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OPLD: On-Policy Latent Distillation for Multimodal Reasoning
Shoutai Zhu, Tianyang Xu, Bin Sun, Mingyuan Xu, Yu Liu, Qinzhen Guo
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Summary
The paper introduces OPLD (On-Policy Latent Distillation), a framework for multimodal reasoning that transfers reasoning capabilities from privileged multimodal Chain-of-Thought (CoT) into latent representations. Unlike existing methods that align latents with compressed visual features, OPLD supervises latent states at the reasoning-process level, allowing a student model to internalize abstract reasoning patterns without auxiliary images or explicit CoT during inference.
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Shoutai Zhu → affiliatedwith → ByteDance
confidence 95% · Shoutai Zhu 1 ... 1 ByteDance
OPLD → uses → On-Policy Latent Distillation
confidence 95% · OPLD consists of a teacher model and a student model... perform on-policy latent distillation.
OPLD → internalizes → abstract reasoning patterns
confidence 92% · OPLD internalizes multimodal reasoning patterns into latent space instead of merely imitating auxiliary visual features
OPLD → improves → Visual Reasoning
confidence 90% · OPLD consistently outperforms existing latent reasoning methods and achieves state-of-the-art performance on multiple benchmarks.
Qwen2.5-VL-7B → isbackbonefor → OPLD
confidence 85% · we use Qwen2.5-VL-7B as the default backbone for
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Abstract
Abstract:Interleaved multimodal Chain-of-Thought (CoT) improves visual reasoning by incorporating auxiliary visual evidence into intermediate reasoning. However, existing approaches remain constrained by externally defined reasoning traces and visual operations, limiting their ability to develop flexible and abstract visual thinking. Reasoning with latent has recently offered a promising direction by internalizing intermediate computation into continuous representations. Nevertheless, existing visual-latent methods mainly supervise latent states through alignment with compressed auxiliary visual features, treating them as proxies for visual observations rather than active reasoning states. Consequently, they capture the provided evidence but fail to fully internalize the abstract reasoning process induced by multimodal CoT. In this paper, we propose OPLD (On-Policy Latent Distillation), a simple framework that transfers the reasoning capability induced by privileged multimodal CoT into latent reasoning representations. Extensive experiments on diverse multimodal benchmarks demonstrate that OPLD consistently outperforms existing latent reasoning methods and achieves state-of-the-art performance on multiple benchmarks. The results suggest that supervising latent representations at the reasoning-process level provides a more effective paradigm for multimodal latent reasoning than conventional feature-level alignment.
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- Source: https://arxiv.org/abs/2607.28154v1
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OPLD: On-Policy Latent Distillation for Multimodal Reasoning Shoutai Zhu 1 , Tianyang Xu 1 , Sun Bin 1 , Xumingyuan 1 , Yu Liu 1 , Qinzhen Guo 1 1 ByteDance shoutaizhu61@gmail.com xutianyang.666, sunbin.824, xumingyuan.0916, liuyu.96, guoqinzhen@bytedance.com Abstract Interleaved multimodal Chain-of-Thought (CoT) improves vi- sual reasoning by incorporating auxiliary visual evidence into intermediate reasoning. However, existing approaches remain constrained by externally defined reasoning traces and vi- sual operations, limiting their ability to develop flexible and abstract visual thinking. Reasoning with latent has recently offered a promising direction by internalizing intermediate computation into continuous representations. Nevertheless, existing visual-latent methods mainly supervise latent states through alignment with compressed auxiliary visual features, treating them as proxies for visual observations rather than ac- tive reasoning states. Consequently, they capture the provided evidence but fail to fully internalize the abstract reasoning process induced by multimodal CoT. In this paper, we propose OPLD (On-Policy Latent Distillation), a simple framework that transfers the reasoning capability induced by privileged multimodal CoT into latent reasoning representations. During training, a CoT-augmented teacher observes privileged multimodal reasoning signals, while a CoT-free student receives the original input. The stu- dent first performs latent reasoning under its current policy, after which the teacher supervises the same reasoning tra- jectory through token-level distribution alignment and latent trajectory distillation. Consequently, the student internalizes multimodal reasoning patterns into latent space instead of merely imitating auxiliary visual features, enabling efficient reasoning without explicit CoT or auxiliary images during in- ference. Extensive experiments on diverse multimodal bench- marks demonstrate that OPLD consistently outperforms exist- ing latent reasoning methods and achieves state-of-the-art per- formance on multiple benchmarks. The results suggest that su- pervising latent representations at the reasoning-process level provides a more effective paradigm for multimodal latent rea- soning than conventional feature-level alignment. Introduction Chain-of-thought reasoning has become an effective mech- anism for improving the reasoning ability of large language models and multimodal large language models (Wei et al. 2022; Kojima et al. 2022; Zhang et al. 2023). For visual reasoning, recent work further shows that CoT need not be restricted to text: injecting visual evidence into inter- mediate reasoning steps can substantially improve the abil- ity of MLLMs to solve perception-intensive and spatially Copyright© 2027, Association for the Advancement of Artificial Intelligence (w.aaai.org). All rights reserved. Figure 1: Comparison of multimodal reasoning paradigms. OPLD learns latent reasoning by distilling privileged mul- timodal reasoning representations, eliminating the need for auxiliary images or textual CoT during inference. grounded problems. This gives rise to interleaved multi- modal CoT, where reasoning is supported not only by textual rationales but also by auxiliary images, such as cropped re- gions, zoomed-in visual evidence, annotated diagrams, or tool-generated observations. Existing methods mainly fol- low two technical paradigms. The first explicitly constructs visual reasoning traces through multi-step interaction, re- gion prediction, visual tool invocation, or image manipu- lation, allowing the model to “think with images” during inference (Zheng et al. 2025; Zhang et al. 2025b; Xia et al. 2025). The second performs reasoning in latent visual space: instead of explicitly materializing all auxiliary visual obser- vations, some methods train MLLMs to generate continuous latent states that represent key visual evidence or interme- diate visual thoughts (Li et al. 2025b; Wang et al. 2026a). Both paradigms demonstrate the importance of visual inter- mediate reasoning, but they also reveal a key limitation: the reasoning process is either externalized as explicit CoT, tool- generated observations or specialized toward representing auxiliary visual features. In this paper, we take a different perspective. We ask whether latent states can learn the abstract internal reasoning representations that an MLLM forms when it leverages inter- arXiv:2607.28154v1 [cs.CV] 30 Jul 2026 leaved multimodal CoT. Latent reasoning provides a natural substrate for this goal. Prior work has shown that language and vision-language models can perform intermediate com- putation through continuous hidden states, from hidden-state feedback in LLMs (Hao et al. 2024) to latent visual reason- ing in MLLMs (Wang et al. 2026a; Jeon et al. 2026; Li et al. 2025b). However, a central challenge remains: latent reasoning states lack explicit supervision. Existing meth- ods often construct surrogate targets by aligning latent to- kens with compressed auxiliary visual features. While con- venient, this introduces several limitations, including infor- mation loss, representation mismatch, and train–inference inconsistency. Moreover, strong feature-level alignment can over-constrain the model’s internal states, making it prone to catastrophic forgetting, shortcut learning, and task-specific overfitting. These issues limit the generality of latent reason- ing methods. In contrast, we seek to supervise latent states at the reasoning-process level, encouraging them to capture the abstract internal representations induced by interleaved multimodal CoT rather than merely imitating auxiliary visual features. We propose OPLD, an On-Policy Latent Distillation framework for multimodal latent reasoning. OPLD consists of a teacher model and a student model with same MLLM backbone and latent reasoning structure, but different input conditions. The teacher is equipped with interleaved mul- timodal CoT, enabling it to form stronger latent reasoning trajectories under guidance. The student is equipped with only original image-question input, encouraging it to de- velop a CoT-free latent reasoning process without relying on explicit rationale tokens. Training proceeds in three stages. We first train the CoT-guided teacher, then warm up the CoT- free student to establish a stable latent reasoning protocol, and finally perform on-policy latent distillation. In the distil- lation stage, the student generates answers from its current policy, and the teacher evaluates these student-generated tra- jectories to provide token-level supervision. Meanwhile, the student’s latent trajectory is aligned with the teacher’s latent trajectory, allowing the abstract reasoning patterns induced by multimodal CoT to be transferred into the student’s latent space. Consequently, the final student model internalizes the abstract reasoning patterns of multimodal CoT into latent space, enabling it to answer through latent reasoning and imagination in the absence of auxiliary information. Our contributions are summarized as follows: • We propose OPLD, a simple and general on-policy latent distillation framework for multimodal latent reasoning. OPLD does not require task-specific visual tools or ex- plicit auxiliary reasoning at inference time. Instead, it internalizes the abstract reasoning patterns induced by textual and interleaved multimodal CoT into latent space. • We introduce an on-policy teacher–student paradigm for latent reasoning. The student rolls out answers with its current policy, and the CoT-augmented teacher supervises the same trajectories through token-level feedback and latent trajectory alignment, enabling the student to answer via latent reasoning without auxiliary information. • OPLD improves both multimodal perception and reason- ing. Extensive experiments show that OPLD consistently outperforms strong latent reasoning methods and achieves state-of-the-art performance on multiple benchmarks. Related Work Reasoning with Images CoT prompting improves complex reasoning by decompos- ing the answer into intermediate steps (Wei et al. 2022; Ko- jima et al. 2022). Early multimodal CoT methods extend this idea to vision-language tasks by generating textual rationales conditioned on both the image and the question (Zhang et al. 2023; Chen et al. 2024; Shao et al. 2024b). However, text- only rationales can be insufficient for visual reasoning, since the model must often revisit fine-grained regions, verify spa- tial relations, read small text, or compare local visual details. This motivates a growing body of work on visual or grounded CoT, where intermediate reasoning steps are explicitly tied to visual evidence. Representative methods guide MLLMs to extract visual rationales step by step, ground reasoning steps to image regions, detect relevant regions before answering, or replay cropped visual evidence during generation (Zhou et al. 2024; Wu et al. 2025; Man et al. 2025; Wang et al. 2025; Jiang et al. 2025; Hu et al. 2026). These methods show that exposing task-relevant visual evidence during intermedi- ate reasoning can substantially improve perception-intensive and spatially grounded tasks. Beyond grounded rationales, recent work further explores the thinking with images paradigm, where vision becomes an active workspace rather than a static input. Some methods perform multi-round visual exploration by predicting where to crop, zoom, or revisit, sometimes optimized with rein- forcement learning or region-level rewards (Jiang et al. 2025; Zheng et al. 2025; Liu et al. 2026). Others introduce gener- ative visual reasoning, where models produce intermediate visual thoughts, subgoal images, RGB visual intermediates, or edited visual states to support downstream reasoning and planning (Li et al. 2025c; Chern et al. 2025; Zhou, Dai, and Ling 2026; Zhao et al. 2025; Yin et al. 2026). These approaches provide a powerful and interpretable way to in- corporate visual evidence into the reasoning process, but they also share a common limitation: the intermediate rea- soning process remains externalized. Inference may require explicit rationales, region selection, tool invocation, image generation, or additional visual observations, which intro- duces error propagation and operational rigidity. In contrast, OPLD uses interleaved multimodal CoT as training guidance and internalizes its abstract reasoning patterns into latent computation, enabling the model to reason without auxiliary visual traces at inference time. Reasoning with Latents Latent reasoning aims to move intermediate computation from explicit token sequences into continuous hidden space. In language models, recent work shows that hidden states can be recurrently fed back as continuous thoughts, allow- ing models to reason beyond discrete chain-of-thought to- kens (Hao et al. 2024). This idea has been extended to multi- modal reasoning, where continuous latents are used to repre- sent visual thoughts, mental imagery, or intermediate visual states. LVR performs autoregressive reasoning directly in the visual embedding space by training latent states to re- construct key visual tokens relevant to the query (Li et al. 2025b). Mirage augments VLM decoding with latent visual tokens interleaved with text tokens, using image-embedding distillation and subsequent task supervision to support mul- timodal mental imagery (Yang et al. 2025). Monet further enables MLLMs to generate continuous embeddings as inter- mediate visual thoughts and introduces visual-latent policy optimization to explicitly optimize latent reasoning (Wang et al. 2026a). SkiLa proposes latent sketch tokens that alter- nate with textual thinking tokens, enabling unified text-visual reasoning in a shared latent space (Tong et al. 2025). Laser improves visual deduction through dynamic windowed align- ment, allowing latent states to maintain coarse-to-fine seman- tic superposition instead of enforcing rigid point-wise pre- diction (Wang et al. 2026b). HyLaR formulates multimodal reasoning as a hybrid discrete-continuous action space and applies decoupled policy optimization to jointly train textual and latent actions (Cheng et al. 2026). However, supervising latent reasoning remains intrin- sically difficult because latent states do not have natu- ral ground-truth annotations. Existing methods therefore often construct surrogate targets by aligning latents with compressed image embeddings, key visual tokens, latent sketches, or intermediate visual observations (Li et al. 2025b; Yang et al. 2025; Wang et al. 2026a; Tong et al. 2025). Al- though effective, such supervision largely treats latent states as proxies for auxiliary visual features. This can introduce in- formation loss, representation mismatch, and train–inference inconsistency, while strong feature-level alignment may over- constrain internal representations and reduce generality. Re- cent diagnostic studies further show that latent tokens may be weakly coupled with both the visual input and the final answer, or become semantically enriched yet under-utilized during answer prediction (Li et al. 2026; Zhang et al. 2026). These findings suggest that the key issue is not merely how to generate latent visual tokens, but how to make them function as active reasoning states. OPLD takes a different perspective. Rather than forcing la- tent states to imitate auxiliary visual features, it learns latent trajectories from the abstract reasoning patterns induced by textual and interleaved multimodal CoT. In this way, OPLD encourages latent states to support answer generation as inter- nal reasoning abstractions, enabling the final model to answer through latent reasoning and imagination without auxiliary information at inference time. Method We propose OPLD, an on-policy latent distillation frame- work for multimodal latent reasoning. As shown in Fig. 2, OPLD contains a teacher model and a student model with the same MLLM backbone and recursive latent reasoning struc- ture, but different input conditions. The teacher reasons with interleaved multimodal CoT, including textual rationales and auxiliary visual evidence, while the student receives only the original image-question input. The objective of OPLD is to transfer the abstract reasoning patterns induced by multi- modal CoT into the student’s latent space, so that the final model can answer through latent reasoning and imagination without auxiliary information at inference time. OPLD follows a three-stage training pipeline. First, we train a CoT-guided teacher with auxiliary multimodal CoT, enabling it to form strong latent reasoning trajectories. Sec- ond, we warm up a CoT-free student using only the original image and question, establishing a stable latent reasoning protocol before distillation. Third, we perform on-policy la- tent distillation. In this stage, the student first generates an- swers with its current policy, and the frozen teacher super- vises the same student-generated trajectories through token- level feedback and latent trajectory alignment. At inference time, the teacher, auxiliary CoT, help images, and all other auxiliary information are discarded. The student performs a fixed number of recursive latent reasoning steps and then generates the answer from the original image and question alone. Problem Setup For each training example, we define two input views. The student view contains only the original image and question: x S = (I,Q),(1) where I denotes the main image and Q denotes the ques- tion. The teacher view additionally contains interleaved mul- timodal CoT: x T = (I,Q,C), C = (R,I help ),(2) where R denotes textual CoT or textual evidence, and I help denotes auxiliary help images, such as cropped regions, zoomed-in visual evidence, annotated visual rationales, or other task-relevant auxiliary images. The teacher view is used only during training, while the deployed model always receives x S . Let y ∗ = (y ∗ 1 ,...,y ∗ N )(3) denote the ground-truth answer. In the first two warmup stages, y ∗ is used for answer-only supervised training. In the third distillation stage, the current student generates an on-policy response: ˆy = (ˆy 1 ,..., ˆy M ),(4) which is then evaluated by the teacher. Moreover, we denote the recursive latent trajectories of the student and teacher as z S 1:K = (z 1 S ,...,z K S ), z T 1:K = (z 1 T ,...,z K T ), (5) where K is the number of latent reasoning slots. Both the teacher and the student use the native MLLM chat template. We append K latent slots between the assistant generation prompt and answer generation. Recursive Latent Reasoning OPLD performs intermediate reasoning through a fixed num- ber of recursive latent slots. Rather than directly reusing raw LLM hidden states as latent thoughts, we project them into Figure 2: Overview of OPLD. The left shows inference, where the model answers from the original image and question through recursive latent reasoning. The right illustrates the three-stage training pipeline: a CoT-guided teacher is first warmed up with interleaved multimodal CoT, a CoT-free student is then warmed up with only the image-question input, and finally the student is optimized by on-policy latent distillation using token-level feedback and latent trajectory alignment from the frozen teacher. a lower-dimensional latent space. This design creates a com- pact abstraction and encourages the latent states to capture the abstract internal reasoning representations induced by multimodal CoT. A lightweight decoder then maps each la- tent code back to the MLLM embedding space, so the model can consume the latent state without changing the backbone architecture. Let p k be the position of the k-th latent slot, and let h L p k −1 ∈R H be the last-layer hidden state at the position immediately before this latent slot. OPLD computes the la- tent code and the corresponding input embedding as z k = Enc(h L p k −1 ), e k = Dec(z k ).(6) Here, z k ∈R D is the latent reasoning code in the projected latent space, and e k ∈R H is the decoded embedding writ- ten into the k-th latent slot. The encoder and decoder are lightweight MLP projection modules: Enc(h) = LN (W 2 GELU(W 1 LN(h))),(7) Dec(z) = W 4 GELU(W 3 LN(z)).(8) The latent trajectory is produced recursively through hidden-state feedback. For the first latent slot, the previous position corresponds to the assistant generation prompt: z 1 = Enc(h L p 1 −1 ), e 1 = Dec(z 1 ).(9) For subsequent latent slots, the model re-runs the forward computation with the decoded embeddings from earlier latent steps inserted into their corresponding positions. The next latent code is then computed as z k = Enc(h L p k −1 ), e k = Dec(z k ), k = 2,...,K. (10) After computing z k , the decoded embedding e k = Dec(z k ) is written into the last latent slot. Therefore, later latent states depend on earlier latent states, forming a fixed-step internal reasoning chain. This recursive process enables the model to accumulate abstract reasoning states before producing any answer token. The mechanism is shared by the teacher and the student. During inference, the student first executes this K-step latent reasoning process and then generates answer tokens. Three-Stage OPLD Training OPLD contains three stages: teacher warmup, student warmup, and on-policy latent distillation. The first two stages establish stable latent reasoning dynamics for the teacher and the student, while the third stage transfers CoT-induced rea- soning from the teacher into the student’s latent space. Stage 1: Teacher Warmup. The first stage trains a CoT- guided teacher using the teacher view x T = (I,Q,C). Since the teacher has access to textual CoT and auxiliary help im- ages, it can learn latent trajectories guided by richer multi- modal reasoning evidence. Given the teacher latent trajec- tory z T 1:K , we optimize the teacher with answer-only cross- entropy: L T =− N X n=1 logp φ y ∗ n | x T ,z T 1:K ,y ∗ <n , (11) where φ denotes the teacher parameters. Only answer to- kens are supervised, while prompt tokens and latent slots are masked. This stage is not used for distillation but to form a teacher whose latent trajectory reflects the abstract reasoning patterns induced by interleaved multimodal CoT. Stage 2: Student Warmup. The second stage trains a CoT- free student using only the student view x S = (I,Q). The student does not observe textual CoT or help images. Given the student latent trajectory z S 1:K , we apply the same answer- only cross-entropy: L S =− N X n=1 logp θ y ∗ n | x S ,z S 1:K ,y ∗ <n ,(12) where θ denotes the student parameters. This warmup stage allows the student to establish a stable CoT-free latent rea- soning protocol before distillation. Without this stage, the student would enter distillation with poorly formed latent dynamics, making latent trajectory alignment unstable. Stage 3: OPLD Distillation. After warmup, the teacher is frozen and only the student is updated. As detailed in Fig. 3, OPLD distillation consists of three forward processes: student on-policy rollout, teacher latent target forward, and teacher scoring forward. First, the current student performs an on-policy rollout. It receives only x S , produces its recursive latent trajectory, and generates an answer: z S 1:K = f lat θ (x S ), ˆy ∼ π θ (·| x S ,z S 1:K ). (13) Second, the frozen teacher performs a latent target forward under the teacher view: z T 1:K = f lat φ (x T ).(14) The teacher latent trajectory provides the CoT-guided target for the student’s latent reasoning. We align the student and teacher latent trajectories using cosine distance: L lat = 1 BK B X b=1 K X k=1 1− cos z k S,b , sg(z k T,b ) , (15) whereB is the batch size and sg(·) denotes stop-gradient. The teacher latent states are treated as fixed targets, and gradients are applied only to the student. This loss encourages the student latent trajectory to approximate the abstract reasoning trajectory formed under multimodal CoT guidance. Third, the teacher and student score the same student- generated trajectory. Different from the latent target forward, the teacher scoring forward does not use the its own latent trajectory. Instead, it takes the student rollout, including both the student latent codes z S 1:K and the student-generated re- sponse ˆy. This design lets the CoT-guided teacher provide token-level feedback on the student’s on-policy trajectory. For each response position t, the teacher distribution is computed under the privileged teacher view while condi- tioning on the student latent rollout: p T t = p φ ·| x T ,z S 1:K , ˆy <t ,(16) and the student distribution is computed under the student view: p S t = p θ ·| x S ,z S 1:K , ˆy <t .(17) Therefore, both models are evaluated on the same trajectory while differing only in their information views. The result- ing distribution gap provides a direct token-level supervision signal for improving the student’s behavior. We use top-k for- ward KL as the text-level distillation loss. For each position t, let V T t = TopK(p T t )(18) denote the set of tokens with the highest teacher probabilities. The text-level distillation loss is defined as L text = 1 |ˆy| |ˆy| X t=1 X v∈V T t p T t (v) logp T t (v)− logp S t (v) . (19) The final OPLD objective combines token-level on-policy distillation and latent trajectory alignment: L OPLD = λ text L text + λ lat L lat .(20) ThroughL text , the student learns from teacher feedback on its own generated answers. ThroughL lat , the student aligns its latent imagination with the CoT-guided teacher trajectory. Together, these two signals enable the student to internalize multimodal CoT-induced reasoning into latent space while requiring no auxiliary information at inference time. Experiments Experimental Setup Training and Evaluation Setup. For fair comparison with related methods, we use Qwen2.5-VL-7B as the default back- bone for both the teacher and the student. OPLD is trained on the cleaned union of Zebra-CoT (Li et al. 2025a) and Visual- CoT (Shao et al. 2024a). Since some auxiliary images in multimodal CoT may contain visual cues that directly re- veal the final answer, the teacher could exploit such leaked evidence as a shortcut and ignore the intended reasoning process. To prevent this teacher-side hacking issue, we fil- ter samples with potential answer leakage and obtain 217K training examples. Unless otherwise specified, we useK = 8 latent slots with latent dimension D = 2048. The distilla- tion stage adopts top-k forward KL with k = 128 and latent cosine weightλ lat = 0.05. We train for one epoch with learn- ing rate 1×10 −6 on 8 NVIDIA B200 GPUs. All evaluations are conducted with LMMS-Eval (Zhang et al. 2025a) using greedy decoding. More details about the training data clean- ing pipeline are provided in the supplementary material. We evaluate OPLD on seven multimodal reasoning benchmarks: V ⋆ , HRBench-4K, HRBench-8K, MMStar, SeedBench2- Plus, BLINK, and HallusionBench. These benchmarks cover fine-grained visual perception, high-resolution image under- standing, general multimodal reasoning, and hallucination robustness. We additionally use MME-RealWorld-Lite in the ablation study to evaluate real-world multimodal robustness. Baselines. We compare OPLD with four groups of meth- ods: proprietary multimodal models, native open-source MLLMs, thinking-with-images agent models, and visual- latent reasoning methods. Main Results Table 1 summarizes the main comparison across seven benchmarks, together with fine-grained metrics on V ⋆ and HRBench. OPLD delivers consistent improvements over Qwen2.5-VL-7B backbone across all evaluated benchmarks. The gains are especially clear on perception-intensive bench- marks: OPLD improves V ⋆ from 71.20 to 85.86, HRBench- 4K from 65.12 to 73.75, and HRBench-8K from 58.00 to Figure 3: OPLD distillation stage. The student rolls out response ˆy with its current policy from the original image-question input. The frozen CoT-guided teacher provides two forms of supervision on this student-generated trajectory: latent alignment between teacher and student latent trajectories, and token-level forward KL on the same response tokens. 71.37. It also improves MMStar, SeedBench2-Plus, BLINK, and HallusionBench, indicating that the proposed latent dis- tillation framework benefits both fine-grained visual percep- tion and general multimodal reasoning. Compared with the SFT baseline, OPLD further improves six out of seven benchmarks. This suggests that the improve- ment is not simply caused by additional supervised train- ing on multimodal CoT data. Instead, the on-policy teacher– student distillation and latent trajectory alignment provide extra reasoning-process supervision. For example, OPLD substantially outperforms Qwen2.5-VL-7B + SFT on V ⋆ and HRBench-8K, where models need to identify subtle visual evidence and integrate high-resolution details before answer- ing. This supports our motivation that latent states should serve as internal reasoning representations rather than only as auxiliary visual feature containers. Compared with existing visual-latent reasoning methods, OPLD achieves the best visual-latent performance on most reported metrics. This shows that learning from CoT-induced teacher trajectories is more effective than directly aligning latent states to visual features or intermediate visual embed- dings. The result indicates that OPLD is also competitive with thinking-with-images agent models. OPLD can internalize part of the reasoning ability induced by multimodal CoT into latent computation, reducing the need for explicit visual traces at inference time. The fine-grained results further reveal where the improve- ments come from. On V ⋆ , OPLD improves the Attribute score from 73.04 to 88.70 over Qwen2.5-VL-7B, showing stronger fine-grained visual discrimination. On HRBench- 4K and HRBench-8K, OPLD brings large gains on FSP, improving from 75.75 to 90.00 on HRBench-4K and from 63.00 to 87.75 on HRBench-8K. These improvements sug- gest that recursive latent reasoning helps the model organize high-resolution visual evidence before answer generation. Meanwhile, the gains on MMStar and BLINK show that the learned latent trajectories are not limited to high-resolution V*HR-4KHR-8KMME-RW-LiteAverage SFT Stu Warmup Tea Warmup Std OPD OPLD +2.62+2.88+2.75+0.58+2.21 +2.62+1.51+0.00+3.13+1.81 +2.10-0.37-1.62-1.77-0.42 +2.10+0.13-2.50-12.92-3.30 +14.66+8.63+13.37+7.61+11.07 −5 0 5 10 15 Figure 4: Training strategy ablation with the same backbone and training data. Each cell reports the gain or drop over the Qwen2.5-VL-7B base model. perception, but also transfer to broader multimodal reasoning tasks. Ablation Studies Effect of Training Strategy. Fig. 4 compares different training strategies under the same backbone and training data, where each cell reports the performance change over the Qwen2.5-VL-7B base model. To ensure a fair compar- ison, all strategies use the same number of training epochs or optimizer steps, with matched batch size and learning- rate schedule. Standard SFT only brings limited gains, with an average improvement of 2.21. This suggests that simply fine-tuning in the textual CoT space is insufficient for these perception-intensive reasoning tasks, motivating the need to transfer multimodal CoT-induced reasoning into an inter- nal latent process. Student warmup only also yields limited improvement (1.81 on average). Although it introduces the latent reasoning structure, the training signal is still applied only to final answer tokens, leaving the latent slots without direct reasoning-state supervision. As a result, the student learns to use latent placeholders, but its latent imagination remains insufficient. We also find that teacher warmup only performs even worse when directly evaluated without aux- iliary CoT, because the teacher is trained under a privileged MethodV ⋆ HR-4KHR-8KMMStar Seed2+ BLINK Hall. Ovr. Attr. Spat. Ovr. FSP FCP Ovr. FSP FCP Proprietary Models GPT-4o67.50 72.20 60.50 59.00 70.00 48.00 55.50 62.00 49.00 65.20–63.00– Gemini-3-Flash86.40–87.90–85.00– Native Open-Source Models and SFT/OPD Variants LLaVA-OV-7B71.25 73.48 67.89 62.50 74.25 50.75 58.25 67.50 49.00 59.1361.2249.34 51.10 Qwen-7B71.20 73.04 68.42 65.12 75.75 54.50 58.00 63.00 53.00 59.7065.3153.60 56.57 Qwen-7B + SFT73.82 73.04 75.00 68.00 78.25 57.75 60.75 66.50 55.00 61.3669.3856.56 66.67 Qwen-7B + 32B OPD 73.30 73.91 72.37 65.25 76.00 54.50 55.50 64.25 46.75 51.5267.7239.35 38.90 InternVL3-8B70.20 67.80 73.70 70.00 78.80 61.30 69.30 78.80 59.80– Thinking-with-Images Agent Models ZoomEye79.85 80.52 78.82 68.75 81.25 56.25 64.50 75.00 54.00 63.2070.2755.55 71.08 Thyme82.20 83.50 80.30 77.00 91.00 63.0072.00 86.50 57.50 65.90–56.10 55.60 DeepEyes83.25–75.10–72.60–58.7369.0851.08 62.57 DeepEyesV281.80–77.90–73.80– Visual-Latent Models LVR80.60 81.70 79.00–57.9347.3953.60 65.19 Laser–72.50–60.2770.0556.92 67.72 SkiLa78.53–72.12–66.50– Monet80.10 81.73 77.63 67.37 78.25 56.50 64.37 74.25 54.49 60.3365.8850.71 56.36 HyLaR83.77 82.61 85.5375.00 93.7556.25 70.50 88.2552.75 62.0070.3257.14 63.68 OPLD85.86 88.70 81.58 73.75 90.00 57.50 71.37 87.75 55.00 63.8670.8858.56 65.19 Table 1: Main results on multimodal reasoning benchmarks. All scores are percentages and higher is better. For visual-latent methods, the best result in each column is marked in bold. The best result among all reported methods is marked with an underline. “Ovr.” denotes the overall score. Qwen-7B denotes Qwen2.5-VL-7B. VariantV ⋆ HR-4K HR-8K MME-RW Avg. Number of latent slots K = 075.39 65.50 58.1350.44 62.36 K = 478.53 72.62 71.7551.90 68.70 K = 885.86 73.75 71.3753.36 71.09 Latent architecture Raw hidden78.53 71.50 67.0048.41 66.36 Enc-Dec adapter 85.86 73.75 71.3753.36 71.09 Loss components RevKL + PG + cos 74.87 71.37 67.7549.92 65.98 Top-k KL only78.53 63.88 58.6348.20 62.31 Top-k KL + cos 85.86 73.75 71.3753.36 71.09 Table 2: Ablation on latent design and loss components. We report the overall accuracy on four representative bench- marks together with the average score (Avg.). input distribution with help images and multimodal ratio- nales. Once these auxiliary inputs are removed at inference time, the model suffers from a clear distribution shift. For the standard OPD baseline, we initialize the student from Qwen2.5-VL-7B and distill it from a stronger Qwen2.5- VL-32B teacher using the same forward KL objective. How- ever, this standard OPD setting is still unstable, with an av- erage drop of 3.30. This indicates that simply transferring token-level preferences from a stronger model does not reli- ably improve the student’s multimodal reasoning, especially when the student’s latent trajectory is not explicitly aligned with the teacher’s reasoning process. In contrast, OPLD con- sistently improves all benchmarks. The average gain reaches 11.07, far exceeding all alternatives. These results validate the necessity of the full OPLD pipeline. Effects of Latent Design and Loss Components. We fur- ther ablate three key design choices of OPLD in Table 2: the number of latent slots, the latent architecture, and the loss components. Increasing the number of latent slots generally improves performance. Compared withK = 0, usingK = 4 brings clear gains on HRBench-4K and HRBench-8K, while K = 8 achieves the best results on V ⋆ , HRBench-4K, and MME-RealWorld-Lite. This suggests that multiple recursive latent steps provide useful internal computation before an- swer generation, and a longer latent chain gives the model stronger capacity to accumulate abstract reasoning states. For the latent architecture, directly aligning the raw hid- den space performs worse than using the encoder-decoder la- tent adapter. This supports our motivation that latent reason- ing should be performed in a separate compact space rather than in the original next-token hidden space. For the objec- tive design, using only the top-k token-level KL leads to a substantial drop, especially on HRBench-4K and HRBench- 8K, showing that token supervision alone is insufficient to transfer the teacher’s reasoning process. Adding cosine latent alignment largely improves the results, while the reverse-KL policy-gradient variant is less stable. These results confirm that stable forward KL supervision and latent trajectory align- ment are complementary for effective OPLD training. Latent Intervention Analysis. To examine whether the learned latent states functionally contribute to answer gen- eration, we conduct controlled test-time interventions on the trained OPLD model. The results are reported in our supple- mentary material. Conclusion In this paper, we proposed OPLD, an on-policy latent distil- lation framework that transfers the abstract reasoning repre- sentations induced by privileged multimodal CoT into latent reasoning. 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Zheng, Z.; Yang, M.; Hong, J.; Zhao, C.; Xu, G.; Yang, L.; Shen, C.; and Yu, X. 2025. DeepEyes: Incentivizing “Thinking with Images” via Reinforcement Learning. arXiv preprint arXiv:2505.14362. Zhou, Q.; Zhou, R.; Hu, Z.; Lu, P.; Gao, S.; and Zhang, Y. 2024. Image-of-Thought Prompting for Visual Reasoning Refinement in Multimodal Large Language Models. arXiv preprint arXiv:2405.13872. Zhou, Z.; Dai, J.; and Ling, X. 2026. Gen-VCoT: Gen- erative Visual Chain-of-Thought Reasoning via Diffusion- Based RGB Intermediate Representations. arXiv preprint arXiv:2606.16783. Supplementary Material Training Data and Filtering Pipeline Data Construction We construct the training set by merging Zebra-CoT and Visual-CoT into a unified teacher–student format. For each sample, the student receives only the original question and main image, while the teacher additionally receives the tex- tual rationale and auxiliary images: x S = (I,Q), x T = (I,Q,R,I help ).(21) All samples are normalized to a common schema containing the student prompt, teacher prompt, student-visible images, teacher-visible images, answer, sample ID, and source meta- data. Data Cleaning Some auxiliary images directly reveal the final answer, which may allow the teacher to solve the task through shortcut recognition rather than reasoning. We therefore use the GPT- 5.4 API to identify and remove such samples. For each sample, GPT-5.4 is given the question, answer, textual rationale, main image, and auxiliary images. A sam- ple is removed when the privileged context directly displays the answer, marks the final solution, or makes the question answerable without meaningful reasoning. Samples are re- tained when the auxiliary images provide only intermediate evidence and still require evidence integration or multi-step inference. The exact filtering prompt is provided below. You are a data-quality reviewer for multimodal reasoning datasets. Determine whether the teacher-only multimodal context contains answer leakage. Mark REMOVE if the auxiliary images or rationale directly reveal the final answer, such as showing the answer, marking the correct option or target, presenting the completed solution, or making meaningful reasoning unnecessary. Mark KEEP if the context provides only intermediate evidence and meaningful reasoning is still required. When uncertain, choose KEEP. Return only valid JSON: “decision”: “KEEP” or “REMOVE”, “reason”: “Brief explanation.” Question: question Ground-truth answer: answer Rationale: rationale Main image: [MAIN_IMAGE] Auxiliary images: [HELP_IMAGES] After semantic filtering, we further remove malformed samples, invalid image references, and duplicated IDs. Training Data Statistics Before filtering, the merged collection contains 266,952 sam- ples: 178,695 from Zebra-CoT and 88,257 from Visual-CoT. The GPT-5.4-based filtering and format validation remove 49,232 Zebra-CoT samples with potential answer leakage or invalid formatting, reducing Zebra-CoT to 129,463 samples. The Visual-CoT split remains unchanged. The final training set therefore contains 217,720 samples with unique identi- fiers and no duplicated IDs. Table 3 summarizes the filtering statistics and the main properties of the resulting dataset. The resulting data exhibit the intended privileged teacher– student asymmetry. The student typically receives one main StatisticValue StatisticValue Filtering and dataset composition Samples before filtering266,952 Samples after filtering217,720 Zebra-CoT before filtering178,695 Zebra-CoT after filtering129,463 (59.5%) Visual-CoT before filtering88,257 Visual-CoT after filtering88,257 (40.5%) Removed samples49,232 (18.4%) Duplicate sample IDs0 Teacher–student input asymmetry Average student-visible images0.97 Average teacher-visible images3.08 Average auxiliary images2.11 Samples without student-visible images6,580 (3.0%) Text length in characters: mean / median / P95 Student prompt147.05 / 104 / 404 Teacher prompt1,219.34 / 783 / 3,163 Answer24.61 / 5 / 136 Number of task configurations13 Task distribution in the final training set GQA Detailed Reasoning88,257 (40.5%) Visual Search29,393 (13.5%) Visual Jigsaw21,485 (9.9%) Chess20,067 (9.2%) Maze19,600 (9.0%) Multi-Hop Object Counting9,794 (4.5%) Tetris9,781 (4.5%) Other scientific and visual tasks19,343 (8.9%) Table 3: Statistics of the OPLD training data before and after filtering. Auxiliary images denote the additional images available to the teacher beyond the student-visible images. Text lengths are measured in characters. image and a short problem description, whereas the teacher observes approximately two additional images and a sub- stantially richer multimodal reasoning prompt. On average, the teacher prompt is more than eight times longer than the student prompt. The final collection covers fine-grained visual understand- ing, visual search, spatial reasoning, multi-step visual plan- ning, and scientific reasoning. GQA Detailed Reasoning forms the largest subset, while the remaining tasks provide diverse reasoning trajectories involving jigsaw puzzles, board games, mazes, object counting, and scientific problems. The small subset without student-visible images mainly comes from scientific reasoning tasks and is retained as comple- mentary abstract reasoning supervision. Additional Implementation Details Both the teacher and student are initialized from Qwen2.5- VL-7B-Instruct and adopt the same recursive latent archi- tecture. We insert K = 8 latent slots with latent dimen- sion D = 2048 between the assistant generation prompt and the answer sequence. The latent states are generated in the continuous_feedback mode, where each decoded la- tent embedding is written back into the corresponding slot before computing the next latent state. The teacher and stu- dent are independently warmed up with privileged and orig- inal inputs, respectively, and the warmed-up checkpoints are then used for OPLD distillation. Table 4 summarizes the main training configurations. During warmup, we perform full-parameter fine-tuning. The language model and multimodal merger use a learning rate of 1× 10 −5 , while the vision encoder uses 2× 10 −6 . Training uses BF16 precision, TF32 computation, scaled dot- product attention, the Liger kernel, and non-reentrant gradi- ent checkpointing. The per-device batch size is 1, and gradi- ent accumulation is used to obtain a global batch size of 16. Input images are dynamically resized within a pixel range of 100,352 to 1,317,120. The answer tokens are supervised with cross-entropy, while prompt tokens and latent slots are excluded from the loss. In the distillation stage, the teacher is frozen and only the student is updated. The student first generates an on-policy latent trajectory and response using greedy decoding. The teacher then independently produces its privileged latent tra- jectory for cosine alignment and scores the student-generated trajectory for token-level distillation. We use forward KL over the 128 highest-probability teacher tokens and set the latent cosine weight to 0.05. Policy-gradient optimization and task- specific rewards are disabled. All reported evaluations are conducted with LMMS-Eval using greedy decoding and the official task configurations. Additional Method Details Training Algorithm Algorithm 1 summarizes the complete three-stage training procedure. The teacher and student are initialized from the same pretrained MLLM but are optimized independently during warmup. In the final stage, the teacher is frozen and only the student is updated. Discussion Warmup and latent-space compatibility. The two warmup stages establish compatible but not necessarily iden- tical latent reasoning spaces. The teacher is warmed up with privileged multimodal CoT, enabling its recursive latent tra- jectory to exploit textual rationales and auxiliary images. The student is independently warmed up using only the orig- inal image and question, which prevents its latent slots from remaining unstructured before distillation. ConfigurationTeacher WarmupStudent WarmupOPLD Distillation InitializationQwen2.5-VL-7B-InstructQwen2.5-VL-7B-InstructWarmed-up student/teacher InputImage, question, multimodal CoTImage and questionStudent and teacher views Trainable modelFull modelFull modelStudent only Training objectiveAnswer CEAnswer CETop-k forward KL + latent cosine Answer-loss weight1.01.0– Latent-loss weight000.05 Top-k–128 Number of latent slots888 Latent dimension204820482048 Learning rate1× 10 −5 1× 10 −5 1× 10 −6 Vision encoder learning rate2× 10 −6 2× 10 −6 – Weight decay0.10.1– LR schedulerCosineCosine– Warmup ratio0.030.03– Global batch size1616– Training epochs111 Maximum prompt length–8192 Maximum generation length512512256 Decoding strategyGreedyGreedyGreedy PrecisionBF16BF16BF16 Attention implementationSDPASDPA– Gradient checkpointingEnabledEnabledEnabled Teacher correction mode–Free rollout Policy gradient / task reward–Disabled Table 4: Training configurations for the three stages of OPLD. The teacher and student warmup stages use answer-only supervised learning, while the distillation stage combines token-level forward KL and latent trajectory alignment. Since both models undergo full-parameter warmup, their latent representations are not mathematically guaranteed to remain in exactly the same coordinate system. OPLD there- fore does not assume that z S k and z T k are already coordinate- wise equivalent before distillation. Instead, the initial mis- match is reduced by shared structural priors: the teacher and student are initialized from the same pretrained MLLM, em- ploy latent encoder–decoder modules with the same archi- tecture and initialization, use the same latent dimensionality, and follow the same recursive slot order. Their latent spaces thus originate from a common representation basis, although they may drift during independent warmup. The frozen teacher latent space subsequently acts as the reference space during distillation. The slot-wise cosine ob- jective is therefore a calibration objective rather than an as- sumption of pre-existing latent equivalence: L lat = 1 K K X k=1 1− ⟨z S k ,z T k ⟩ ∥z S k ∥ 2 ∥z T k ∥ 2 . All student parameters, including its latent encoder and de- coder, remain trainable, allowing the student representa- tion to be progressively calibrated toward the frozen teacher space. Cosine distance further reduces sensitivity to differ- ences in latent magnitude. Tensor-level path of the three forward processes. For clarity, we distinguish the student rollout, teacher latent- target rollout, and teacher scoring forward. Let E θ ,D θ de- note the student latent encoder and decoder, and let E φ ,D φ denote their frozen teacher counterparts. During the student rollout, the student recursively gener- ates z S k = E θ h S,L p k −1 , e S k = D θ (z S k ), where h S,L p k −1 is the last-layer hidden state immediately pre- ceding the k-th latent slot. The decoded embedding e S k is written into the k-th student slot before the next latent state is computed. After K recursive steps, the student generates the answer trajectory ˆy using its current parameters. Although greedy decoding is deterministic, this trajectory is on-policy because it is generated by the current student rather than from ground-truth prefixes or an offline teacher trajectory. The teacher latent-target rollout independently performs the same recursive computation under the privileged input x T : z T k = E φ h T,L p k −1 , e T k = D φ (z T k ). This pass invokes both the teacher encoder and teacher de- coder and produces the privileged trajectory z T 1:K used by L lat . The teacher scoring forward follows a different path. It does not recompute teacher latent codes and does not reuse the student-decoded embeddings e S k . Instead, each stop- gradient student code is decoded by the frozen teacher de- coder: e S→T k = D φ sg(z S k ) , k = 1,...,K, where sg(·) denotes stop-gradient. The resulting embeddings are inserted into the corresponding latent positions of the teacher input sequence: E T,score = h Emb φ (x T );e S→T 1 ,...,e S→T K ; Emb φ (ˆy <t ) i . The teacher then computes p T t = p φ ·| x T , sg(z S 1:K ), ˆy <t . Thus, the teacher latent encoder E φ is bypassed in the scoring forward because the latent codes are supplied by the student. The teacher decoder D φ is used to interpret these codes in the teacher’s embedding interface. This differs from directly insertinge S k = D θ (z S k ), which would condition the teacher on student-decoded embeddings rather than on student latent codes and would not match the notation above. A tensor-level summary is: Student rollout: h S E θ −→ z S D θ −→ e S student MLLM −→ ˆy, Teacher target: h T E φ −→ z T D φ −→ e T , Teacher scoring: sg(z S ) D φ −→ e S→T teacher MLLM −→ p T . The teacher parameters are frozen in both teacher for- wards. Teacher outputs and teacher-decoded student embed- dings are treated as detached targets; gradients are propagated only through the student computation. Why decode student codes with the teacher decoder? Using D φ ensures that the scoring forward receives em- beddings expressed through the teacher’s own latent-to- embedding interface. At the beginning of distillation, the stu- dent codes may still be imperfectly calibrated for D φ . How- ever, the shared initialization and student warmup prevent them from being arbitrary, while L lat progressively moves z S k toward the region represented by z T k . The teacher scor- ing signal therefore becomes increasingly reliable as latent calibration improves. The encoder–decoder bottleneck is useful in this setting because it provides an explicit, trainable interface for cor- recting teacher–student representation drift. This interpreta- tion is consistent with the empirical advantage of aligning compact encoder–decoder latents over directly matching the original high-dimensional MLLM hidden states. Complementary distillation objectives. The teacher scor- ing forward evaluates token preferences at the latent and tex- tual states visited by the current student. The top-k forward KL objective transfers these preferences: L text = 1 T T X t=1 D KL p T t,top-k p S t,top-k . However, token-level supervision alone does not explicitly calibrate the student latent coordinates. Conversely, latent cosine alignment does not guarantee that the aligned states induce the desired answer distribution. OPLD therefore com- bines the two objectives: L OPLD =L text + λ lat L lat . No policy-gradient loss or task-specific reward is used in the final configuration. Interpretation and limitation of slot-wise alignment. The fixed slot index provides a shared structural correspon- dence: the k-th state in both models is computed after k− 1 recursive latent feedback steps. It therefore represents the same recursive depth and removes the permutation ambigu- ity associated with an unordered set of latent tokens. Nev- ertheless, equal recursive depth does not guarantee that the teacher and student encode exactly the same semantic rea- soning stage at slot k. The slot-wise cosine loss should con- sequently be viewed as an effective temporal inductive bias, rather than a theoretical guarantee of one-to-one semantic correspondence. Our ablations show that this ordered alignment improves downstream performance, while the latent intervention ex- periments demonstrate that the input-conditioned latent tra- jectory functionally affects answer generation. These results support the practical utility of the learned trajectory, but they do not establish an interpretable semantic meaning for every slot or dimension. More flexible cross-space alignment, such as a learned latent mapper, optimal-transport matching, or diagnostic probing of individual slots, remains an important direction for future work. Inference. At inference time, the teacher, teacher decoder, and all privileged inputs are removed. The student receives only the original image and question, performs K = 8 re- cursive latent steps using E θ and D θ , and then generates the answer. OPLD therefore requires neither textual CoT gener- ation nor auxiliary visual operations during deployment. Additional Experimental Results Fine-Grained Training Strategy Comparison Table 5 reports the complete results of different train- ing strategies, including the fine-grained metrics of V ⋆ , HRBench, and MME-RealWorld-Lite. All variants use the same Qwen2.5-VL-7B student backbone and training data. OPLD provides the most consistent improvements across both overall and fine-grained metrics. Compared with the base model, it improves the V ⋆ Attribute and Spatial scores by 15.66 and 13.16 points, respectively. On HRBench, the largest gains occur on FSP, increasing from 75.75 to 90.00 at 4K resolution and from 63.00 to 87.75 at 8K resolution. These results indicate that OPLD substantially strengthens fine-grained evidence perception and high-resolution visual reasoning. It also improves both the Reasoning and Percep- tion components of MME-RealWorld-Lite. In contrast, ordinary SFT and student warmup provide only moderate and inconsistent gains. Teacher warmup degrades when privileged CoT is removed during evaluation, reflecting the input-distribution shift between training and inference. Standard OPD with a larger 32B teacher also performs poorly on HRBench-8K and MME-RealWorld-Lite, showing that token-level distillation from a stronger teacher alone does not reliably transfer multimodal reasoning ability. Fine-Grained Ablation Results Table 6 presents the complete fine-grained results for the latent-slot number, latent architecture, and distillation objec- tives. MethodV ⋆ HRBench-4KHRBench-8KMME-RW-Lite Ovr. Attr. Spat. Ovr. FSP FCP Ovr. FSP FCP Ovr. Reason. Percep. Qwen2.5-VL-7B71.20 73.04 68.42 65.12 75.75 54.50 58.00 63.00 53.00 45.75 39.7349.62 Qwen2.5-VL-7B + SFT73.82 73.04 75.00 68.00 78.25 57.75 60.75 66.50 55.00 46.33 42.4048.85 Student Warmup73.82 72.17 76.32 66.63 73.50 59.75 58.00 61.50 54.50 48.88 44.5351.67 Teacher Warmup73.30 73.04 73.68 64.75 72.25 57.25 56.38 61.25 51.50 43.98 38.5347.48 Qwen2.5-VL-7B + 32B OPD 73.30 73.91 72.37 65.25 76.00 54.50 55.50 64.25 46.75 32.83 25.6037.47 OPLD85.86 88.70 81.58 73.75 90.00 57.50 71.37 87.75 55.00 53.36 47.8756.89 Table 5: Fine-grained comparison of different training strategies. “Ovr.”, “Attr.”, “Spat.”, “Reason.”, and “Percep.” denote overall, attribute, spatial, reasoning, and perception scores, respectively. The best result in each column is highlighted in bold. VariantV ⋆ HRBench-4KHRBench-8KMME-RW-Lite Ovr. Attr. Spat. Ovr. FSP FCP Ovr. FSP FCP Ovr. Reason. Percep. Number of latent slots K = 075.39 75.65 75.00 65.50 74.25 56.75 58.13 61.75 54.50 50.44 46.2753.12 K = 478.53 77.39 80.26 72.62 89.25 56.00 71.75 86.00 57.50 51.90 45.8755.77 K = 885.86 88.70 81.58 73.75 90.00 57.50 71.37 87.75 55.00 53.36 47.8756.89 Latent architecture Raw hidden states78.53 80.87 75.00 71.50 88.25 54.75 67.00 79.25 54.75 48.41 43.7351.41 Enc–Dec adapter85.86 88.70 81.58 73.75 90.00 57.50 71.37 87.75 55.00 53.36 47.8756.89 Distillation objectives Reverse KL + PG + cosine 74.87 76.52 72.37 71.37 85.75 57.00 67.75 81.50 54.00 49.92 43.3354.15 Top-k forward KL only78.53 80.87 75.00 63.88 74.75 53.00 58.63 66.25 51.00 48.20 43.7351.07 Top-k forward KL + cosine 85.86 88.70 81.58 73.75 90.00 57.50 71.37 87.75 55.00 53.36 47.8756.89 Table 6: Fine-grained ablation results for the number of latent slots, latent architecture, and distillation objectives. The best result within each ablation group is highlighted in bold. Increasing the number of latent slots generally improves performance. Although K = 4 slightly outperforms K = 8 on the HRBench-8K overall and FCP metrics, K = 8 achieves the strongest results on most other metrics, espe- cially V ⋆ Attribute and HRBench FSP. This suggests that additional recursive latent steps primarily benefit the integra- tion of fine-grained and spatially distributed visual evidence. The encoder–decoder adapter consistently outperforms di- rect alignment in the raw hidden-state space. The largest im- provements appear on V ⋆ and HRBench-8K FSP, supporting the use of a compact projected space for learning abstract reasoning representations. Finally, top-k forward KL alone performs substantially worse on HRBench, despite achieving reasonable V ⋆ results. Adding cosine latent alignment improves every reported met- ric, demonstrating that token-level feedback alone is insuffi- cient to transfer the teacher’s intermediate reasoning process. The reverse-KL policy-gradient variant is also less effective than direct top-k forward KL combined with latent trajectory alignment. Latent Intervention Analysis To evaluate whether the learned latent trajectory function- ally contributes to answer generation, we conduct controlled test-time interventions on the same trained OPLD model. We keep the model parameters, original input, and decoding con- Latent Setting V ⋆ HR-4K HR-8K MME-RW Avg. Drop Original Latents 85.86 73.75 71.3753.36– Noisy Latents 76.96 64.12 57.5048.629.29 Zeroed Latents 76.44 59.62 51.3748.5112.10 Shuffled Latents 65.45 54.63 48.2544.6117.85 Table 7: Test-time interventions on the latent trajectory of the same trained OPLD model. figuration unchanged, and modify only the latent states used before answer generation. We compare the original trajec- tory with three interventions: adding random noise, setting all latent states to zero, and shuffling latent trajectories across different samples. No additional training is performed for any intervention. As shown in Table 7, modifying the latent trajectory con- sistently degrades performance across all four benchmarks. Adding noise results in an average drop of 9.29 points, while completely removing the latent information by zeroing the states increases the drop to 12.10 points. These results show that the answer decoder relies on information carried by the learned latent trajectory rather than merely on the presence of latent positions. Shuffling produces the largest degradation, reducing the Figure 5: In-domain accuracy on 5K held-out samples. OPLD substantially closes the gap to the teacher with privileged multimodal CoT. average score by 17.85 points. Unlike zeroing or random perturbation, shuffled latents remain valid representations produced by the same model, but they no longer correspond to the current input. The substantially larger drop therefore indicates that the effectiveness of latent reasoning depends on its sample-specific content, rather than only its numerical scale or distribution. The fine-grained results exhibit the same pattern. Shuf- fling reduces the V ⋆ Attribute score from 88.70 to 57.39, HRBench-4K FSP from 90.00 to 58.75, and HRBench-8K FSP from 87.75 to 50.25. The degradation is particularly pro- nounced on metrics requiring fine-grained evidence identifi- cation and high-resolution perception, suggesting that the re- cursive latent trajectory plays an important role in integrating task-relevant visual information before answer generation. Privileged Teacher Reference We further evaluate how closely the OPLD student ap- proaches a teacher that retains access to privileged multi- modal CoT. The comparison is conducted on a held-out in- domain test set containing about 5K samples. The warmed-up teacher receives the original input together with textual ra- tionales and auxiliary images, whereas both student models receive only the original question and main image. As shown in Fig. 5, the warmed-up teacher achieves 72.6% accuracy with privileged multimodal CoT, while the warmed- up student reaches only 29.4% using the original input. After on-policy latent distillation, the OPLD student improves to 65.4%, corresponding to a gain of 36.0 percentage points over student warmup. OPLD therefore recovers 83.3% of the initial perfor- mance gap between the warmed-up student and the privileged teacher, leaving only a 7.2-point difference. Importantly, the OPLD student obtains this performance without access to textual CoT or auxiliary images at inference time. These re- sults indicate that OPLD transfers a substantial portion of the reasoning capability induced by privileged multimodal CoT into the student’s latent reasoning process. The teacher result is used as a privileged reference rather than a strict theoretical upper bound. Case Studies We provide a collection of qualitative case studies to compare model predictions across the three stages of OPLD training. Each case contains the original question, the main input im- age, the privileged multimodal CoT available to the teacher, and the predictions produced by the warmed-up teacher, the warmed-up student, and the final OPLD student. The Question and Question Image fields correspond to the original student input and are available to all models. The Privileged Multimodal CoT field contains the textual ratio- nale and auxiliary images used only by the teacher during training. The Predictions field reports results after the three training stages. Warmed-up Teacher denotes the teacher trained with the original input and privileged multimodal CoT. Warmed-up Student denotes the student trained with answer-only supervision using the original input. OPLD Stu- dent denotes the same student after on-policy latent distilla- tion. The warmed-up student and the OPLD student receive identical inputs during inference, so their prediction differ- ence reflects the effect of the distillation stage. For readability, theK recursive<latent> slots are omit- ted. In the actual model input, these latent slots are inserted between the assistant generation prompt and the answer se- quence. Each model first performs K-step recursive latent reasoning and then generates the reported prediction. The case-study figures show only the observable inputs and final outputs, rather than the intermediate continuous latent states. An interesting phenomenon is that, in several examples, the warmed-up teacher produces an incorrect final answer, whereas the OPLD student produces the correct answer af- ter distillation. This does not imply that the student directly copies and then surpasses the teacher’s displayed hard pre- diction. OPLD does not use the teacher’s decoded answer as a hard supervision target. Instead, it transfers two forms of soft supervision: the teacher’s token-level probability distri- bution on the student-generated trajectory and the teacher’s privileged latent trajectory. A teacher may select an incorrect token under greedy decoding while still assigning informa- tive probability mass to the correct token or providing useful preferences over competing answers. Forward KL can trans- fer this richer distributional information without forcing the student to reproduce the teacher’s top-1 prediction. Moreover, the displayed warmed-up teacher prediction is generated from the teacher’s own free rollout, whereas token- level distillation uses a separate teacher scoring forward pass. In the scoring pass, the teacher conditions on the student’s latent codes and student-generated answer prefix: p T t = p φ ·| x T ,z S 1:K , ˆy <t . Consequently, the supervision received by the student is not identical to the sequence obtained from the teacher’s inde- pendent greedy rollout. The teacher may make an incorrect final prediction along its own trajectory while still provid- ing useful corrective preferences at the states visited by the student. The latent objective should likewise not be interpreted as requiring the student to reproduce the teacher’s complete an- swer behavior. It aligns intermediate representations formed under privileged multimodal evidence, while the student re- tains its own pretrained knowledge, student-warmup initial- ization, and inference-time input pathway. The final student is therefore constrained jointly by its original capabilities, the token-level teacher signal, and the privileged latent regular- ization. Because these signals are optimized over the entire training distribution rather than on a single example, the student can integrate transferable reasoning patterns while avoiding some example-specific errors of the teacher. Algorithm 1: Three-Stage Training of OPLD Require: Training setD =(x S ,x T ,y ∗ ); base model ψ 0 ; latent steps K; top-k size k KL ; loss weights λ text and λ lat Ensure: Distilled student parameters θ 1: Initialize teacher φ← ψ 0 and student θ ← ψ 0 2: Stage 1: Teacher warmup 3: for each minibatch (x T ,y ∗ ) fromD do 4: z T 1:K ← f lat φ (x T ) 5: L T ←− N X n=1 logp φ (y ∗ n | x T ,z T 1:K ,y ∗ <n ) 6: Update φ using∇ φ L T 7: end for 8: Stage 2: Student warmup 9: for each minibatch (x S ,y ∗ ) fromD do 10: z S 1:K ← f lat θ (x S ) 11: L S ←− N X n=1 logp θ (y ∗ n | x S ,z S 1:K ,y ∗ <n ) 12: Update θ using∇ θ L S 13: end for 14: Freeze teacher parameters φ 15: Stage 3: On-policy latent distillation 16: for each minibatch (x S ,x T ) fromD do 17: Student on-policy rollout 18: z S 1:K ← f lat θ (x S ) 19: ˆy ← GreedyDecode(π θ (·| x S ,z S 1:K )) 20: Teacher latent-target forward 21: z T 1:K ← f lat φ (x T ) 22: L lat ← 1 BK B X b=1 K X j=1 h 1− cos z j S,b , sg(z j T,b ) i 23: Teacher scoring forward 24: for t = 1,...,|ˆy| do 25: p T t ← p φ ·| x T , sg(z S 1:K ), ˆy <t 26: p S t ← p θ ·| x S ,z S 1:K , ˆy <t 27: V T t ← TopK(p T t ,k KL ) 28: end for 29: L text ← 1 |ˆy| |ˆy| X t=1 X v∈V T t p T t (v) logp T t (v)− logp S t (v) 30: L OPLD ← λ text L text + λ lat L lat 31: Update θ using∇ θ L OPLD 32: end for 33: return θ Case Study: Visual Logic & Strategic Games - Maze (from Zebra-CoT) Question: What secure route arrives at the termination point without encountering danger nodes? Options: (A) ⏬ ⏬ ⏬ ⏬ ⏬ ⏬ ⏩ ⏬ ⏩ ⏩ (B) ⏬ ⏬ ⏩ ⏩ ⏬ ⏬ ⏩ ⏩ ⏬ ⏬ (C) ⏬ ⏩ ⏩ ⏩ ⏩ ⏩ ⏬ ⏬ ⏬ ⏬ (D) ⏬ ⏬ ⏬ ⏬ ⏬ ⏩ ⏩ ⏬ ⏬ ⏬ (E) ⏬ ⏩ ⏩ ⏬ ⏬ ⏩ ⏬ ⏬ ⏬ ⏩ Question Image: Privileged Multimodal CoT (teacher only): What secure route arrives at the termination point without encountering danger nodes? Options: (A) ⏬ ⏬ ⏬ ⏬ ⏬ ⏬ ⏩ ⏬ ⏩ ⏩ (B) ⏬ ⏬ ⏩ ⏩ ⏬ ⏬ ⏩ ⏩ ⏬ ⏬ (C) ⏬ ⏩ ⏩ ⏩ ⏩ ⏩ ⏬ ⏬ ⏬ ⏬ (D) ⏬ ⏬ ⏬ ⏬ ⏬ ⏩ ⏩ ⏬ ⏬ ⏬ (E) ⏬ ⏩ ⏩ ⏬ ⏬ ⏩ ⏬ ⏬ ⏬ ⏩ Here is a reference solution that may help you understand the problem: The objective is to find a path from the starting point (the elf) to the termination point (the gift box) on the grid. The path must avoid all "danger nodes," which are represented by the ice block obstacles. Each option provides a sequence of movements (down '⏬' or right '⏩'). I need to evaluate each given route to determine which one successfully reaches the goal without colliding with any obstacles. Let's begin by tracing the path described in Option A on the provided grid. This visual representation will clearly show if the route is safe or if it encounters a danger node. As depicted in the image for Option A, the path immediately moves downwards, eventually hitting an ice block obstacle. Therefore, this route is not secure and fails to reach the destination. Next, I will evaluate Option B by tracing its sequence of movements on the grid. This will allow for a visual confirmation of its safety... Step 1Step 2Step 3 Step 4Step 5 Predictions: Warmed-up TeacherThe correct option is C.✓ Baseline StudentThe correct option is B.✗ OPLD Student (ours)The correct option is C.✓ Figure 6: Inference Result Case Study: 3D Visual Reasoning - Multi-Hop Objects Counting (from Zebra-CoT) Question: Given the collection of objects shown in the image below, viewed from a Front0 perspective, execute the following instructions sequentially: Step 1: Eliminate one DONUT-shaped object from the scene. Step 2: Remove all objects that are BLACK in color. After completing these steps, determine the total count of objects remaining. Question Image: Privileged Multimodal CoT (teacher only): Given the collection of objects shown in the image below, viewed from a Front0 perspective, execute the following instructions sequentially: Step 1: Eliminate one DONUT-shaped object from the scene. Step 2: Remove all objects that are BLACK in color. After completing these steps, determine the total count of objects remaining. Here is a reference solution that may help you understand the problem: I will begin by analyzing the initial state, which contains 7 distinct objects as depicted in the problem image. To better visualize the arrangement and types of objects before applying any operations, I will generate a view from a Right45 angle. The initial view from the Right45 angle confirms the presence of seven objects: a black cylinder, a red donut, a green polyhedron, a brown cube, an orange cylinder, a red capsule, and a black cone. Now, I will proceed with the first operation: removing one DONUT object. There is only one donut in the scene, which is red. I will generate a new image to reflect this removal. After removing the red donut as per Step 1, the scene now contains six objects. These include the black cylinder, green polyhedron, brown cube, orange cylinder, red capsule,... Step 1Step 2 Step 3 Predictions: Warmed-up Teacher4✓ Baseline Student5✗ OPLD Student (ours)4✓ Figure 7: Inference Result Case Study: Visual Logic & Strategic Games - Tetris (from Zebra-CoT) Question: Apply the following sequence of transformations to the yellow shape: mirror horizontally, then translate 2 left, then translate 2 up and 2 left, then translate 1 up and 2 right. Choose the option that shows the resulting shape. Question Image: Privileged Multimodal CoT (teacher only): Apply the following sequence of transformations to the yellow shape: mirror horizontally, then translate 2 left, then translate 2 up and 2 left, then translate 1 up and 2 right. Choose the option that shows the resulting shape. Here is a reference solution that may help you understand the problem: The problem asks to apply a series of geometric transformations to the initial yellow shape on the grid. I will apply each transformation step-by-step and visualize the shape's position after each stage, starting with the original shape. The first transformation is to mirror the shape horizontally. Next, translate the shape 2 units to the left. Then, translate the shape 2 units up and 2 units left. The final transformation is to translate the shape 1 unit up and 2 units right. The image above shows the shape after all transformations have been applied. I will now compare this final transformed shape with the provided answer options to identify the correct one. After understanding the reference solution, please solve the problem again using your own reasoning. Step 1Step 2Step 3 Step 4Step 5 Predictions: Warmed-up TeacherThe correct answer is A.✗ Baseline StudentThe correct answer is D.✗ OPLD Student (ours)The correct answer is C.✓ Figure 8: Inference Result Case Study: 2D Visual Reasoning - Visual Jigsaw (from Zebra-CoT) Question: A jigsaw puzzle image has several missing parts shown as gray areas. Identify which set of pieces from the options below the image correctly fills the missing areas. Question Image: Privileged Multimodal CoT (teacher only): A jigsaw puzzle image has several missing parts shown as gray areas. Identify which set of pieces from the options below the image correctly fills the missing areas. Here is a reference solution that may help you understand the problem: Analyze the provided image to locate the grayed-out areas representing the missing puzzle pieces. To determine the correct pieces, visualize or find the complete scene to understand what should be in the missing sections. The complete image reveals the content that fills the missing areas in the puzzle. Compare these areas in the complete image to the shapes and content of the pieces in the options provided in the original problem image. By matching the visual content and shapes from the complete scene to the options, the correct set of pieces can be identified. After understanding the reference solution, please solve the problem again using your own reasoning. Step 1 Predictions: Warmed-up TeacherA✗ Baseline StudentC✗ OPLD Student (ours)D✓ Figure 9: Inference Result Case Study: Visual Logic & Strategic Games - Tetris (from Zebra-CoT) Question: Apply the following sequence of transformations to the orange shape: scale by 2×, then translate 2 right, then translate 1 down, then rotate 90° clockwise. Choose the option that shows the resulting shape. Question Image: Privileged Multimodal CoT (teacher only): Apply the following sequence of transformations to the orange shape: scale by 2×, then translate 2 right, then translate 1 down, then rotate 90° clockwise. Choose the option that shows the resulting shape. Here is a reference solution that may help you understand the problem: The problem requires applying a specific sequence of geometric transformations to an initial shape and identifying the final result among the options. I will apply each transformation step by step to the original shape shown in the puzzle grid. The first step is to scale the shape by 2x. The visual thought shows the shape after this scaling. Next, translate the scaled shape 2 units to the right. The image shows the shape's new position after this translation. Now, translate the shape 1 unit down. The image displays the shape after this downward movement. The final transformation is a 90° clockwise rotation. The image shows the shape after this rotation. After understanding the reference solution, please solve the problem again using your own reasoning. Step 1Step 2Step 3 Step 4Step 5 Predictions: Warmed-up TeacherA✓ Baseline StudentD✗ OPLD Student (ours)A✓ Figure 10: Inference Result Case Study: GQA Detailed Reasoning (from Visual-CoT) Question: What kind of furniture is the pillow on? Question Image: Privileged Multimodal CoT (teacher only): What kind of furniture is the pillow on? Here is a reference solution that may help you understand the problem: In the right side of the room, there is a cushioned seating piece with patterned upholstery and a pillow resting on its seat area. The pillow is positioned against the backrest, indicating it’s placed on a piece of seating furniture rather than a table or shelf. The surrounding details, like the armrest and the way the cushion is set into the frame, reinforce that the pillow is on a seating surface. The pillow’s placement aligns with where someone would sit, confirming the type of furniture it’s on. After understanding the reference solution, please solve the problem again using your own reasoning. Step 1 Predictions: Warmed-up Teacherchair✓ Baseline Studentcouch✗ OPLD Student (ours)chair✓ Figure 11: Inference Result Case Study: 2D Visual Reasoning - Visual Jigsaw (from Zebra-CoT) Question: Identify which option correctly fills the missing grayed-out sections in the provided jigsaw puzzle image. Question Image: Privileged Multimodal CoT (teacher only): Identify which option correctly fills the missing grayed-out sections in the provided jigsaw puzzle image. Here is a reference solution that may help you understand the problem: Analyze the input image to locate the areas where puzzle pieces are missing. To determine the correct pieces, it is helpful to see the complete scene without the missing parts. Comparing the complete image with the options provided, select the option that matches the content and shape of the missing areas in the original puzzle. After understanding the reference solution, please solve the problem again using your own reasoning. Step 1 Predictions: Warmed-up TeacherD✗ Baseline StudentB✗ OPLD Student (ours)A✓ Figure 12: Inference Result