artificially confident reasoning trace conditioned on privileged information, OPSD inadvertently suppresses expressions of uncertainty and penalizes the exploratory, self-corrective behaviors required to solve challenging problems. To address this, we introduce Negative Self-Distillation (NSD), a new framework that optimizes LLMs by diverging from flawed reasoning rather than imitating privileged solutions. Instead of relying on ground-truth answers or external supervision, NSD uses the model itself to generate a question-specific negative condition (eg, acting as a ``careless reasoner'') and pushes the student's distribution away from this self-generated negative teacher. Naively applying unlearning objectives to achieve this divergence is problematic, as flawed reasoning tokens are confounded with basic linguistic tokens; indiscriminately penalizing both risks catastrophically degrading the model's foundational language capabilities. We resolve this by designing a dynamic gating mechanism that automatically identifies and isolates reasoning-critical tokens, ensuring gradient updates target only behavioral flaws while preserving the model's linguistic priors. Empirically, NSD consistently outperforms OPSD and other label-free, self-bootstrapping reinforcement learning (RL) baselines.

Recently, diffusion-based removal methods have achieved promising visual quality in removing both target objects and their associated effects. However, they typically rely on multi-step denoising, leading to high inference cost. Directly applying existing one-step distillation methods is also suboptimal, since their global objectives lack explicit region-wise calibration and may weaken the asymmetric edit-and-preserve behavior required by object-effect removal. To address these challenges, we propose TurboClear, a one-step SDXL-based object-effect removal model. During training, we design Region-Calibrated Distribution Matching (RDM) for region-aware distillation to preserve the teacher model's asymmetric edit-and-preserve behavior. Furthermore, we propose Learnable Spatial Fusion (LSF) for lightweight inference-time fusion. Extensive experiments show that TurboClear significantly improves inference efficiency while maintaining competitive visual quality. TurboClear reduces the computational overhead by up to 40.04times compared to ObjectClear, and by up to 665times against the Flux-based method OmniPaint, all while maintaining comparable or better visual removal quality. Code is available at https://github.com/GuoCalix/TurboClear.

We introduce the Self-Evaluating Model (Self-E), a novel, from-scratch training approach for text-to-image generation that supports any-step inference. Self-E learns from data similarly to a Flow Matching model, while simultaneously employing a novel self-evaluation mechanism: it evaluates its own generated samples using its current score estimates, effectively serving as a dynamic self-teacher. Unlike traditional diffusion or flow models, it does not rely solely on local supervision, which typically necessitates many inference steps. Unlike distillation-based approaches, it does not require a pretrained teacher. This combination of instantaneous local learning and self-driven global matching bridges the gap between the two paradigms, enabling the training of a high-quality text-to-image model from scratch that excels even at very low step counts. Extensive experiments on large-scale text-to-image benchmarks show that Self-E not only excels in few-step generation, but is also competitive with state-of-the-art Flow Matching models at 50 steps. We further find that its performance improves monotonically as inference steps increase, enabling both ultra-fast few-step generation and high-quality long-trajectory sampling within a single unified model. To our knowledge, Self-E is the first from-scratch, any-step text-to-image model, offering a unified framework for efficient and scalable generation.

Large language models (LLMs) have become increasingly prevalent in our daily lives, leading to an expectation for LLMs to be trustworthy -- - both accurate and well-calibrated (the prediction confidence should align with its ground truth correctness likelihood). Nowadays, fine-tuning has become the most popular method for adapting a model to practical usage by significantly increasing accuracy on downstream tasks. Despite the great accuracy it achieves, we found fine-tuning is still far away from satisfactory trustworthiness due to "tuning-induced mis-calibration". In this paper, we delve deeply into why and how mis-calibration exists in fine-tuned models, and how distillation can alleviate the issue. Then we further propose a brand new method named Efficient Trustworthy Distillation (FIRST), which utilizes a small portion of teacher's knowledge to obtain a reliable language model in a cost-efficient way. Specifically, we identify the "concentrated knowledge" phenomenon during distillation, which can significantly reduce the computational burden. Then we apply a "trustworthy maximization" process to optimize the utilization of this small portion of concentrated knowledge before transferring it to the student. Experimental results demonstrate the effectiveness of our method, where better accuracy (+2.3%) and less mis-calibration (-10%) are achieved on average across both in-domain and out-of-domain scenarios, indicating better trustworthiness.

Deep search agents operate over trajectories spanning dozens of steps, yet standard reinforcement learning provides only a single outcome reward per trajectory, which is far too sparse for effective credit assignment. On-policy self-distillation (OPSD) addresses this by using the model's own logits as dense token-level teachers, but extending it to search agents introduces a fundamental tension: the teacher, having access to privileged information such as the correct answer, produces a distribution that differs systematically from the student's exploration-based reasoning, and naive distillation causes the student to inherit this information asymmetry rather than learn better search strategies. We resolve this tension through two contributions. First, we construct Evidence Anchors, which are concise, step-level evidence snippets extracted from the web, as privileged information that captures key reasoning steps without revealing the entire answer path. Second, we propose Step-Level Self-Distilled Policy Optimization (SSPO), which converts teacher-student disagreement into step-level advantage weights within GRPO, applied exclusively to incorrect trajectories. This design decouples what to update from how much to update: the outcome reward determines the direction of policy change, while the teacher modulates its magnitude at each step. Correct trajectories are left untouched, preserving their diversity. On Qwen3-8B, SSPO consistently outperforms GRPO across BrowseComp, GAIA, and FRAMES, surpassing or matching GRPO trained with twice as many gradient steps while adding only about 5 percent overhead per step from a single additional forward pass.

Weak-to-strong generalization asks whether stronger models can learn from weaker supervisors and surpass them. This question is particularly important for successive model generations and multi-domain consolidation, where repeating frontier-scale post-training from scratch can be prohibitively expensive. Yet conventional distillation treats the weak teacher as an optimization target, potentially imposing its capacity ceiling on the student. We introduce On-Policy Reverse Distillation (OPRD), which evaluates the teacher's policy shift relative to its reference policy on student rollouts and amplifies the component of the student's verifier-driven policy gradient along that direction. By rescaling only verifier-supported updates, OPRD preserves the stationary points of policy optimization while accelerating learning beyond the teacher. In both successive model transfer and multi-teacher distillation, OPRD achieves higher performance with fewer student updates than existing RL and distillation approaches. Response-style analysis shows that OPRD students remain closer to models trained with verifier-based RL alone than to their weak teachers, suggesting that teacher guidance accelerates rather than redirects the student's own optimization. Results in conventional strong-to-weak distillation further demonstrate that OPRD effectively combines verifier-driven policy optimization with teacher guidance regardless of capacity ordering.

In-context watermarking (ICW) prepends an instruction to a query asking the model to embed a statistically detectable signal in its response. It thus equips LLMs with a watermarking interface that third parties can invoke without access to model internals. Its reliability hinges on the LLM following the instruction without degrading answer quality, yet how well current LLMs do so has not been measured. We introduce ICWBench, a benchmark of three verifiable ICW instruction families, each scored on both detectability and answer quality. Evaluating 14 frontier proprietary and open-source LLMs, we find that none of the evaluated LLMs achieves both objectives across all three families. To address this, we propose a self-contained two-stage training method, requiring no distillation from a stronger model, no manual annotation, and no pre-existing ICW IF ability. The first stage, self-distillation with logits perturbation (SDLP), uses the same base LLM as both teacher and student: an instruction-equivalent decoding-time logits perturbation makes the teacher follow the ICW instruction, and the student is trained to match the teacher's output distribution. The second stage applies reinforcement learning with the automatic verifier as the reward. Applied to Qwen3-14B and GPT-OSS-20B, our method raises average TPR@1%FPR across three ICW instructions from 0.100 to 0.974 and from 0.337 to 0.968, respectively, while maintaining high response quality under both perplexity evaluation and LLM-as-a-Judge.

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