Daily Papers

On-policy distillation (OPD) trains compact language agents with teacher feedback on student-generated trajectories. In multi-turn tasks, compounding errors can move students beyond the teacher's effective supervision. We introduce Graph-Conditioned On-Policy Agent Distillation (GC-OPD), which enriches an off-the-shelf teacher's scoring context with execution evidence. A graph indexes repeated teacher executions by shared states while preserving complete successful and failed histories. After each student episode, GC-OPD retrieves current-state references or historical alternatives and combines them with student hindsight to score the original thought-action tokens. Using the same original teachers, GC-OPD improves mean success over vanilla OPD from 24.70% to 48.78% on ScienceWorld (4B student), from 53.36% to 85.26% on ALFWorld Unseen, and from 29.10% to 37.65% on WebShop. At matched student sizes, it also achieves higher mean success than every evaluated OPD baseline using GRPO-trained teachers on ScienceWorld and ALFWorld; the strongest such ScienceWorld 4B baseline reaches 46.66%. GC-OPD requires no task-specific teacher optimization.

On-policy distillation is pivotal for transferring reasoning capabilities to capacity-constrained models, yet remains prone to instability and negative transfer. We show that on-policy distillation can be interpreted, both theoretically and empirically, as a form of policy optimization, where the teacher-student log-likelihood ratio acts as a token reward. From this insight, we introduce REOPOLD (Relaxed On-Policy Distillation) a framework that stabilizes optimization by relaxing the strict imitation constraints of standard on-policy distillation. Specifically, REOPOLD temperately and selectively leverages rewards from the teacher through mixture-based reward clipping, entropy-based token-level dynamic sampling, and a unified exploration-to-refinement training strategy. Empirically, REOPOLD surpasses its baselines with superior sample efficiency during training and enhanced test-time scaling at inference, across mathematical, visual, and agentic tool-use reasoning tasks. Specifically, REOPOLD outperforms recent RL approaches achieving 6.7~12x greater sample efficiency and enables a 7B student to match a 32B teacher in visual reasoning with a ~3.32x inference speedup.

We study on-policy distillation (OPD) for agentic tasks, where an LLM agent interacts with an environment over multiple turns and a student imitates a teacher over these multi-turn interaction histories. Fully online OPD is costly because each update requires fresh student rollouts through the environment and teacher queries at visited histories. We propose Replayed-Prefix On-Policy Distillation (ReOPD), an off-environment alternative that reuses pre-collected teacher trajectories as replayed prefixes: the student acts at selected steps, while the teacher provides dense per-step supervision without executing new environment interactions. We show that multi-turn OPD introduces a prefix trap: making histories more student-on-policy improves relevance to the student, but can query the teacher on histories where its target is unreliable. This creates a two-sided distribution shift between student occupancy and teacher reliability. ReOPD addresses this by treating multi-turn OPD as a reliability-aware prefix distribution design and implements it with a simple step-decaying sampling schedule that emphasizes early, lower-shift prefixes. Across mathematical reasoning with Python and search environments over multiple teacher and student model scales, ReOPD preserves or improves OPD-level accuracy, uses zero tool calls during student training, and is at least 4times faster per rollout than OPD. ReOPD therefore turns expensive agent-environment interaction into a reusable offline resource, enabling scalable distillation across tools, tasks, and environments.

Developing lightweight, on-device vision-language GUI agents is essential for efficient cross-platform automated interaction. However, current on-device agents are constrained by limited model capacity, and further performance improvements remain urgently needed. Traditional Supervised Fine-Tuning (SFT) for small-scale models often leads to overfitting, catastrophic forgetting and policy rigidity, and thus fails to fully address these challenges. In this work, we propose a novel SFT-free training paradigm that significantly enhances the performance of small-scale models. We first present the initial systematic integration of generalized knowledge distillation into the GUI agent domain via Guided On-policy Distillation. By incorporating oracle reference trajectories together with a dynamic retrieval mechanism, our method reduces hallucinations and mitigates the cognitive misalignment inherent in multi-solution GUI tasks. Building on this foundation, we further introduce a Multi-solution Dual-level GRPO framework that jointly aligns macro-level subtask planning with micro-level execution matching, thereby improving exploration in long-horizon GUI agent scenarios. In addition, we construct an automated data generation pipeline to synthesize GUI task trajectories with rich multi-solution annotations. Extensive experiments show that our method achieves state-of-the-art performance among lightweight models while remaining competitive with substantially larger-scale models across all benchmarks. Ablation studies further demonstrate that structured on-policy distillation and multi-solution dual-level exploration can fully unlock the capabilities of 2B/3B scale agents, surpassing the performance limits of conventional imitation learning.

Tool-integrated reasoning (TIR) is difficult to scale to small language models due to instability in long-horizon tool interactions and limited model capacity. While reinforcement learning methods like group relative policy optimization provide only sparse outcome-level rewards. Recently, on-policy distillation (OPD) has gained popularity by supplying dense token-level supervision from a teacher on student-generated trajectories. However, our experiments indicate that applying OPD to TIR leads to a critical failure mode: erroneous tool calls tend to cascade across subsequent reasoning steps, progressively amplifying student-teacher divergence and rendering the teacher's token-level supervision increasingly unreliable. To address this, we propose SOD, a step-wise on-policy distillation framework for small language model agents, which adaptively reweights distillation strength at each step based on step-level divergence. Therefore, SOD can attenuate potentially misleading teacher signals in high-divergence regions while preserving dense guidance in well-aligned states. Experiments on challenging math, science, and code benchmarks show that SOD achieves up to 20.86% improvement over the second-best baseline. Notably, our 0.6B student achieves 26.13% on AIME 2025, demonstrating effective transfer of agentic reasoning to lightweight models. Our code is available at https://github.com/YoungZ365/SOD.

We propose Algorithm Distillation (AD), a method for distilling reinforcement learning (RL) algorithms into neural networks by modeling their training histories with a causal sequence model. Algorithm Distillation treats learning to reinforcement learn as an across-episode sequential prediction problem. A dataset of learning histories is generated by a source RL algorithm, and then a causal transformer is trained by autoregressively predicting actions given their preceding learning histories as context. Unlike sequential policy prediction architectures that distill post-learning or expert sequences, AD is able to improve its policy entirely in-context without updating its network parameters. We demonstrate that AD can reinforcement learn in-context in a variety of environments with sparse rewards, combinatorial task structure, and pixel-based observations, and find that AD learns a more data-efficient RL algorithm than the one that generated the source data.

Agentic search enables large language models to solve knowledge-intensive tasks by interleaving multi-step reasoning with retrieval, yet optimizing this with outcome-based reinforcement learning (RL) provides only sparse supervision. Knowledge distillation can supply denser guidance, and advanced proprietary models with their strong reasoning capabilities are promising teachers. While distilling from proprietary models can densify this supervisory signal, conventional logit-matching is precluded by hidden logits and mismatched tokenizers, whereas raw natural language trajectory imitation transfers superficial stylistic artifacts rather than core reasoning competence. To address the heterogeneous distillation problem and bridge the distribution gap, we propose Multi-Agent Protocol Distillation (MAPD), a joint distillation and RL framework uses a structured, style-normalized protocol as an intermediate representation. An offline multi-agent system (MAS) decomposes each query, retrieves supporting evidence, repairs failed searches, and converts the resulting exploration trace into a JSON protocol containing the task type, reasoning plan, and extractive grounding facts. During training, the protocol is provided only to a privileged branch of the student policy, whose token distributions furnish a dense distillation signal alongside the sparse RL objective. Extensive evaluations across seven QA benchmarks demonstrate that MAPD consistently outperforms competitive distillation and RL, achieving average success rates of 39.4\% on Qwen3-1.7B and 44.4\% on Qwen3-4B. Crucially, the framework generalizes robustly across diverse proprietary teachers while effectively mitigating the student policy from style drift and verbosity degeneration.

We study on-policy distillation (OPD) through the lens of reinforcement learning, establishing a connection between the reverse-KL objective in OPD and KL-regularized policy optimization. Building on this connection, we introduce Least-Square Policy Distillation (LSPD), an RL-inspired framework that brings optimistic exploration and off-policy data reuse from value-based RL into policy distillation. LSPD preserves policy diversity through exploration while improving rollout efficiency by repeatedly learning from previously collected trajectories. Our theoretical analysis connects LSPD to optimistic value-based learning and shows that its idealized formulation achieves a sharp mathcal O(log K) regret bound under online exploration. Empirically, LSPD consistently outperforms existing distillation baselines across six mathematical reasoning benchmarks and diverse teacher-student settings, with average gains of +1.59 points in Avg@16. Remarkably, through Pass@k evaluations up to k=64, we found that LSPD better preserves policy diversity by achieving stronger performance as k grows. Its fully off-policy variant achieves comparable performance to vanilla OPD using only the first 25% of rollout batches. Together, these results provide an RL perspective on OPD that offers both a principled interpretation and a practical route toward more effective and rollout-efficient language model distillation.

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/

Reinforcement Learning has emerged as a post-training approach to elicit agentic RAG behaviors such as search and planning from language models. However, compact language models (e.g., 0.5B parameters) struggle due to poor reasoning ability, resulting in sparse rewards and unstable training. To overcome these difficulties, we propose Distillation-Guided Policy Optimization (DGPO), which addresses the challenges through cold-start initialization from teacher demonstrations and continuous teacher guidance during policy optimization. To systematically evaluate our approach, we introduce Agentic RAG Capabilities (ARC), a fine-grained metric analyzing reasoning, search coordination, and response synthesis. Comprehensive experiments demonstrate that DGPO enables compact models to achieve sophisticated agentic search behaviors, even outperforming the larger teacher model in some cases. DGPO makes agentic RAG feasible in computing resource-constrained environments.

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.

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.

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 distillation is an alternative post-training method in reinforcement learning that alleviates the constraints imposed by reward models by providing token-level supervision from a teacher model. Although on-policy distillation has been studied and applied across various settings, its fundamental design remains underexplored. In this paper, we introduce a new distillation reward, termed the delta signal, instead of directly imitating the teacher's output distribution. The delta signal is defined as the difference between the teacher model and its base model prior to instruction tuning for reasoning capability. It therefore captures the changes induced by reasoning tuning and provides a more direct signal for transferring reasoning capabilities. Using extensive empirical evidence, we show that the delta signal substantially improves on-policy distillation and refer to the new distillation method as On-Policy Delta Distillation (OPD^2). Experiments across mathematics, science, and code-reasoning benchmarks demonstrate that OPD^2 consistently outperforms conventional on-policy distillation, enabling reasoning LLMs to achieve strong performance with only a short post-training period. Code will be available at https://github.com/naver-ai/opd2

Knowledge distillation improves large language model (LLM) reasoning by compressing the knowledge of a teacher LLM to train smaller LLMs. On-policy distillation advances this approach by having the student sample its own trajectories while a teacher LLM provides dense token-level supervision, addressing the distribution mismatch between training and inference in off-policy distillation methods. However, on-policy distillation typically requires a separate, often larger, teacher LLM and does not explicitly leverage ground-truth solutions available in reasoning datasets. Inspired by the intuition that a sufficiently capable LLM can rationalize external privileged reasoning traces and teach its weaker self (i.e., the version without access to privileged information), we introduce On-Policy Self-Distillation (OPSD), a framework where a single model acts as both teacher and student by conditioning on different contexts. The teacher policy conditions on privileged information (e.g., verified reasoning traces) while the student policy sees only the question; training minimizes the per-token divergence between these distributions over the student's own rollouts. We demonstrate the efficacy of our method on multiple mathematical reasoning benchmarks, achieving 4-8x token efficiency compared to reinforcement learning methods such as GRPO and superior performance over off-policy distillation methods.

Reinforcement learning for multi-turn agents suffers from a credit-assignment mismatch: rewards are sparse and trajectory-level, while success often hinges on a few local decisions. Existing online policy distillation (OPD) provides denser token-level supervision, but typically treats heterogeneous agent trajectories as monolithic strings rather than causal interaction units. We present StepOPSD, a post-rollout preference self-distillation framework that takes the agent step as the unit of credit redistribution. StepOPSD decomposes trajectories into action-centered step segments, rescoring them under hindsight-enriched teacher contexts and converting token-level log-probability gaps into sign-preserving advantage shaping with a normalized per-step credit budget before the GRPO update. Across ALFWorld and Search-QA with Qwen3-1.7B and Qwen2.5-3B-Instruct, StepOPSD attains best or second-best results on subsets most sensitive to local causal errors, including first-place performance on ALFWorld Heat (79.1%), PickTwo (95.0%), Search-QA TriviaQA (61.6%), and tied-best performance on HotpotQA (40.4%). The results further reveal a consistent two-knob law: smaller α_clip acts as a broadly stabilizing local trust region, whereas the optimal global mixing strength λ_mix remains task-dependent. These findings suggest that step-aware distillation is most useful when trajectory-level rewards are weakly aligned with the local action that determines downstream success.

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) 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.

Context distillation enables language models to internalize in-context knowledge into their parameters. In our work, we propose On-Policy Context Distillation (OPCD), a framework that bridges on-policy distillation with context distillation by training a student model on its own generated trajectories while minimizing reverse Kullback-Leibler divergence against a context-conditioned teacher. We demonstrate the effectiveness of OPCD on two important applications: experiential knowledge distillation, where models extract and consolidate transferable knowledge from their historical solution traces, and system prompt distillation, where models internalize beneficial behaviors encoded in optimized prompts. Across mathematical reasoning, text-based games, and domain-specific tasks, OPCD consistently outperforms baseline methods, achieving higher task accuracy while better preserving out-of-distribution capabilities. We further show that OPCD enables effective cross-size distillation, where smaller student models can internalize experiential knowledge from larger teachers.

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.

While knowledge distillation has become a mature field for compressing large language models (LLMs) into smaller ones by aligning their outputs or internal representations, the distillation of LLM-based agents, which involve planning, memory, and tool use, remains relatively underexplored. Existing agent distillation methods typically replay full teacher trajectories or imitate step-by-step teacher tool usage, but they often struggle to train student agents to dynamically plan and act in novel environments. We propose AgentDistill, a novel, training-free agent distillation framework that enables efficient and scalable knowledge transfer via direct reuse of Model-Context-Protocols (MCPs), which are structured and reusable task-solving modules autonomously generated by teacher agents. The reuse of these distilled MCPs enables student agents to generalize their capabilities across domains and solve new problems with minimal supervision or human intervention. Experiments on biomedical and mathematical benchmarks demonstrate that our distilled student agents, built on small language models, can achieve performance comparable to advanced systems using large LLMs such as OctoTools (GPT-4o), highlighting the effectiveness of our framework in building scalable and cost-efficient intelligent agents.

Graphical User Interface (GUI) grounding maps natural language instructions to the visual coordinates of target elements and serves as a core capability for autonomous GUI agents. Recent reinforcement learning methods (e.g., GRPO) have achieved strong performance, but they rely on expensive multiple rollouts and suffer from sparse signals on hard samples. These limitations make on-policy self-distillation (OPSD), which provides dense token-level supervision from a single rollout, a promising alternative. However, its applicability to GUI grounding remains unexplored. In this paper, we present GUI-SD, the first OPSD framework tailored for GUI grounding. First, it constructs a visually enriched privileged context for the teacher using a target bounding box and a Gaussian soft mask, providing informative guidance without leaking exact coordinates. Second, it employs entropy-guided distillation, which adaptively weights tokens based on digit significance and teacher confidence, concentrating optimization on the most impactful and reliable positions. Extensive experiments on six representative GUI grounding benchmarks show that GUI-SD consistently outperforms GRPO-based methods and naive OPSD in both accuracy and training efficiency. Code and training data are available at https://zhangyan-ucas.github.io/GUI-SD/.

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 distillation (OPD) trains a student policy by matching a stronger teacher on the student's own trajectories, offering a promising framework for language agent training. However, its application to long-horizon agentic tasks remains insufficiently explored. We identify two key inefficiencies in vanilla agent OPD: (1) full-horizon rollouts often waste wall-clock resources on tail turns that provide weak and noisy KL supervision, and (2) trajectory-level KL objectives concentrate most of the loss on shallow tokens, leaving deeper decision turns under-trained once initial behaviors are aligned. To address these challenges, we propose TurnOPD, a turn-level budgeting strategy for efficient on-policy distillation of long-horizon agents. TurnOPD consists of two budget controllers: adaptive rollout-depth budgeting, which uses probe-based turn statistics to determine rollout length, and progressive turn-normalized loss budgeting, which gradually shifts KL weighting from token-level to turn-balanced supervision. Experiments on ALFWorld, WebShop, and Multi-Hop Search with task-specialized teacher models show that TurnOPD achieves superior validation accuracy under equal wall-clock training budgets and advances the accuracy--time frontier beyond vanilla OPD.

Policies for complex visual tasks have been successfully learned with deep reinforcement learning, using an approach called deep Q-networks (DQN), but relatively large (task-specific) networks and extensive training are needed to achieve good performance. In this work, we present a novel method called policy distillation that can be used to extract the policy of a reinforcement learning agent and train a new network that performs at the expert level while being dramatically smaller and more efficient. Furthermore, the same method can be used to consolidate multiple task-specific policies into a single policy. We demonstrate these claims using the Atari domain and show that the multi-task distilled agent outperforms the single-task teachers as well as a jointly-trained DQN agent.

Large language models (LLMs) excel at complex reasoning tasks but remain computationally expensive, limiting their practical deployment. To address this, recent works have focused on distilling reasoning capabilities into smaller language models (sLMs) using chain-of-thought (CoT) traces from teacher LLMs. However, this approach struggles in scenarios requiring rare factual knowledge or precise computation, where sLMs often hallucinate due to limited capability. In this work, we propose Agent Distillation, a framework for transferring not only reasoning capability but full task-solving behavior from LLM-based agents into sLMs with retrieval and code tools. We improve agent distillation along two complementary axes: (1) we introduce a prompting method called first-thought prefix to enhance the quality of teacher-generated trajectories; and (2) we propose a self-consistent action generation for improving test-time robustness of small agents. We evaluate our method on eight reasoning tasks across factual and mathematical domains, covering both in-domain and out-of-domain generalization. Our results show that sLMs as small as 0.5B, 1.5B, 3B parameters can achieve performance competitive with next-tier larger 1.5B, 3B, 7B models fine-tuned using CoT distillation, demonstrating the potential of agent distillation for building practical, tool-using small agents. Our code is available at https://github.com/Nardien/agent-distillation.

On-policy distillation is a promising approach for transferring knowledge between language models, where a student learns from dense token-level signals along its own trajectories. This framework typically uses reverse KL divergence, encouraging the student to match the teacher's high-confidence predictions. However, we show that the mode-seeking property of reverse KL reduces generation diversity and yields unstable learning signals when the teacher distribution has high entropy. To address this, we introduce Entropy-Aware On-Policy Distillation. Our key idea is augmenting the standard reverse KL objective with forward KL when teacher entropy is high, capturing the full range of plausible outputs while retaining precise imitation elsewhere. It balances mode-seeking precision with mode-covering robustness without sacrificing on-policy training efficiency. Experiments show that our method maintains generation diversity (sustained token-level entropy) and improves student-teacher alignment (lower forward KL on high-entropy tokens). Across six math reasoning benchmarks, this yields Pass@8 accuracy gains of +1.37 for Qwen3-0.6B-Base, +2.39 for Qwen3-1.7B-Base, and +5.05 for Qwen3-4B-Base compared to baseline on-policy distillation methods. These results demonstrate that accounting for teacher uncertainty is essential for maintaining diversity and achieving effective knowledge transfer.

Since the advent of knowledge distillation, KL divergence has been the standard loss in distillation. Recently, on-policy distillation (OPD) has emerged as an efficient post-training paradigm for LLMs. As a distillation method, OPD naturally inherits KL divergence as its standard loss. However, in this work, we find that KL divergence may not be necessary for OPD. We show that simply preserving the update direction is sufficient for effective OPD. As long as the update direction is toward the teacher, OPD works. More precisely, it is not the direction of every token, but the direction of a small subset of tokens where the teacher and student disagree strongly. We first show that simply assigning a reward of (+1) to tokens where the teacher probability is higher than the student probability and (-1) where it is lower, which merely encourages updates toward the teacher, reproduces almost the same training mode as OPD with reverse KL. We further show that only the direction of a small subset of tokens with large teacher-student disagreement is critical, and training works as long as their update direction is toward the teacher, even if other tokens are pulled away from the teacher. And as an application of these findings, we introduce Consensus Multi-Teacher On-Policy Distillation (C-MOPD) to improve Multi-Teacher On-Policy Distillation (MOPD). Unlike MOPD, which routes each sample to a single teacher and may cause capability conflicts across domains, C-MOPD lets every sample be supervised by all teachers. Experiments show that C-MOPD consistently outperforms MOPD on both math and code benchmarks. Our code is available at https://github.com/LeapLabTHU/KL-Free-OPD.

On-Policy Distillation (OPD) has emerged as a dominant post-training paradigm for large language models, especially for reasoning domains. However, OPD remains unstable in practice due to the high gradient variance of its single-sample Monte Carlo estimator, and recipes for stable training are still immature. We propose vOPD (On-Policy Distillation with a control variate baseline), which casts OPD as policy-gradient RL and stabilizes it by introducing a control variate baseline-canonically a value function -- from the RL literature. We show that the OPD value function admits a closed form as the per-token negative reverse KL divergence between the student and the teacher, available directly from the already-computed forward pass with no additional critic or inference. Existing stabilization methods either compute the full token-level reverse KL over the entire vocabulary, adding significant overhead, or restrict it to a top-k support, biasing the objective. vOPD instead preserves the lightweight single-sample estimator, subtracting the value function as a detached baseline to keep the gradient unbiased while reducing variance. Furthermore, we show that a top-k approximation of the baseline further lowers cost without compromising performance. Across mathematical and scientific reasoning benchmarks, vOPD consistently outperforms vanilla OPD and matches the most expensive full-vocabulary baseline, offering an efficient stabilization of On-Policy Distillation through principled RL variance reduction.

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.

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.

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.

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 distillation (OPD) has shown strong potential for transferring reasoning ability from frontier or domain-specific models to smaller students. While effective on static single-turn tasks, its behavior in multi-turn agent settings remains underexplored. In this work, we identify a key limitation of vanilla OPD in such settings, which we term Trajectory-Level KL Instability. Specifically, we observe that KL divergence increases together with a drop in success rate, and even after convergence, the KL remains high, leading to unstable training. This instability arises from inter-turn error compounding: as errors accumulate, the student is driven beyond the teacher's effective support, rendering the supervision signal unreliable. To address this, we propose TCOD (Temporal Curriculum On-Policy Distillation), a simple yet effective framework that controls the trajectory depth exposed to the student and progressively expands it from short to long with a curriculum schedule.Experimental results across four student-teacher pairs on three multi-turn agent benchmarks (ALFWorld, WebShop, ScienceWorld) show that TCOD mitigates KL escalation and enhances KL stability throughout training, improving agent performance by up to 18 points over vanilla OPD. Further evaluations show that TCOD can even surpass the teacher's performance and generalize to tasks on which the teacher fails.

Outcome-based reinforcement learning provides a stable optimization backbone for language agents, but its sparse trajectory-level rewards provide little guidance on which intermediate decisions should be reinforced or suppressed. On-policy self-distillation offers dense token-level supervision, yet existing skill-conditioned variants often rely on external skill memories or retrieved privileged context, which are costly to maintain and can be mismatched with the state distribution induced by the current policy in multi-turn interaction. We propose OPID (On-Policy Skill Distillation), a framework that extracts skill supervision directly from completed on-policy trajectories. OPID represents trajectory hindsight as hierarchical skills: episode-level skills capture global workflows or failure-avoidance rules, while step-level skills capture local decision knowledge at critical timesteps. A critical-first routing mechanism uses step-level skills when critical decisions are identified and falls back to episode-level skills as default guidance otherwise. The selected skill is injected into the interaction history, allowing the old policy to re-score the same sampled response under both original and skill-augmented contexts. The resulting log-probability shift yields a token-level self-distillation advantage, which is combined with the outcome advantage for policy optimization. OPID thus preserves RL as the primary training objective while introducing dense, distribution-matched hindsight supervision. Experiments on ALFWorld, WebShop and Search-based QA demonstrate that OPID generally improves agent performance, sample efficiency, and robustness over outcome-only RL and existing skill-distillation baselines. Our code is available at https://github.com/jinyangwu/OPID/tree/main.

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.

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.

Group-based Reinforcement Learning (RL) has significantly enhanced Large Language Models (LLMs) in agentic scenarios. To achieve finer-grained policy updates, recent agentic RL frameworks have shifted from trajectory-level to step-level training. However, long-horizon agentic RL suffers from severe reward sparsity and delay, as feedback is often deferred for dozens of interaction steps. While existing step-level frameworks refine training granularity, their credit assignment remains coarse-grained and still treats agent exploration as isolated, linear trajectories. This oversimplified perspective ignores the inherent graph structure of state transitions, leading to high-variance state-value estimation and myopic, localized credit assignment. To overcome these critical bottlenecks, we propose Group-Graph Policy Optimization (G2PO), a novel group-based RL algorithm tailored for multi-turn agentic tasks. G2PO explicitly transforms linear interaction trajectories into a global state-transition graph. By aggregating identical observations across different trajectories, we introduce group-aggregation state-value estimation that reduces sampling variance and trajectory-dependent bias. Furthermore, we redefine agent actions as transitions between state nodes and propose an edge-centric advantage estimation strategy. By globally standardizing Temporal Difference (TD) errors across the entire graph, G2PO explicitly identifies and prioritizes critical transitions that drive absolute task progress. Extensive experiments on representative long-horizon benchmarks-WebShop, ALFWorld, and AppWorld-demonstrate that G2PO substantially outperforms state-of-the-art prompt-based and RL baselines, achieving remarkable success rate improvements of up to 22.2% over GRPO.

On-policy distillation (OPD) adapts diffusion models by querying a teacher along trajectories generated by the current student, but how it should behave under classifier-free guidance (CFG), a default component of modern diffusion systems, remains poorly understood. Existing OPD methods naturally extend velocity matching to the CFG-composed prediction, directly matching teacher and student guided velocities. We show that this objective is under-identified at the branch level: positive- and negative-branch errors can compensate in the guided prediction. Through two contrasting cases, we find that naive matching remains effective under shared negative conditioning, where both branch errors decrease jointly. When the model's native CFG schema retains privileged information in the teacher's negative branch that is unavailable to the student, however, this joint reduction breaks down and the composed objective induces antagonistic branch-error dynamics, reducing the positive-branch error while increasing the negative-branch error. We term this failure mode Negative Branch Asymmetry (NBA). To address NBA, we introduce Positive--Direction Matching (PDM), a branch-aware OPD objective that separately constrains the positive prediction and the CFG conditional direction. We apply PDM to dense-to-sparse video control, where naive guided matching is highly sensitive to inference guidance scales, while branch-aware supervision enables more robust and effective knowledge transfer.

Multi-teacher on-policy distillation (MOPD) has emerged as a popular post-training paradigm for integrating specialized capabilities in frontier language models. Existing OPD research has primarily focused on optimizing single-task distillation through objective design, distillation scope, and teacher signal construction, whereas MOPD must aggregate multiple capabilities in shared parameters and address the resulting capability seesaw, in which improving one domain suppresses capabilities acquired from another. Inspired by the distinctive update geometry of OPD, we find that parameter updates from different tasks rapidly concentrate in their respective low-dimensional subspaces during MOPD, providing a direct geometric basis for identifying and controlling cross-task interference. We therefore propose PMOPD (Projection-based Multi-Teacher On-Policy Distillation), which constructs subspace memories from the cumulative parameter displacements of different tasks and projects both gradients and optimizer updates to remove components that interfere with protected task directions. We further develop a lightweight conflict probe to characterize task interactions and guide task ordering, together with a cycling strategy that balances subspace estimation and timely task revisitation. Experiments on representative Code, Reason, and Math tasks show that PMOPD improves every evaluated capability over MOPD, raising the average score across the three tasks by 2.54 points on Qwen2.5-7B and 2.09 points on Llama-3.1-8B. These consistent gains establish geometry-aware optimization as an effective and transferable approach to balanced multi-teacher distillation.

Reinforcement learning has become a central component of large language model (LLM) post-training, yet token-level credit lacks a generally accepted mathematical definition, leaving its relationship to commonly used training signals unclear. We formulate three regularity conditions, namely Completeness, Prefix Consistency, and Neutrality, and prove that they uniquely determine token-level credit. This characterization provides a unified basis for explaining phenomena across existing algorithms and guides the development of an improved actor-critic training procedure. Through this lens, an ideal teacher in On-Policy Distillation (OPD) acts as an implicit critic, yielding an expected policy gradient proportional to that induced by token-level credit. Response-level REINFORCE Leave-One-Out (RLOO) signals match the expected policy-gradient contribution of token-level credit despite their coarser granularity. We further establish approximate credit sparsity under bounded outcome rewards and show how intermediate critic errors in Generalized Advantage Estimation (GAE) can become comparable to the underlying credit. These motivate Policy Aligned Critic Training (PACT), which adopts an Actor-then-Critic update order to apply importance sampling correction to critic training and better align the critic with the updated policy. In agentic mathematical reasoning, PACT achieves 72.87% average accuracy across four benchmarks, outperforming GRPO and PPO by 8.80 and 13.16 percentage points, respectively. On SWE-bench Verified, PACT achieves a pass rate of 67.4%, outperforming PPO, GRPO, and SAO by 2.4, 2.0, and 3.8 percentage points, respectively.

Reinforcement learning with verifiable rewards (RLVR) has become a standard paradigm for post-training large language models (LLMs). While Group Relative Policy Optimization (GRPO) is widely adopted, it suffers from sparse reward signals and loses gradients entirely when all responses within a group receive identical rewards. On-policy distillation (OPD) offers a natural remedy by providing dense, token-level supervision from a teacher model. However, naively combining GRPO with OPD leads to degraded performance, due to three underlying causes: not all samples benefit from distillation; fitting too quickly to the teacher undermines the exploratory capacity of RL; and OPD's advantages are asymmetric, suppressing most tokens. To address these challenges, we propose RSTG (Recovering Learning Signals via Adaptive Teacher Guidance), which applies distillation selectively and precisely where it matters most. At the sample level, OPD is restricted to negative zero-variance prompts with each sample weighted by the teacher's confidence score. At the token level, distillation targets only tokens with high student entropy or large teacher-student divergence. We further augment training with SFT on correct trajectories generated by the teacher model, injecting positive gradient signals where RL yields none. Experiments demonstrate that RSTG substantially outperforms naive GRPO+OPD by +4.02% on math and +3.05% on code.

Recent advances in large language models (LLMs) and multi-agent systems have demonstrated remarkable capabilities in complex problem-solving tasks such as deep research, vibe coding, and mathematical reasoning. However, most existing multi-agent systems are built upon manual prompt/workflow engineering with sophisticated agent frameworks, making them computationally inefficient, less capable, and can not benefit from data-centric learning. In this work, we introduce Chain-of-Agents (CoA), a novel paradigm of LLM reasoning that enables native end-to-end complex problem-solving in the same way as a multi-agent system (i.e., multi-turn problem solving with multiple tools and multiple agents) within one model. In chain-of-agents problem-solving, the model dynamically activates different tool agents and role-playing agents to simulate multi-agent collaboration in an end-to-end fashion. To elicit end-to-end chain-of-agents problem-solving abilities in LLMs, we introduce a multi-agent distillation framework to distill state-of-the-art multi-agent systems into chain-of-agents trajectories for agentic supervised fine-tuning. We then use agentic reinforcement learning on verifiable agentic tasks to further improve the models' capabilities on chain-of-agents problem solving. We call the resulting models Agent Foundation Models (AFMs). Our empirical studies demonstrate that AFM establishes new state-of-the-art performance across diverse benchmarks in both web agent and code agent settings. We make the entire research, including the model weights, code for training and evaluation, and the training data, fully open-sourced, which offers a solid starting point for future research on agent models and agentic RL.

Standard knowledge distillation for autoregressive models often suffers from distribution mismatch. While on-policy methods mitigate this by leveraging student-generated outputs, they rely on computationally expensive Reinforcement Learning (RL) frameworks. To improve efficiency, we propose Near-Policy Distillation (NPD), an asynchronous approach that decouples student generation from training. This reformulation enables Supervised Fine-Tuning (SFT) with sequence packing. However, asynchronous updates inevitably introduce policy lag and sample noise, which can cause the behavior to drift from near-policy toward off-policy. To counteract this without sacrificing efficiency, NPD integrates sparse student updates and the Δ-IFD filtering mechanism, a heuristic sample selection mechanism that empirically stabilizes the optimization trajectory. By filtering extreme out-of-distribution samples, Δ-IFD prevents noise from dominating the gradients, ensuring updates remain within a safe proximal learning zone. Empirically, the NPD framework achieves a 8.1x speedup over on-policy baselines and outperforms SFT by 8.09%. Crucially, by effectively narrowing the exploration space for subsequent RL, our method enables openPangu-Embedded-1B to reach a state-of-the-art score of 68.73%, outperforming the substantially larger Qwen3-1.7B. Codes will be released soon.

Large language models (LLMs) exhibit strong capabilities as decision-making agents by interleaving reasoning and actions, as seen in ReAct-style frameworks. Yet, their practical deployment is constrained by high inference costs and large model sizes. We propose Structured Agent Distillation, a framework that compresses large LLM-based agents into smaller student models while preserving both reasoning fidelity and action consistency. Unlike standard token-level distillation, our method segments trajectories into {[REASON]} and {[ACT]} spans, applying segment-specific losses to align each component with the teacher's behavior. This structure-aware supervision enables compact agents to better replicate the teacher's decision process. Experiments on ALFWorld, HotPotQA-ReAct, and WebShop show that our approach consistently outperforms token-level and imitation learning baselines, achieving significant compression with minimal performance drop. Scaling and ablation results further highlight the importance of span-level alignment for efficient and deployable agents.

GNNs, like other deep learning models, are data and computation hungry. There is a pressing need to scale training of GNNs on large datasets to enable their usage on low-resource environments. Graph distillation is an effort in that direction with the aim to construct a smaller synthetic training set from the original training data without significantly compromising model performance. While initial efforts are promising, this work is motivated by two key observations: (1) Existing graph distillation algorithms themselves rely on training with the full dataset, which undermines the very premise of graph distillation. (2) The distillation process is specific to the target GNN architecture and hyper-parameters and thus not robust to changes in the modeling pipeline. We circumvent these limitations by designing a distillation algorithm called Mirage for graph classification. Mirage is built on the insight that a message-passing GNN decomposes the input graph into a multiset of computation trees. Furthermore, the frequency distribution of computation trees is often skewed in nature, enabling us to condense this data into a concise distilled summary. By compressing the computation data itself, as opposed to emulating gradient flows on the original training set-a prevalent approach to date-Mirage transforms into an unsupervised and architecture-agnostic distillation algorithm. Extensive benchmarking on real-world datasets underscores Mirage's superiority, showcasing enhanced generalization accuracy, data compression, and distillation efficiency when compared to state-of-the-art baselines.

Training small language-model agents for long-horizon interactive tasks requires both fast imitation and reward-driven improvement. On-policy distillation (OPD) provides dense teacher guidance and typically improves rapidly in the early stage, but its gains saturate once the student approaches the teacher, limiting the final performance ceiling. Reinforcement learning (RL) directly optimizes environment rewards and encourages exploratory improvement toward a higher reward-defined ceiling, but sparse and delayed feedback makes early-stage learning much less efficient than OPD. In this paper, we propose ATOD (Annealed Turn-aware On-policy Distillation), a hybrid online distillation algorithm that explicitly exploits this complementarity. (1) ATOD uses an annealed OPD-RL schedule: OPD dominates early training to approach teacher-level behavior, while RL is gradually strengthened to drive reward-based exploration. (2) ATOD introduces Turn-level Disagreement-Uncertainty Reweighting (T-DUR), which softly amplifies high-utility turns and improves dense supervision in long trajectories. Experiments on ALFWorld, WebShop, and Search-QA show that ATOD consistently outperforms competing post-training baselines: across the three student sizes, ATOD improves average success rate by 3.03 points over OPD and 23.62 points over GRPO, while surpassing the corresponding teacher models by 2.16 points.

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.

Recent years have witnessed remarkable progress in world models, which primarily aim to capture the spatio-temporal correlations between an agent's actions and the evolving environment. However, existing approaches often suffer from tight runtime coupling or depend on offline reward signals, resulting in substantial inference overhead or hindering end-to-end optimization. To overcome these limitations, we introduce WPT, a World-to-Policy Transfer training paradigm that enables online distillation under the guidance of an end-to-end world model. Specifically, we develop a trainable reward model that infuses world knowledge into a teacher policy by aligning candidate trajectories with the future dynamics predicted by the world model. Subsequently, we propose policy distillation and world reward distillation to transfer the teacher's reasoning ability into a lightweight student policy, enhancing planning performance while preserving real-time deployability. Extensive experiments on both open-loop and closed-loop benchmarks show that our WPT achieves state-of-the-art performance with a simple policy architecture: it attains a 0.11 collision rate (open-loop) and achieves a 79.23 driving score (closed-loop) surpassing both world-model-based and imitation-learning methods in accuracy and safety. Moreover, the student sustains up to 4.9x faster inference, while retaining most of the gains.

While large language model (LLM) multi-agent systems achieve superior reasoning performance through iterative debate, practical deployment is limited by their high computational cost and error propagation. This paper proposes AgentArk, a novel framework to distill multi-agent dynamics into the weights of a single model, effectively transforming explicit test-time interactions into implicit model capabilities. This equips a single agent with the intelligence of multi-agent systems while remaining computationally efficient. Specifically, we investigate three hierarchical distillation strategies across various models, tasks, scaling, and scenarios: reasoning-enhanced fine-tuning; trajectory-based augmentation; and process-aware distillation. By shifting the burden of computation from inference to training, the distilled models preserve the efficiency of one agent while exhibiting strong reasoning and self-correction performance of multiple agents. They further demonstrate enhanced robustness and generalization across diverse reasoning tasks. We hope this work can shed light on future research on efficient and robust multi-agent development. Our code is at https://github.com/AIFrontierLab/AgentArk.

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.

On-policy distillation (OPD) has become a promising paradigm for reasoning-oriented post-training of large language models (LLMs), especially when combined with reinforcement learning from verifiable rewards (RLVR). Existing OPD methods rely on reverse KL (RKL)-based teacher supervision over trajectories sampled from the student policy. However, we identify a critical limitation: under large teacher--student policy divergence, RL-driven exploration often produces trajectories outside the teacher distribution, resulting in uninformative negative feedback. To address this, we propose Teacher-Guided Policy Optimization (TGPO), an on-policy reasoning distillation method that remains effective under large policy divergence settings. Rather than relying solely on evaluative supervision, TGPO uses teacher to directly guide token level generation conditioning on student-generated contexts; together with RLVR-style trajectory level rewards, TGPO steers exploration toward improved continuations. Experiments on reasoning benchmarks show that TGPO consistently outperforms existing RKL-based OPD methods and remains robust across different teacher models.

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

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.

On-policy learning has been argued to reduce catastrophic forgetting, produce sparser parameter updates, and improve generalisation. However, existing comparisons between supervised fine-tuning and reinforcement learning vary many factors simultaneously, making the contribution of rollout policy difficult to isolate. We study the effect of rollout policy in a controlled strong-to-weak distillation setting, by independently varying rollout policy, token-level KL direction, and learning rate across the Llama3 and Qwen2.5 model families and reasoning tasks spanning scientific, medical, and arithmetic domains. Our analysis reveals a nuanced picture of distillation dynamics in which rollout policy does not necessarily play a central role. Instead, token-level KL direction more clearly shapes task performance and output coverage, while learning rate governs forgetting and update sparsity. Analysis of KL gradients and experiments along a continuous student-teacher rollout-policy spectrum explain this pattern: forward KL is remarkably robust to rollout policy, with its performance stable and strong despite changes to the rollout policy, whereas reverse KL is substantially more sensitive and favours student-generated rollouts. On-policy data nevertheless improves generalisation to harder variants of the Countdown arithmetic task under both KL directions, although this advantage does not reliably persist after subsequent RLVR. Our broader conclusions remain robust to removing gradient clipping, using sampled KL estimators, and training on tasks requiring longer reasoning chains. Overall, our results challenge the view that on-policy rollouts are inherently preferable and show that their value depends critically on the objective, evaluation setting, and optimisation hyperparameters.

Graph Neural Networks (GNNs) are the go-to model for graph data analysis. However, GNNs rely on two key operations - aggregation and update, which can pose challenges for low-latency inference tasks or resource-constrained scenarios. Simple Multi-Layer Perceptrons (MLPs) offer a computationally efficient alternative. Yet, training an MLP in a supervised setting often leads to suboptimal performance. Knowledge Distillation (KD) from a GNN teacher to an MLP student has emerged to bridge this gap. However, most KD methods either transfer knowledge uniformly across all nodes or rely on graph-agnostic indicators such as prediction uncertainty. We argue this overlooks a more fundamental, graph-centric inquiry: "How important is a node to the structure of the graph?" We introduce a framework, InfGraND, an Influence-guided Graph KNowledge Distillation from GNN to MLP that addresses this by identifying and prioritizing structurally influential nodes to guide the distillation process, ensuring that the MLP learns from the most critical parts of the graph. Additionally, InfGraND embeds structural awareness in MLPs through one-time multi-hop neighborhood feature pre-computation, which enriches the student MLP's input and thus avoids inference-time overhead. Our rigorous evaluation in transductive and inductive settings across seven homophilic graph benchmark datasets shows InfGraND consistently outperforms prior GNN to MLP KD methods, demonstrating its practicality for numerous latency-critical applications in real-world settings.

GUI agents are commonly trained offline from successful interaction trajectories. Standard training decomposes each trajectory into prefix-action pairs: the agent predicts an action from the current screen and interaction history, while the subsequent observation is discarded. This removes the rationale of why an action is correct: the evidence often appears only on the subsequent screen. For example, to enable Soft Wrap, the agent should click Edit or View, but nothing reveals this until the menu opens. Without such evidence, standard imitation gives the model little chance of ever sampling and thus learning the correct reasoning. To address this issue, we propose Gated Hindsight Distillation (GHD), which uses the next screenshot as privileged information during training. A student predicts from the observable trajectory prefix, while a parameter-sharing teacher additionally observes the next screenshot and re-scores the student's on-policy responses. We apply distillation only when the student fails and the hindsight-conditioned teacher recovers the demonstrated action. GHD improves task success over GRPO on AndroidWorld and AndroidLab across two vision-language models. The code and checkpoints will be made available.

On-policy distillation (OPD) has recently emerged as a promising post-training paradigm in which the student learns from trajectories generated by its own policy under dense teacher supervision. However, OPD introduces a fundamental asymmetry: although the sampled trajectories are on-policy for the student, they are off-policy for the teacher. The teacher is typically optimized to continue from prefixes generated by its own policy, but during OPD it must instead supervise prefixes generated by the student. Empirically, we find that its continuation performance degrades as these prefixes grow longer. To address this issue, we propose Student-COnditioned Updates of the Teacher (SCOUT), a co-training framework that adapts the teacher to student-generated prefixes. Alongside standard OPD updates, SCOUT periodically optimizes the teacher's conditional ability using reinforcement learning with verifiable rewards, where the teacher generates continuations from student prefixes and learns from outcome rewards. Controlled experiments show that SCOUT improves the teacher's ability to continue from student-generated prefixes, supporting the intended mechanism of student-conditioned teacher adaptation. Across multiple teacher--student configurations, model scales, and reasoning domains, SCOUT also consistently improves the effectiveness of on-policy distillation.

Large language models trained with reinforcement learning (RL) for mathematical reasoning face a fundamental challenge: on problems the model cannot solve at all - "cliff" prompts - the RL gradient vanishes entirely, preventing any learning signal from reaching these failure modes. We introduce Hybrid Distillation Policy Optimization (HDPO), which augments standard RL with privileged self-distillation targeting cliff prompts. On each training step, HDPO identifies prompts where all rollouts fail, generates privileged rollouts by providing the model with ground-truth information, filters for correct solutions, and distills the teacher's token-level distribution into the student. Because teacher and student share the same weights - differing only in their input - the realizability gap is provably bounded, unlike cross-model distillation. We prove that R=1 filtered privileged generation recovers the optimal KL-regularized RL policy in the hard-threshold limit. Experiments on OpenMathInstruct-2 with Qwen2.5-Math-1.5B-Instruct show that HDPO consistently improves coverage metrics (pass@4 by +0.8-1.1%, pass@8 by +0.4-1.7%) while maintaining greedy accuracy, with the distillation weight lambda providing direct control over the exploration-exploitation tradeoff.

On-policy distillation (OPD) is increasingly used to improve large language model reasoning, but its training dynamics remain poorly understood. We characterize the trajectory of OPD updates in parameter space and compare it with supervised fine-tuning (SFT) and reinforcement learning with verifiable rewards (RLVR). A suite of parameter-space diagnostics consistently places OPD in a relaxed off-principal regime: compared with SFT, its updates affect fewer weights and avoid principal directions more strongly, while compared with RLVR, they remain less tightly constrained. Beyond this static localization, OPD exhibits subspace locking: its cumulative updates rapidly enter a narrow low-dimensional channel. Constraining training to the update subspace formed early in training preserves OPD performance but substantially degrades SFT, indicating that the locked subspace is functionally sufficient for OPD. Control experiments further show that sparsifying the update tokens and shifting rollout generation off-policy preserve the rank dynamics, whereas mixing the OPD objective with RLVR changes them. Overall, these results suggest that OPD is not merely an intermediate point between SFT and RLVR, but induces its own update geometry in parameter space.

Multi-turn long-horizon planning is critical for foundation model agents, yet how to fundamentally improve it remains unclear. Existing models are trained on uncontrollable and opaque Internet data, making it difficult to identify how planning ability is acquired, shaped, and integrated. To address this challenge, we introduce a unified and controlled multi-turn environment that enables precise control. It allows systematically study long-horizon planning across three stages. (1) Planning ability acquisition during pre-training. We study data format, distribution, and quality. Explicit world model construction through CoT state transition modeling yields stronger long-horizon generalization. Atomic skills alone are insufficient for compositional generalization, whereas a litte long-horizon data works. Moreover, suboptimal trajectories severely impair performance because errors amplify over long horizons. (2) Planning ability shaping via GRPO and OPD post-training. Through mutual information, we distinguish general planning patterns from task-specific planning knowledge. For planning patterns, we identify three application regions of post-training: unnecessary, effective, and unsupported. OPD has a broader effective region than GRPO under low-quality and long-horizon settings, as it provides more consistent update directions. For planning knowledge, distilling unseen procedures from a teacher with different knowledge may impair student's prior world modeling without fully establishing new knowledge. (3) Planning ability integration through MOPD post-training. We show that multi-teacher on-policy distillation (MOPD) integrates capabilities by converging to shared planning-pattern across environments. Compatible patterns enable cross-environment generalization, partially shared patterns support continual learning, while completely conflicting patterns cause severe interference.

Language model agents are deployed with a harness, the software around the model that manages its context, tools, and feedback. When such an agent is distilled into a smaller one, the harness stays in place, so the student mainly needs the teacher-specific abilities that the harness cannot provide, such as acting correctly on harness information. Standard distillation, however, imitates the teacher's full outputs and treats the harness as part of the input. We propose Harness-Aware Distillation (HAD), which focuses distillation on what the teacher adds beyond the harness. HAD complements on-policy distillation with two components: an action preference that contrasts the same teacher's actions with and without the harness information, scored after the student's own reasoning, and a validity check that drops preference pairs whose preferred action contradicts the harness records. We show that the contrast gives the student information that imitating the teacher alone cannot provide, and HAD needs no task rewards, success labels, or future information. Across multiple long-horizon agent benchmarks and models, HAD outperforms on-policy distillation baselines with the same fixed harness. Our analysis shows that HAD enters fewer unproductive loops and recovers from errors more often than the baselines, and suggests that it adaptively keeps learnable feedback in its weights while reading state information from the harness.

Reinforcement learning from verifiable rewards (RLVR) suffers from sparse outcome signals, creating severe exploration bottlenecks on complex reasoning tasks. Recent on-policy self-distillation methods attempt to address this by utilizing language feedback to generate dense, token-level supervision. However, these approaches rely on a fixed, passive teacher to interpret the feedback. As the student policy improves, the teacher's zero-shot assessment capabilities plateau, ultimately halting further learning. To overcome this, we propose Variational Policy Distillation (VPD), a framework that formalizes learning from language feedback as a Variational Expectation-Maximization (EM) problem. VPD co-evolves both policies: in the E-step, the teacher is actively refined on trajectory outcomes via an adaptive trust-region update, translating textual feedback into a dynamically improved target token distribution. In the M-step, the student internalizes this dense distributional guidance on its own on-policy rollouts. By continuously improving the teacher's ability to extract actionable signals from textual critique, VPD overcomes the limitations of passive distillation. Evaluated across diverse sources of diagnostic feedback on scientific reasoning and code generation tasks, VPD consistently outperforms both standard RLVR and existing self-distillation baselines. Finally, by stress-testing our framework on rigid mathematical reasoning and cold-start regimes, we illuminate the fundamental bounds of feedback-driven self-distillation compared to pure environment-driven RL.

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.

Knowledge distillation (KD) is a powerful paradigm for compressing large language models (LLMs), whose effectiveness depends on intertwined choices of divergence direction, optimization strategy, and data regime. We break down the design of existing KD methods and present a unified view that establishes connections between them, reformulating KD as a reweighted log-likelihood objective at the token level. We further propose Hybrid Policy Distillation (HPD), which integrates the complementary advantages of forward and reverse KL to balance mode coverage and mode-seeking, and combines off-policy data with lightweight, approximate on-policy sampling. We validate HPD on long-generation math reasoning as well as short-generation dialogue and code tasks, demonstrating improved optimization stability, computational efficiency, and final performance across diverse model families and scales. The code related to this work is available at https://github.com/zwhong714/Hybrid-Policy-Distillation.

On-Policy Distillation (OPD) is a fundamental technique for efficient post-training of large language models (LLMs), with broad applications in agent learning, multi-task enhancement, and model compression. However, OPD training becomes unstable when the teacher and student distributions differ substantially, as teacher supervision on student-generated tokens may yield unreliable policy gradients and even cause optimization failure. This work addresses reliable on-policy token-level supervision through credit assignment strategies, and proposes Trust Region On-Policy Distillation, TrOPD. It features the following characteristics: 1) Trust-Region On-Policy Learning: TrOPD performs OPD only in regions where the teacher provides reliable supervision, mitigating the optimization difficulty of the K1 reverse-KL estimator under distribution mismatch. 2) Outlier Estimation: For outlier regions, we explore gradient clipping, masking, and forward-KL estimation to reduce the adverse effects of unreliable supervision. 3) Off-Policy Guidance: The student continues generation from teacher prefixes and uses forward KL to imitate off-policy guidance, encouraging on-policy exploration toward reliable regions. Experiments show that TrOPD consistently outperforms SoTA OPD baselines, including OPD, EOPD, and REOPOLD, across mathematical reasoning, code generation, and general-domain benchmarks.

While large-scale text-to-image generative models have achieved unprecedented visual performance, their inherent reliance on multi-step iterative solvers incurs severe inference latency. Few-step distillation targeting the Classifier-Free Guidance (CFG) trajectory has emerged as the prevalent dual-dimensional compression paradigm. However, existing frameworks remain subjugated by a coarse-grained blind injection paradigm that perpetually enforces a globally static guidance strength while indiscriminately sampling the supervisor timestep. This state-agnostic design completely disregards the intrinsic nature of image generation as a dynamic evolutionary process characterized by progressive entropy reduction, which not only restricts the performance boundary of few-step compression but also precipitates severe CFG over-conditioning artifacts. To transcend these limitations, we re-examine the distillation procedure through the theoretical lens of Information Theory, formally modeling it as a dynamic mutual information game constrained by the Information Bottleneck (IB) principle. Specifically, we dismantle traditional blind assumptions via a dual-track adaptive framework. To determine the injection target, we propose an instance-aware selection mechanism that transmutes the intractable KL divergence constraint into a zero-overhead closed-form solution predicated on the local vector field norm. To regulate the injection strength, we introduce an entropy-aware schedule that dynamically decays alongside the SNR, applying maximal thrust for initial structural anchoring before smoothly reverting to the natural manifold to refine micro-details. Extensive empirical evaluations corroborate that our framework fundamentally eradicates over-conditioning artifacts, shattering the performance ceiling to achieve SOTA generative fidelity under extremely stringent 2-step configurations.

Reinforcement learning (RL) post-training has recently driven major gains in long chain-of-thought reasoning large language models (LLMs), but the high inference cost of such models motivates distillation into smaller students. Most existing knowledge distillation (KD) methods are designed for supervised fine-tuning (SFT), relying on fixed teacher traces or teacher-student Kullback-Leibler (KL) divergence-based regularization. When combined with RL, these approaches often suffer from distribution mismatch and objective interference: teacher supervision may not align with the student's evolving rollout distribution, and the KL regularizer can compete with reward maximization and require careful loss balancing. To address these issues, we propose RL-aware distillation (RLAD), which performs selective imitation during RL -- guiding the student toward the teacher only when it improves the current policy update. Our core component, Trust Region Ratio Distillation (TRRD), replaces the teacher-student KL regularizer with a PPO/GRPO-style likelihood-ratio objective anchored to a teacher--old-policy mixture, yielding advantage-aware, trust-region-bounded distillation on student rollouts and naturally balancing exploration, exploitation, and imitation. Across diverse logic reasoning and math benchmarks, RLAD consistently outperforms offline distillation, standard GRPO, and KL-based on-policy teacher-student knowledge distillation.

On-policy distillation (OPD), which supervises a student on its own sampled trajectories, has emerged as a data-efficient post-training method for improving reasoning while avoiding the reward dependence of reinforcement learning and the catastrophic forgetting often observed in standard supervised fine-tuning. However, standard OPD typically computes teacher supervision under noisy student-generated contexts and often relies on a single stochastic teacher rollout per prompt. As a result, the supervision signal can be high-variance: the sampled teacher trajectory can be incorrect, uninformative, or poorly matched to the student's current reasoning behavior. To address this limitation, we propose BRTS, a Best-of-N Rollout Teacher Selection framework for on-policy distillation. BRTS augments standard student-context OPD with a teacher-context supervision branch constructed from the curated teacher trajectory. Rather than distilling from the first sampled teacher rollout, BRTS samples a small pool of teacher trajectories and selects the auxiliary trajectory using a simple priority rule: correctness first, student alignment second. When multiple correct teacher trajectories are available, BRTS chooses the one most aligned with the student's current behavior; when unconditioned teacher samples fail on harder prompts, it invokes a ground-truth-conditioned recovery step to elicit a natural derivation. The selected trajectory is then used to provide reliable teacher-context supervision inside the OPD loop, augmented with an auxiliary loss on the teacher trajectory. Experiments on AIME 2024, AIME 2025, and AMC 2023 show that BRTS improves over standard OPD on challenging reasoning benchmarks, with the largest gains on harder datasets. Our code is available at https://github.com/BWGZK-keke/BRTS.

Black-box knowledge distillation for large language models presents a strict trade-off. Simple off-policy methods (e.g., sequence-level knowledge distillation) struggle to correct the student's inherent errors. Fully on-policy methods (e.g., Generative Adversarial Distillation) solve this via adversarial training but introduce well-known training instability and crippling computational overhead. To address this dilemma, we propose SODA (Semi On-policy Distillation with Alignment), a highly efficient alternative motivated by the inherent capability gap between frontier teachers and much smaller base models. Because a compact student model's natural, zero-shot responses are almost strictly inferior to the powerful teacher's targets, we can construct a highly effective contrastive signal simply by pairing the teacher's optimal response with a one-time static snapshot of the student's outputs. This demonstrates that exposing the small student to its own static inferior behaviors is sufficient for high-quality distribution alignment, eliminating the need for costly dynamic rollouts and fragile adversarial balancing. Extensive evaluations across four compact Qwen2.5 and Llama-3 models validate this semi on-policy paradigm. SODA matches or outperforms the state-of-the-art methods on 15 out of 16 benchmark results. More importantly, it achieves this superior distillation quality while training 10 times faster, consuming 27% less peak GPU memory, and completely eliminating adversarial instability.

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.

On-Policy Distillation (OPD) improves the learning efficiency of standard reinforcement learning through dense, token-level supervision from teachers. In the standard KL objective of OPD, token-level losses are uniformly averaged, implying equal weights for all tokens. However, we discover that not all tokens are created equal: as student rollouts grow longer, they deviate further from the teacher's distribution, leading to degraded supervision quality at later positions. As a result, OPD using only the first 30% of tokens can perform comparably to using all tokens, whereas OPD using only the last 30% of tokens barely learns anything. In this work, we provide a principled understanding of this issue through the lens of constrained optimization. Based on these insights, we derive Importance-Weighted On-Policy Distillation (IW-OPD), in which the weight assigned to each token depends on the accumulated discrepancy between the student's and teacher's distributions, naturally upweighting earlier tokens and downweighting later ones with larger deviations. We show that IW-OPD converges significantly faster than OPD, with better learning efficiency, and achieves better final performance than standard OPD in both same-size and cross-scale settings, improving performance up to 6.9 points on AIME-2025.

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.

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.

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.

Big goals are hard to achieve all at once; breaking them into small steps is wiser. We present Trust Region Policy Distillation (TOP-D), which transforms the notoriously unstable, high-variance On-Policy Distillation (OPD) into a stable training paradigm by dynamically constructing a proximal teacher. Theoretically, we establish a rigorous framework demonstrating that TOP-D inherently controls gradient variance. By providing a formal global convergence analysis alongside a monotonic improvement bound, we mathematically formalize the reliability and stability of the overall training dynamics. Empirically, TOP-D dramatically enhances training stability, sample efficiency, and final performance on mathematical reasoning tasks. More importantly, TOP-D introduces zero additional computational overhead, positioning itself as a promising alternative to the well-established OPD paradigm.

Diffusion distillation, exemplified by Distribution Matching Distillation (DMD), has shown great promise in few-step generation but often sacrifices quality for sampling speed. While integrating Reinforcement Learning (RL) into distillation offers potential, a naive fusion of these two objectives relies on suboptimal raw sample evaluation. This sample-based scoring creates inherent conflicts with the distillation trajectory and produces unreliable rewards due to the noisy nature of early-stage generation. To overcome these limitations, we propose GDMD, a novel framework that redefines the reward mechanism by prioritizing distillation gradients over raw pixel outputs as the primary signal for optimization. By reinterpreting the DMD gradients as implicit target tensors, our framework enables existing reward models to directly evaluate the quality of distillation updates. This gradient-level guidance functions as an adaptive weighting that synchronizes the RL policy with the distillation objective, effectively neutralizing optimization divergence. Empirical results show that GDMD sets a new SOTA for few-step generation. Specifically, our 4-step models outperform the quality of their multi-step teacher and substantially exceed previous DMDR results in GenEval and human-preference metrics, exhibiting strong scalability potential.

Off-policy and on-policy distillation have traditionally been formulated as separate paradigms, each favoring a different property of distillation trajectories. Teacher-generated (off-policy) traces are typically high-quality but lie far from the student's distribution, whereas student-generated (on-policy) rollouts are more learnable but often contain erroneous reasoning. We view these paradigms as the endpoints of a policy continuum and posit that a more effective rollout policy may lie in between. We introduce Interpolated Policy Distillation (IPD), which defines the next-token distribution at every decoding step as an explicit linear interpolation between the student and teacher distributions. The interpolation operates at the distribution level, token by token, and its coefficient provides direct control over the balance between trajectory quality and student learnability. Naively sampling from this policy would require sequentially querying the teacher at every token and is thus expensive. To make IPD practical, we accelerate it with a new speculative-decoding rule while exactly preserving the interpolated next-token distribution.At the trajectory level, the resulting rollouts naturally interleave student- and teacher-generated segments. Unlike recent heuristic segment-interleaving methods, however, this interleaving is induced by an exactly realized token-level interpolated policy rather than by hand-designed switching rules. Across text-only and multimodal reasoning benchmarks, IPD consistently outperforms both endpoint policies (SFT and OPD), their conventional two-stage combination (SFT-then-OPD), and recent heuristic segment-interleaving methods, demonstrating that token-level policy interpolation better balances trajectory quality and student learnability.

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

Black-box distillation creates student large language models (LLMs) by learning from a proprietary teacher model's text outputs alone, without access to its internal logits or parameters. In this work, we introduce Generative Adversarial Distillation (GAD), which enables on-policy and black-box distillation. GAD frames the student LLM as a generator and trains a discriminator to distinguish its responses from the teacher LLM's, creating a minimax game. The discriminator acts as an on-policy reward model that co-evolves with the student, providing stable, adaptive feedback. Experimental results show that GAD consistently surpasses the commonly used sequence-level knowledge distillation. In particular, Qwen2.5-14B-Instruct (student) trained with GAD becomes comparable to its teacher, GPT-5-Chat, on the LMSYS-Chat automatic evaluation. The results establish GAD as a promising and effective paradigm for black-box LLM distillation.

On-policy distillation (OPD) trains a student on prefixes sampled from its own policy while matching a stronger teacher. This addresses the prefix mismatch of offline distillation, but early student rollouts can still be poor, placing teacher supervision on weak or low-quality prefixes. We propose Trust-Region behavior Blending (TRB), a warmup method that replaces the early rollout policy with the closest-to-teacher behavior policy inside a student-centered KL trust region, while keeping the per-prefix reverse-KL OPD loss unchanged. The KL budget is annealed to zero, so training returns to pure student rollouts after warmup. Across two math-reasoning distillation settings, TRB attains the strongest average among the compared methods.

Post-training has become central to turning pretrained large language models (LLMs) into aligned, capable, and deployable systems. Recent progress spans supervised fine-tuning (SFT), preference optimization, reinforcement learning (RL), process supervision, verifier-guided methods, distillation, and multi-stage pipelines. Yet these methods are often discussed in fragmented ways, organized by labels or objectives rather than by the behavioral bottlenecks they address. This survey argues that LLM post-training is best understood as structured intervention on model behavior. We organize the field first by trajectory provenance, which defines two primary regimes: off-policy learning on externally supplied trajectories and on-policy learning on learner-generated rollouts. We then interpret methods through two recurring roles -- effective support expansion, which makes useful behaviors more reachable, and policy reshaping, which improves behavior within already reachable regions -- together with a complementary systems-level role, behavioral consolidation, which preserves, transfers, and amortizes useful behavior across stages and model transitions. Under this view, SFT may serve either support expansion or policy reshaping; preference optimization is usually off-policy reshaping, though online variants move closer to learner-generated states. On-policy RL often improves behavior on learner-generated states, but stronger guidance can also make hard-to-reach reasoning paths reachable. Distillation is often better understood as consolidation rather than only compression, and hybrid pipelines emerge as coordinated multi-stage compositions. Overall, the framework helps diagnose post-training bottlenecks and reason about stage composition, suggesting that progress increasingly depends on coordinated systems design rather than any single dominant objective.

Sampled-token on-policy distillation (OPD) efficiently transfers capabilities from teacher to student using student-generated tokens, requiring teacher probabilities only for sampled tokens. Yet it frequently suffers from diversity distillation failure: the student's pass@1 improves while its pass@k plateaus, failing to inherit the teacher's diversity. To explain this, we introduce First-Order Local Entropy Influence, a signed first-order proxy that decouples each update's entropy effect into the teacher--student log-probability gap and the student's local probability structure, and empirically links entropy contraction to negative-influence positions. Motivated by this, we propose Influence-Directed Adaptive On-Policy Distillation (IDA-OPD): rather than relying on costly full-vocabulary Forward-KL objectives, it preserves entropy-expanding updates while replacing entropy-contracting ones with divergence-adaptive advantage shrinkage, using only the teacher's sampled-token log-probability. Experiments on reasoning-oriented distillation show IDA-OPD consistently improves pass@k, inheriting the teacher's diversity through distillation, matches the strongest teacher-informed methods at strictly lower cost, and broadly maintains vanilla OPD's pass@1, all without full-vocabulary teacher information.

Diffusion Policies have demonstrated impressive performance in robotic manipulation tasks. However, their long inference time, resulting from an extensive iterative denoising process, and the need to execute an action chunk before the next prediction to maintain consistent actions limit their applicability to latency-critical tasks or simple tasks with a short cycle time. While recent methods explored distillation or alternative policy structures to accelerate inference, these often demand additional training, which can be resource-intensive for large robotic models. In this paper, we introduce a novel approach inspired by the Real-Time Iteration (RTI) Scheme, a method from optimal control that accelerates optimization by leveraging solutions from previous time steps as initial guesses for subsequent iterations. We explore the application of this scheme in diffusion inference and propose a scaling-based method to effectively handle discrete actions, such as grasping, in robotic manipulation. The proposed scheme significantly reduces runtime computational costs without the need for distillation or policy redesign. This enables a seamless integration into many pre-trained diffusion-based models, in particular, to resource-demanding large models. We also provide theoretical conditions for the contractivity which could be useful for estimating the initial denoising step. Quantitative results from extensive simulation experiments show a substantial reduction in inference time, with comparable overall performance compared with Diffusion Policy using full-step denoising. Our project page with additional resources is available at: https://rti-dp.github.io/.

Reinforcement learning has emerged as a powerful tool for improving diffusion-based text-to-image models, but existing methods are largely limited to single-task optimization. Extending RL to multiple tasks is challenging: joint optimization suffers from cross-task interference and imbalance, while cascade RL is cumbersome and prone to catastrophic forgetting. We propose DiffusionOPD, a new multi-task training paradigm for diffusion models based on Online Policy Distillation (OPD). DiffusionOPD first trains task-specific teachers independently, then distills their capabilities into a unified student along the student own rollout trajectories. This decouples single-task exploration from multi-task integration and avoids the optimization burden of solving all tasks jointly from scratch. Theoretically, we lift the OPD framework from discrete tokens to continuous-state Markov processes, deriving a closed-form per-step KL objective that unifies both stochastic SDE and deterministic ODE refinement via mean-matching. We formally and empirically demonstrate that this analytic gradient provides lower variance and better generality compared to conventional PPO-style policy gradients. Extensive experiments show that DiffusionOPD consistently surpasses both multi-reward RL and cascade RL baselines in training efficiency and final performance, while achieving state-of-the-art results on all evaluated benchmarks.

Training and evaluating interactive language agents typically requires rich user interactions, yet collecting human feedback is expensive and difficult to scale. Simulated users offer a scalable alternative, but they must both resemble real user behavior and provide useful learning experiences for agents. In contrast, most agent-training frameworks rely on off-the-shelf assistant LLMs, whose helpfulness can make them overly cooperative, explicit, and behaviorally homogeneous compared with real users. We introduce MIMESIS, a purpose-built user simulator trained on human conversations with explicit reasoning supervision and 13 realistic behavioral patterns derived from real user interactions. Empirically, our 9B model achieves a SOUL-Index of 65.7, surpassing the strongest frontier model. Compared with Claude-Opus-5, the strongest baseline on RealUserSim and SimulatorArena, MIMESIS improves behavioral fidelity by 13.4 points and reduces Turing distance by 3.6 points, respectively. We then freeze the simulator and train an agent by interacting with the frozen simulator using multi-turn reinforcement learning. Across eight environments, training with MIMESIS yields better agent performance than training with GPT-5.5 under all nine unseen user simulators, demonstrating stronger generalization to new user simulators. Moreover, we propose Coached On-Policy Self-Distillation (CSD), which leverages simulator-generated private reasoning traces and subsequent utterances as feedback on how well the agent addresses user needs. A coach converts this information into concise coaching notes that describe how the agent can better anticipate user needs and adapt its behavior over the course of an interaction. CSD turns this feedback into dense, token-level supervision beyond sparse task rewards, yielding further gains across all nine evaluation user models.

On-Policy Distillation (OPD) has become a core technique in the post-training of Large Language Models (LLMs) for transferring knowledge from domain experts to student models. However, existing OPD distillation methods require teacher and student models to share the same tokenizer, restricting the applicability of OPD within the model series. Current mainstream practice typically employs Supervised Fine-Tuning (SFT) on teacher-generated responses for cross-tokenizer distillation, which fails to capture the rich knowledge embedded in the teacher's probability distribution. In this work, we enable the standard on-policy distillation method to operate across model families, ensuring that high-fidelity token-level signals can propagate across different tokenizers with a precise token-mapping algorithm. Extensive experiments show that cross-tokenizer OPD is significantly more compute-efficient than baselines on various benchmarks. Our results unlock a broader range of teacher-student pairs for OPD, opening up new avenues for adapting and enhancing interactions between LLMs.

Reinforcement learning from human feedback (RLHF) is a key driver of quality and safety in state-of-the-art large language models. Yet, a surprisingly simple and strong inference-time strategy is Best-of-N sampling that selects the best generation among N candidates. In this paper, we propose Best-of-N Distillation (BOND), a novel RLHF algorithm that seeks to emulate Best-of-N but without its significant computational overhead at inference time. Specifically, BOND is a distribution matching algorithm that forces the distribution of generations from the policy to get closer to the Best-of-N distribution. We use the Jeffreys divergence (a linear combination of forward and backward KL) to balance between mode-covering and mode-seeking behavior, and derive an iterative formulation that utilizes a moving anchor for efficiency. We demonstrate the effectiveness of our approach and several design choices through experiments on abstractive summarization and Gemma models. Aligning Gemma policies with BOND outperforms other RLHF algorithms by improving results on several benchmarks.

On-policy distillation (OPD), which aligns the student with the teacher's logit distribution on student-generated trajectories, has demonstrated strong empirical gains in improving student performance and often outperforms off-policy distillation and reinforcement learning (RL) paradigms. In this work, we first theoretically show that OPD is a special case of dense KL-constrained RL where the reward function and the KL regularization are always weighted equally and the reference model can by any model. Then, we propose the Generalized On-Policy Distillation (G-OPD) framework, which extends the standard OPD objective by introducing a flexible reference model and a reward scaling factor that controls the relative weight of the reward term against the KL regularization. Through comprehensive experiments on math reasoning and code generation tasks, we derive two novel insights: (1) Setting the reward scaling factor to be greater than 1 (i.e., reward extrapolation), which we term ExOPD, consistently improves over standard OPD across a range of teacher-student size pairings. In particular, in the setting where we merge the knowledge from different domain experts, obtained by applying domain-specific RL to the same student model, back into the original student, ExOPD enables the student to even surpass the teacher's performance boundary and outperform the domain teachers. (2) Building on ExOPD, we further find that in the strong-to-weak distillation setting (i.e., distilling a smaller student from a larger teacher), performing reward correction by choosing the reference model as the teacher's base model before RL yields a more accurate reward signal and further improves distillation performance. However, this choice assumes access to the teacher's pre-RL variant and incurs more computational overhead. We hope our work offers new insights for future research on OPD.

Reinforcement learning fine-tuning has proven effective for steering generative diffusion models toward desired properties in image and molecular domains. Graph diffusion models have similarly been applied to combinatorial structure generation, including neural architecture search (NAS). However, neural architectures are directed acyclic graphs (DAGs) where edge direction encodes functional semantics such as data flow-information that existing graph diffusion methods, designed for undirected structures, discard. We propose Directed Graph Policy Optimization (DGPO), which extends reinforcement learning fine-tuning of discrete graph diffusion models to DAGs via topological node ordering and positional encoding. Validated on NAS-Bench-101 and NAS-Bench-201, DGPO matches the benchmark optimum on all three NAS-Bench-201 tasks (91.61%, 73.49%, 46.77%). The central finding is that the model learns transferable structural priors: pretrained on only 7% of the search space, it generates near-oracle architectures after fine-tuning, within 0.32 percentage points of the full-data model and extrapolating 7.3 percentage points beyond its training ceiling. Bidirectional control experiments confirm genuine reward-driven steering, with inverse optimization reaching near random-chance accuracy (9.5%). These results demonstrate that reinforcement learning-steered discrete diffusion, once extended to handle directionality, provides a controllable generative framework for directed combinatorial structures.

Knowledge distillation offers a promising path to transfer reasoning capabilities from large teacher models to efficient student models; however, existing token-level on-policy distillation methods require token-level alignment between the student and teacher models, which restricts the student model's exploration ability, prevent effective use of interactive environment feedback, and suffer from severe memory bottlenecks in reinforcement learning. We introduce On-policy Verbal Distillation (OVD), a memory-efficient framework that replaces token-level probability matching with trajectory matching using discrete verbal scores (0--9) from teacher models. OVD dramatically reduces memory consumption while enabling on-policy distillation from teacher models with verbal feedback, and avoids token-level alignment, allowing the student model to freely explore the output space. Extensive experiments on Web question answering and mathematical reasoning tasks show that OVD substantially outperforms existing methods, delivering up to +12.9% absolute improvement in average EM on Web Q&A tasks and a up to +25.7% gain on math benchmarks (when trained with only one random samples), while also exhibiting superior training efficiency. Our project page is available at https://OVD.github.io

Vision-Language-Action Models (VLAs) have demonstrated remarkable generalization capabilities in real-world experiments. However, their success rates are often not on par with expert policies, and they require fine-tuning when the setup changes. In this work, we introduce Refined Policy Distillation (RPD), a novel Reinforcement Learning (RL)-based policy refinement method that bridges this performance gap through a combination of on-policy RL with behavioral cloning. The core idea of RPD is to distill and refine VLAs into compact, high-performing expert policies by guiding the student policy during RL exploration using the actions of a teacher VLA, resulting in increased sample efficiency and faster convergence. We complement our method by fine-tuned versions of Octo and OpenVLA for ManiSkill3 to evaluate RPD in simulation. While this is a key requirement for applying RL, it also yields new insights beyond existing studies on VLA performance in real-world settings. Our experimental results across various manipulation tasks show that RPD enables the RL student to learn expert policies that outperform the VLA teacher in both dense and sparse reward settings, while also achieving faster convergence than the RL baseline. Our approach is even robust to changes in camera perspective and can generalize to task variations that the underlying VLA cannot solve. Our code, dataset, VLA checkpoints, and videos are available at https://refined-policy-distillation.github.io

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/

Subgraph GNNs are provably expressive neural architectures that learn graph representations from sets of subgraphs. Unfortunately, their applicability is hampered by the computational complexity associated with performing message passing on many subgraphs. In this paper, we consider the problem of learning to select a small subset of the large set of possible subgraphs in a data-driven fashion. We first motivate the problem by proving that there are families of WL-indistinguishable graphs for which there exist efficient subgraph selection policies: small subsets of subgraphs that can already identify all the graphs within the family. We then propose a new approach, called Policy-Learn, that learns how to select subgraphs in an iterative manner. We prove that, unlike popular random policies and prior work addressing the same problem, our architecture is able to learn the efficient policies mentioned above. Our experimental results demonstrate that Policy-Learn outperforms existing baselines across a wide range of datasets.

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.

On-policy distillation (OPD) has emerged as an effective framework for post-training language models by pairing student-generated trajectories with dense token-level supervision from a teacher. However, OPD implicitly assumes that teacher-derived rewards are an appropriate proxy for reasoning progress, and therefore treats all teacher feedback equally during policy optimization. While in practice, this assumption does not always hold. We observe that teacher-derived rewards often conflict with genuine reasoning progress, as reasoning steps with clear reasoning advancement may still receive lower distillation rewards, simply due to deviation from teacher's outputs. To address this mismatch, we propose Reasoning-Progress-Aware Reward Filtering for On-Policy Distillation (R2-OPD), which constructs two within-trajectory rankings of reasoning spans, one from teacher-derived rewards and the other from independently estimated progress reward. Distillation rewards are selectively suppressed whenever the two rankings disagree, reducing supervision that conflicts with reasoning progress while preserving effective teacher guidance. Our approach shows consistent improvement over standard OPD especially regarding reasoning performances.

Real-time video generation via diffusion is essential for building general-purpose multimodal interactive AI systems. However, the simultaneous denoising of all video frames with bidirectional attention via an iterative process in diffusion models prevents real-time interaction. While existing distillation methods can make the model autoregressive and reduce sampling steps to mitigate this, they focus primarily on text-to-video generation, leaving the human-AI interaction unnatural and less efficient. This paper targets real-time interactive video diffusion conditioned on a multimodal context, including text, image, and audio, to bridge the gap. Given the observation that the leading on-policy distillation approach Self Forcing encounters challenges (visual artifacts like flickering, black frames, and quality degradation) with multimodal conditioning, we investigate an improved distillation recipe with emphasis on the quality of condition inputs as well as the initialization and schedule for the on-policy optimization. On benchmarks for multimodal-conditioned (audio, image, and text) avatar video generation including HDTF, AVSpeech, and CelebV-HQ, our distilled model matches the visual quality of the full-step, bidirectional baselines of similar or larger size with 20x less inference cost and latency. Further, we integrate our model with audio language models and long-form video inference technique Anchor-Heavy Identity Sinks to build LiveTalk, a real-time multimodal interactive avatar system. System-level evaluation on our curated multi-turn interaction benchmark shows LiveTalk outperforms state-of-the-art models (Sora2, Veo3) in multi-turn video coherence and content quality, while reducing response latency from 1 to 2 minutes to real-time generation, enabling seamless human-AI multimodal interaction.

On-policy distillation (OPD) has become a key paradigm in LLM post-training, yet its training dynamics remain poorly understood. We present a systematic study examining the role, pathologies, and regulations of OPD. We first clarify the role of OPD as an exploration catalyst: it steers the student toward correct reasoning paths via dense token-level guidance, without expanding capability ceiling. We confirm this by showing that prompt diversity matters more than per-problem sampling numbers, and critically, that the effectiveness of OPD hinges entirely on the quality of its guiding signal. This dependency exposes two pathologies that derail exploration. The Student-Teacher Mismatch occurs when a large teacher-student distributional gap causes the guiding signal to misalign with task correctness, steering exploration in counterproductive directions. Length Exploitation arises when the aggregated token-level objective creates length-dependent shortcuts, allowing the student to game the reward landscape through response truncation or redundant padding, exploring degenerate length modes rather than reasoning strategies. To tame these pathologies, we investigate lightweight signal regulations: advantage clipping and log-scale compression, ensuring exploration is guided by faithful signals. Experiments across seven benchmarks demonstrate that these regulations alleviate length exploitation and enable effective distillation, stably surpassing OPD variants and RLVR baselines, thereby confirming that well-regulated signal quality, rather than mere teacher scale, governs successful exploration in OPD.

Knowledge distillation is central to LLM post-training, yet its design space remains poorly understood, especially alongside reinforcement learning (RL). We show that the prevailing paradigms, off-policy distillation and on-policy distillation (OPD), implicitly couple two orthogonal choices: prefix source and token-level KL direction. This follows from decomposing sequence-level KL over autoregressive response distributions: forward KL pairs teacher prefixes with token-level forward KL, and reverse KL pairs student prefixes with token-level reverse KL. We argue this coupling is not intrinsic: decoupling the two axes yields four valid objectives. We establish gradient-level identities showing forward KL gives SFT-style cross-entropy matching with teacher soft targets, whereas reverse KL gives an RL-style policy-gradient objective with a dense teacher-student log-ratio reward, connecting them to off-policy SFT, DAgger-style on-policy SFT, offline-RL-style distillation, and OPD. We conduct an extensive controlled study on math reasoning, evaluating the four objectives both as standalone methods and as initializations for subsequent RL. The results reveal three tradeoffs: KL direction induces an accuracy-entropy tradeoff, prefix source a quality-compute tradeoff, and training length an accuracy-stability tradeoff. Motivated by these findings, we propose KL mixing and an entropy-gated length curriculum. KL mixing shows long-sequence distillation requires substantial forward-KL weight to prevent entropy collapse and length inflation without sacrificing accuracy. The entropy-gated length curriculum improves Avg@k and Pass@k by 3.6 and up to 5.8 points, and cuts average response length by roughly 3x versus fixed long-horizon training. Our results provide a framework and practical methods for designing reasoning distillation objectives that balance accuracy, diversity, compute, and RL behavior.

On-policy distillation (OPD) specializes pretrained video diffusion models through teacher supervision along the student's own generation trajectory. Although large video models are natural teachers, developing specialized video experts can require costly video data and training, while querying them incurs substantially higher latency than querying image experts. More readily available and cheaper to query, image experts offer a cost-effective alternative, particularly for largely temporal-agnostic capabilities such as aesthetics and OCR that admit frame-level supervision. However, heterogeneous image and video latent spaces prevent direct supervision of intermediate student states, while image experts lack cross-frame motion supervision, making temporal consistency vulnerable to frame-level improvements. In this paper, we propose MILD, a Motion-Preserving Image-to-Video Latent Distillation framework that transfers specialized image expertise while preserving pretrained video dynamics. MILD uses a learnable linear connector that aligns student latent states and predicted updates with those of image experts, enabling supervision transfer across heterogeneous latent spaces. We further constrain image-guided corrections around the pretrained student's predictions to preserve video dynamics and incorporate an optical-flow-based motion reward to improve motion quality and temporal consistency. Across specialized image experts and multiple video-student backbones, our method consistently outperforms video-teacher OPD baselines, with further studies demonstrating effective transfer across connector designs and heterogeneous architectures. These results establish image-to-video distillation as an effective route to improving video generation by drawing on the diverse and evolving capabilities of the image-generation ecosystem.

We introduce the Pistis model family, comprising 27B- and 9B-parameter multimodal large language models built on Qwen3.6 and Qwen3.5, respectively, and developed through a general and scalable post-training framework. The framework first establishes a strong foundation through large-scale multimodal supervised fine-tuning (SFT). Building on this SFT foundation, we propose Interleaved Distillation and Reinforcement Learning (IDRL), a novel post-training paradigm that tightly integrates on-policy distillation and reinforcement learning within a single training loop. By alternating between the two objectives, rather than optimizing either in isolation or combining them in a static joint loss, IDRL enables more effective knowledge transfer, greater optimization stability, and more precise credit assignment for long-horizon agentic trajectories, leading to stronger performance while mitigating common capability trade-offs. At both model scales, the framework produces two specialized variants: Pistis-Thinking, designed to strengthen deep multimodal reasoning, and Pistis-Agentic, which additionally incorporates agentic trajectory data to support long-horizon planning, iterative reasoning, and tool use. Pistis-Agentic is particularly strong in multimodal search. Both scales outperform their corresponding base models. Beyond model-parameter optimization, we further introduce Pistis-Auto-Harnessing (PAH), a system-level method that automatically improves the agent's inference harness through iterative optimization. Experiments demonstrate that PAH enhances the model performance without updating the model parameters or increasing the interaction budget.

Wrapping an image generation model in an agentic harness can effectively boost Text-to-Image task performance: the harness can leverage memory, skills, workflow orchestration, result verification, and iterative refinement to continually construct and revise prompts, thereby eliciting better images. These gains, however, remain external to the diffusion model and are realized only while the full harness runs. We propose Diffusion On-Policy Context Distillation (D-OPCD), which treats the agent-improved prompt as privileged context and distills the knowledge encoded in the agent harness into the weights of the diffusion model, so that the model retains part of the harness's benefit when conditioned on the original query alone. Using a Text-to-Image agent equipped with our proposed Auto Skill Evolver (ASE), we show that D-OPCD can internalize harness capabilities into the generator's weights, raising the average direct-generation score from 60.52 to 65.09 across four benchmarks. With this knowledge absorbed into the weights, the harness can shed its saturated skills and resume evolving: a second ASE round on the updated generator improves on a skill-free harness by additional 1.83 points, pointing toward text-to-image systems in which harness and model keep improving each other through continual co-evolution.

Distilling capable language-model agents into smaller models requires aligning the student's behavior with the teacher's. This raises a fundamental question: at which states and at what granularity should this alignment be performed? Offline imitation provides dense but token-specific supervision and can suffer from state-distribution mismatch. Token-level on-policy distillation (OPD) addresses this mismatch but typically requires teacher token probabilities and compatible tokenization. We argue that semantic actions provide a natural unit of supervision for agent distillation. We introduce ActionOPD, an action-level on-policy distillation method motivated by maximizing expected teacher-action likelihood at student-encountered states. At each such state, ActionOPD samples actions from both the student and a black-box teacher, rewarding student actions according to their semantic agreement with the sampled teacher actions. Through policy optimization, ActionOPD aligns the student's action-level behavior with the teacher's decisions without requiring reproduction of teacher-written reasoning or access to teacher token probabilities. Training Qwen3-4B and Qwen3-8B with two teachers on diverse, curated tool-use tasks yields average gains of 3.3-6.9 percentage points across four out-of-distribution benchmarks. ActionOPD scales favorably with student size and teacher capability, without requiring the teacher and student to share a model family or tokenizer. On τ^2-bench, ActionOPD achieves competitive performance against offline distillation and token-level OPD. We further explore Self-ActionOPD with a same-model teacher and privileged context. These results establish ActionOPD as a promising approach to agent distillation.

We introduce a novel approach to large language model (LLM) distillation by formulating it as a constrained reinforcement learning problem. While recent work has begun exploring the integration of task-specific rewards into distillation processes, existing methods typically rely on ad-hoc reward weighting. We propose a principled optimization framework that maximizes task-specific rewards while constraining the divergence from the teacher model to remain below a specified threshold. Our approach adapts constrained state augmented reinforcement learning to the distillation setting, introducing a modified reward function that maintains theoretical guarantees of constraint satisfaction without requiring state augmentation or teacher model access during deployment and without the computational overhead of the dual Lagrangian methods. Through extensive experiments on mathematical reasoning tasks, we demonstrate that our method achieves better constraint satisfaction rates and better reasoning compared to the soft Lagrangian relaxation baselines while maintaining competitive task performance. Our framework provides a theoretically grounded and practically efficient solution for reward-aware distillation in resource-constrained settings.

Scaling on-policy distillation (OPD) for large language models (LLMs) confronts a fundamental tension: asynchronous execution is necessary for system efficiency, but structurally deviates from the ideal on-policy objective. To address this challenge, we theoretically decompose the objective discrepancy into rollout drift and supervision drift, capturing staleness in student rollout and teacher context, respectively. Building on this, we introduce a sample-level freshness score that quantifies the reliability of a buffered sample with respect to the on-policy objective. Guided by this signal, we further propose f-OPD, a novel framework that adaptively regulates stale-sample influence and constrains policy drift accumulated under asynchronous training. Across reasoning, tool-use, and coding-agent tasks of increasing interaction horizon, f-OPD consistently achieves task performance comparable to synchronous optimization while largely retaining the throughput advantages of asynchronous execution. Our results establish the first recipe for achieving a performance-efficiency trade-off in OPD, paving the way for long-horizon agentic post-training at scale.

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.

Repository-level software engineering (SWE) comprises heterogeneous task categories, whose progress under pooled agentic reinforcement learning can be uneven: gains in some categories coincide with regressions in others, while aggregate resolution obscures these changes. Motivated by this category see-saw, we develop a category-aware expert-training and policy-integration framework. Executable task construction and SWE Labeler, an evidence-grounded multi-axis labeling system, organize the training pools. Initial category-specific RL improves average training success while leaving uneven instance-level progress, motivating explicit consolidation of successful behavior and policy-adaptive task selection. Same-origin category experts alternate long-horizon Agentic-miniRL with Refresh-Repair-Expand (RRE): the updated policy refreshes instance mastery, reuses its own verified successful trajectories for Repair SFT, and reselects tasks for further RL. Label-routed multi-teacher on-policy distillation (MOPD) consolidates the experts into one deployable student, with ReLU-gated reward extrapolation keeping only each teacher's improving direction over the reference. Expert training and policy integration require no external model to provide solution trajectories or action targets. We evaluate Pooled RL and Balanced RL, expert development, and single-model integration through aggregate and per-category resolution, the minimum category lift over each joint-RL baseline, and expert-gain recovery. The final MOPD policy achieves mean resolution of 58.04% on Pro-618 and 59.00% on SWE-bench Multilingual, improving over the base model by 5.39 and 2.78 percentage points, respectively.

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.

On-policy (self) distillation (OPSD) is increasingly adopted for language-model post-training. It strengthens the teacher with privileged information but can induce a privilege illusion: the student learns privilege-dependent behavior it cannot reproduce from its inference-time context, yet behaves as if the training-time privileged information remained available, ultimately degrading performance. In this paper, we identify information asymmetry between the privileged teacher and the student at inference as the root cause of this failure in OPSD. To resolve this asymmetry, we propose Dual-Anchored Policy Distillation (DAPD), a unified framework with two levels of anchoring. Dual-Path Anchoring (DPA) introduces a self-conditioned bridge and aligns reference and rollout behavior along two matched-information paths, preventing privilege-dependent behavior from being transferred to the inference-time student. Dual-Source Anchoring (DSA) applies these paths in both reference-to-rollout and rollout-to-reference directions, reducing reliance on privileged reference guidance while preserving correctness supervision. Extensive experiments show that DAPD significantly alleviates privilege illusion, outperforming OPSD on Qwen3-4B by +2.00 points on average across tasks. Notably, its gains persist across scales, reaching +2.69 at 4B and +2.78 at 32B.

On-policy distillation (OPD) has emerged as a widely used paradigm for post-training large language models, reducing the train--test mismatch of conventional distillation by supervising the student on its own generated trajectories. However, existing OPD objectives remain largely token-local and outcome-agnostic, optimizing teacher--student agreement at each prefix despite reasoning quality being determined at the trajectory level. Reinforcement learning with verifiable rewards (RLVR), particularly Group Relative Policy Optimization (GRPO), provides complementary outcome-level supervision but suffers from sparse rewards and coarse credit assignment. We show that OPD and RLVR exhibit complementary blind spots: teacher signals provide dense local guidance but are weakly aligned with rollout correctness, whereas group-relative rewards capture task success but provide coarse token-level credit and vanish on all-failure groups. We introduce DiffGate, an outcome-gated objective that combines GRPO with selective, bounded teacher guidance. Teacher supervision is applied only to failed trajectories, scaled by group difficulty, and smoothly bounded to prevent extreme teacher--student discrepancies from dominating optimization. The verifier therefore determines which trajectories receive teacher guidance, while the teacher provides dense token-level update directions within those trajectories. Across Qwen3-0.6B and Qwen3-1.7B students, DiffGate improves code avg@8 over matched GRPO by +1.7 and +1.8 points and pass@8 by +1.6 and +5.7 points, respectively. On mathematics, avg@8 remains within 0.5 points of GRPO while pass@8 improves by +1.1 and +3.9 points. Overall, DiffGate improves pass@8 across all four model--domain settings, demonstrating improved solution coverage under our evaluation protocol.

Large language models are increasingly trained as interactive agents for long-horizon tasks involving multi-turn interaction, tool use, and environment feedback. Outcome-based reinforcement learning (RL) provides a practical optimization paradigm, but its sparse trajectory-level rewards offer limited guidance on intermediate decisions, leaving a supervision gap between episode-level outcomes and token-level policy learning. We propose SEED (SElf-Evolving On-Policy Distillation), a self-evolving framework that converts completed on-policy trajectories into training-time hindsight skills and distills their behavioral effect back into the policy model. SEED first fine-tunes the policy to analyze completed trajectories and generate natural-language skills that capture reusable workflows, decisive observations, or failure-avoidance rules. During RL, the current policy both collects trajectories and serves as the analyzer that extracts hindsight skills from them. Policy updates therefore improve subsequent decision making and skill analysis together, allowing hindsight supervision to evolve with the policy. SEED then re-scores the sampled actions under ordinary and skill-augmented contexts, converting the skill-induced probability shift into a dense token-level on-policy distillation signal. This signal is jointly optimized with outcome-based RL, keeping the auxiliary supervision aligned with the current trajectory distribution. Extensive experiments on text-based and vision-based agentic tasks show that SEED consistently improves performance and sample efficiency, exhibiting robust generalization to unseen scenarios. Our code is available at https://github.com/jinyangwu/SEED.

Existing Large Language Model (LLM) agents struggle in interactive environments requiring long-horizon planning, primarily due to compounding errors when simulating future states. To address this, we propose ProAct, a framework that enables agents to internalize accurate lookahead reasoning through a two-stage training paradigm. First, we introduce Grounded LookAhead Distillation (GLAD), where the agent undergoes supervised fine-tuning on trajectories derived from environment-based search. By compressing complex search trees into concise, causal reasoning chains, the agent learns the logic of foresight without the computational overhead of inference-time search. Second, to further refine decision accuracy, we propose the Monte-Carlo Critic (MC-Critic), a plug-and-play auxiliary value estimator designed to enhance policy-gradient algorithms like PPO and GRPO. By leveraging lightweight environment rollouts to calibrate value estimates, MC-Critic provides a low-variance signal that facilitates stable policy optimization without relying on expensive model-based value approximation. Experiments on both stochastic (e.g., 2048) and deterministic (e.g., Sokoban) environments demonstrate that ProAct significantly improves planning accuracy. Notably, a 4B parameter model trained with ProAct outperforms all open-source baselines and rivals state-of-the-art closed-source models, while demonstrating robust generalization to unseen environments. The codes and models are available at https://github.com/GreatX3/ProAct

On-policy self-distillation has recently emerged as an effective approach for improving language-model reasoning by supervising students with a frozen or EMA version of themselves that receives privileged information. Its application to multimodal large language models (MLLMs), however, remains largely unexplored. Recent approaches use privileged visual information, such as image crops corresponding to a question, to improve fine-grained perception, but their gains are confined to tasks that benefit from such visual zooming and require either human-annotated grounding data or external teacher models. We introduce a different form of on-policy self-distillation for MLLMs that provides the teacher with textual, spatially grounded guidance identifying the visual elements relevant to a query. We use procedurally generated scenes with automatically available object identities and spatial coordinates, enabling scalable and annotation-free post-training. The teacher uses this spatial guidance to locate and integrate evidence from multiple relevant image regions, while the student learns to reproduce the resulting behavior from the image and question alone. Our approach consistently improves performance on counting, document and chart understanding benchmarks across multiple models. Importantly, although post-training uses only synthetic scenes, the resulting improvements transfer to real-world perception benchmarks, yielding a 3.23-point gain in average performance across CVBench, V*, ZoomBench, BLINK, HR-Bench, and MME-RealWorld. These results show that spatially grounded privileged information can induce broader perceptual capabilities through on-policy self-distillation, enabling substantial synthetic-to-real transfer beyond the task and data distribution used for post-training. Project page: https://github.com/sirkosophia/Where-OPD

Large Language Models (LLMs) increasingly rely on agentic capabilities-iterative retrieval, tool use, and decision-making-to overcome the limits of static, parametric knowledge. Yet existing agentic frameworks treat external information as unstructured text and fail to leverage the topological dependencies inherent in real-world data. To bridge this gap, we introduce Agentic Graph Learning (AGL), a paradigm that reframes graph learning as an interleaved process of topology-aware navigation and LLM-based inference. Specifically, we propose AgentGL, the first reinforcement learning (RL)-driven framework for AGL. AgentGL equips an LLM agent with graph-native tools for multi-scale exploration, regulates tool usage via search-constrained thinking to balance accuracy and efficiency, and employs a graph-conditioned curriculum RL strategy to stabilize long-horizon policy learning without step-wise supervision. Across diverse Text-Attributed Graph (TAG) benchmarks and multiple LLM backbones, AgentGL substantially outperforms strong GraphLLMs and GraphRAG baselines, achieving absolute improvements of up to 17.5% in node classification and 28.4% in link prediction. These results demonstrate that AGL is a promising frontier for enabling LLMs to autonomously navigate and reason over complex relational environments. The code is publicly available at https://github.com/sunyuanfu/AgentGL.

On-policy distillation (OPD) is a promising approach for training language agents, providing dense teacher supervision on student-generated trajectories. However, in multi-turn interaction, an incorrect action changes the states the student encounters later, so errors compound across turns. In preliminary experiments across three Qwen3 models (8B to 235B), we find that more than half of the failed rollouts contain a pivotal mistake, an action that moves the agent farther from completing the task, and this mistake typically occurs early. These pivotal mistakes often remain recoverable: guiding the model for only a few turns after the pivotal turn can restore task success. We therefore propose PivotOPD, an on-policy distillation framework that jointly trains the student to prevent pivotal mistakes and to recover from the states they create. At each pivotal mistake, a teacher model provides a gold action and then names a recovery action at each of the next few turns. Preventive distillation uses the gold action with reverse KL to steer the student away from the pivotal mistake, while recovery distillation uses the recovery actions with forward KL to transfer recovery behaviors that the student rarely samples. Against 13 baselines on ALFWorld, WebShop, and Search-based QA, PivotOPD achieves the strongest average performance for both Qwen3-1.7B and Qwen3-8B students, improving over the strongest baseline on ALFWorld by +5.5% with the 1.7B student. The gains also transfer to another model family on the software engineering domain, where PivotOPD raises the resolve rate of a Nemotron-3.5 student on SWE-Bench Verified by +3.2%. Project page: https://research.nvidia.com/labs/lpr/pivotopd/

On-policy knowledge distillation has proven effective for language models, yet its application to vision-language models (VLMs) remains underexplored. We observe that standard on-policy distillation can improve a student's output quality while failing to strengthen its reliance on visual input: on vision-critical tokens, the student's predictions remain largely unchanged whether or not fine-grained visual detail is present, even though the teacher's predictions depend heavily on it.To make this difference observable, we introduce visual advantage (VA), the token-level log-probability difference when the teacher scores a student-generated rollout with versus without access to fine-grained visual detail. VA is concentrated in a small minority of tokens, and these high-VA tokens are the ones that actually carry the visual supervision signal. This motivates a distillation objective that treats them differently from language scaffolding, so their contribution is not diluted by the abundant surrounding language tokens.We propose Visual-Advantage On-Policy Distillation (VA-OPD), which uses VA at two granularities: rollout-level reweighting by trajectory-averaged VA, and token-level KL averaged within high-VA and low-VA groups separately. We train on two math datasets (Geometry3K and ViRL39K) and evaluate on eight benchmarks covering both mathematical reasoning and visual understanding, across three teacher sizes (4B, 8B, and 32B) on the Qwen3-VL family. VA-OPD improves over standard on-policy distillation on every benchmark, with the gain growing monotonically along both the teacher-size and data-scale axes, suggesting that these factors compound consistently.

Large language model (LLM) post-training is essential for improving reasoning, adaptation, and alignment. Existing methods mainly follow two paradigms: reinforcement learning (RL) and on-policy distillation (OPD). However, RL relies on coarse-grained outcome supervision, resulting in difficult credit assignment and limited capability to acquire new knowledge. OPD, meanwhile, unconditionally matches teacher logits through KL divergence, which creates a dilemma: similar teachers provide little new knowledge, while substantially different teachers often yield ineffective guidance, largely restricting OPD to within-family distillation. We propose Distilled Reinforcement Learning (Distilled RL), which integrates teacher supervision into the RL objective to provide fine-grained guidance, selectively transfer new knowledge and avoid unconditional imitation. Distilled RL contains three components: reverse importance sampling with clipping, negative sample reset, and sequence-level geometric normalization. Through a concise and interpretable case study, we demonstrate that Distilled RL can effectively transfer previously unavailable knowledge from a teacher model to a student model. Extensive experiments across both within-family and cross-family distillation settings show that Distilled RL substantially outperforms standard RL and OPD in terms of both pass@1 and pass@k. Our code is available at https://github.com/597358816/Distilled-RL.

Reinforcement learning for large language models faces a fundamental trade-off between sample efficiency and asymptotic performance: strictly on-policy methods discard trajectories after a single update, while off-policy reuse introduces distribution mismatch that existing trust-region techniques mitigate primarily by enforcing conservative optimization, often leaving rich training signals underutilized. To investigate this, we perform extensive off-policy updates on fixed data. Our experiments reveal that aggressive multi-step optimization brings rapid initial gains, but excessive updates cause trajectory probabilities to deviate and entropy to collapse, with performance plateauing early. Tightening KL constraints merely lowers the ceiling without resolving the degradation. This motivates Extreme Region Policy Distillation (ERPD), a two-stage framework that decouples sample efficiency from KL efficiency. The first stage performs weakly constrained off-policy optimization on fixed data to maximally extract training signals. The resulting policy provides token-level supervision. In the second stage, we distill these signals into the base policy under trust-region constraints, filtering harmful drift while preserving useful signals. The distilled policy achieves comparable or better performance with substantially smaller KL divergence, indicating that much of the first-stage divergence was spent on unnecessary drift rather than genuine improvement. Crucially, ERPD accommodates both strong and weak teachers: when aggressive optimization yields no stronger policy, even degenerate teachers provide effective supervision via alternative signal construction strategies. We validate ERPD on mathematical reasoning, showing gains for strong base models where on-policy training plateaus, and reliable improvements with weak teachers.

On-policy distillation (OPD) has demonstrated two important capabilities in language models: compressing large teachers into smaller students and merging expert models into a single model. Existing diffusion OPD, however, mostly focus on the latter, with teachers and students sharing the same backbone and scale. We investigate large-to-small diffusion opd from large teachers to a small student and find that the standard recipe fails. To find the underlying cause, we propose Fixed-State KL, an effective and fair way to measure the distribution gap between student and teacher during OPD training for diffusion models. We are the first to clarify why large-to-small OPD is challenging for diffusion models: a smaller student struggles to perfectly match the distribution of a larger teacher, while classifier-free guidance can accumulate and amplify the distributional discrepancies between the student's conditional and unconditional branches and those of the teacher. To solve this problem, we propose GFD-OPD, a simple yet effective method that reduces the student-teacher gap while avoiding the error amplification of the CFG composition. Across numerous experiments, GFD outperforms previous baselines in both training efficiency and final performance, achieving state-of-the-art results on all benchmarks.