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Progressive-View On-Policy Distillation for Regional-to-Global Transfer in Multimodal LLMs

Shanfeng Huang, Zhou Fang, Song Xiao, Hai Du

Year: 2026Venue: arXiv preprintArea: cs.CVType: PreprintEmbeddings: 36

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Abstract

Abstract:Regional-to-global distillation uses crop-conditioned guidance to improve full-image understanding. The challenge is to effectively transfer the teacher's crop-based advantage to the student's full-image inference. We propose progressive-view on-policy distillation (PVD), which shifts the student's view distribution from the crop toward the full image through an intermediate aspect-preserving padded crop. The padded crop preserves regional content while matching the full image's visual-token grid. Across stages, the view mixture assigns increasing probability to the full image. A lightweight regional-advantage weighting reallocates token-level supervision using the crop-conditioned teacher-student log-probability gap. Evaluated under each sampled input, it applies mild reweighting when the gap is small and emphasizes higher-gap tokens when the gap widens. A Jensen-Shannon metric decomposition interprets this schedule as a shift from matched-input imitation toward the deployment objective. Across benchmarks spanning perception, visual mathematics and general multimodal question answering, PVD-full reaches an average accuracy of 77.51 over three seeds, improving on the reward-free distillation baseline by 2.01 points and on its reward-matched variant by 1.00 point. In the reward-free setting, PVD-distill still gains 1.16 points.

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PROGRESSIVE-VIEW ON-POLICY DISTILLATION FOR REGIONAL-TO-GLOBAL TRANSFER IN MULTIMODAL LLMS Shanfeng Huang Zhou Fang Song Xiao Hai Du Abstract Regional-to-global distillation uses crop-conditioned guidance to improve full-image understanding. The challenge is to effectively transfer the teacher’s crop-based advantage to the student’s full-image inference. We propose progressive-view on-policy distillation (PVD), which shifts the student’s view distribution from the crop toward the full image through an intermediate aspect-preserving padded crop. The padded crop preserves regional content while matching the full image’s visual-token grid. Across stages, the view mixture assigns increasing probability to the full image. A lightweight regional-advantage weighting reallocates token-level supervision using the crop-conditioned teacher–student log-probability gap. Evaluated under each sampled input, it applies mild reweighting when the gap is small and emphasizes higher-gap tokens when the gap widens. A Jensen–Shannon metric decomposition interprets this schedule as a shift from matched-input imitation toward the deployment objective. Across benchmarks spanning perception, visual mathematics and general multimodal question answering, PVD-full reaches an average accuracy of 77.5177.51 over three seeds, improving on the reward-free distillation baseline by 2.012.01 points and on its reward-matched variant by 1.001.00 point. In the reward-free setting, PVD-distill still gains 1.161.16 points. Index Terms: Multimodal large language models, on-policy self-distillation, fine-grained visual understanding, regional-to-global transfer, progressive view sampling †address: Baidu Inc. huangshanfeng, fangzhou07, xiaosong, duhai02@baidu.com 1 INTRODUCTION Fine-grained visual detail remains a bottleneck for multimodal large language models, because the evidence a question depends on often occupies a tiny fraction of a high-resolution image. Much prior work resolves this at inference time through guided visual search, tree-structured zooming, or agentic crop-and-reask loops [18, 12], which recover the detail at the cost of added latency and deployment machinery for every query. Regional-to-global distillation transfers this benefit into the weights [20, 17]. Conditioning the same model on the annotated region makes it a privileged teacher that sees the same evidence at a larger effective scale and produces sharper next-token distributions. These distributions supervise the full-image student on its own rollouts [1, 8]. Inference uses one student forward pass on the full image. On-policy distillation avoids the exposure bias of offline supervision [1, 4, 8] and has been extended to self-distillation with the same model serving both roles [20, 6]. Token-level variants show that teacher–student disagreement concentrates in a small subset of response tokens, motivating learnability-based token selection or visual-advantage-based reweighting [16, 7]. In regional-to-global distillation, however, the standard objective uses the student’s full-image view from the outset and weights response tokens uniformly, even though the privileged-view advantage is concentrated in a minority of tokens. We address these problems with progressive-view on-policy distillation (PVD), which integrates progressive view sampling with view-dependent token weighting in a single objective. The student’s view distribution shifts in stages from the crop toward the full image through an aspect-preserving padded crop, and every stage keeps mass on more than one view. The padded crop preserves regional content on the full image’s visual-token grid, separating token-grid alignment from the later introduction of surrounding context. Progressive sampling therefore bridges the input mismatch over graded stages, and view-dependent weighting concentrates supervision on the tokens the privileged view resolves. The two components are linked through the teacher–student gap under the sampled view. RA remains mild when this gap is small and becomes more selective for high-gap tokens in later, more deployment-aligned view mixtures. Our contributions are: • We propose PVD, a progressive regional-to-global transfer objective that shifts sampling mass in stages from privileged crops toward the deployment view. View-conditioned regional-advantage (RA) token weighting is a complementary refinement that reuses the same teacher–student gap and adds no extra forward pass. • An exposure-matched control isolates the source of the gain: the progressive schedule beats a static mixture with the same expected exposure to each view, so temporal progression, not added crop exposure, accounts for most of the reward-free improvement over Vision-OPD. • A Jensen–Shannon metric decomposition (Section 2.3) explains why the schedule runs in this direction: the crop aligns the teacher and student visual inputs, while the full image matches the deployment input. • Augmenting the curriculum with a complementary task-reward term, PVD-full reaches 77.5177.51, +2.01+2.01 over the reward-free Vision-OPD and +1.00+1.00 over a reward-matched control, and neither signal alone matches the combination. Figure 1: Progressive-view on-policy distillation. Student training uses stagewise mixtures of a regional crop, a grid-aligned padded crop containing the same regional content, and the full image, with sampling mass shifting toward the deployment view while the teacher remains conditioned on the privileged crop. View-conditioned teacher–student matching produces the top-K JSD and regional-advantage (RA) token weights. At deployment, only the student processes the full image. 2 PROPOSED METHOD 2.1 Regional-to-global self-distillation Let x be an image, q a question and b a region annotation marking the area the question depends on. We use a view v to denote one of the student input constructions. The student is πθ _θ conditioned on v, and the teacher πT _T is an exponential-moving average of the same weights, conditioned on the crop xbx_b. Rollouts are drawn on-policy under the student’s own view, y∼πθ(⋅∣v,q)y _θ(· v,q), and the per-token loss is a top-K Jensen–Shannon divergence between the two next-token distributions, ℓt(v)=JSDK(πT(⋅∣xb,q,y<t)∥πθ(⋅∣v,q,y<t)). _t(v)=JSD_K\! ( _T(· x_b,q,y_<t)\, \|\, _θ(· v,q,y_<t) ). (1) The support is the student’s top-K vocabulary entries, where the teacher’s log-probabilities are gathered, and both are renormalized with a tail bucket for the residual mass. 2.2 A view-conditioned transfer objective Vision-OPD [20], the representative method in this direction, fixes v=xv=x and averages ℓt _t over the response mask, giving every token the same weight. PVD replaces this fixed-view uniform average with a single objective in which the student’s observation is itself a random variable, and the discrepancy that observation induces decides where supervision is spent: ℒPVD=v∼p(τ),y∼πθ(⋅∣v,q)[1|y|∑twt(v)ℓt(v)], _PVD=E_v p(τ),\,y _θ(· v,q) [ 1|y| _tw_t(v)\, _t(v) ], (2) gt(v)=[log⁡πT(yt∣xb,q,y<t)−log⁡πθ(yt∣v,q,y<t)]+, g_t(v)= [ _T(y_t x_b,q,y_<t)- _θ(y_t v,q,y_<t) ]_+, (3) g¯t(v)=min⁡(gt(v),gmax)−⟨min⁡(g⁡(v),gmax)⟩t, g_t(v)= \! (g_t(v),\,g_ )- (g(v),\,g_ ) _t, (4) wt(v)=⁡[clip⁡(1+λg¯t(v),wmin,wmax)], w_t(v)=N [clip (1+λ\, g_t(v),\;w_ ,\;w_ ) ], (5) Here p⁡(τ)p(τ) is the view distribution at progress τ=s/Sτ=s/S, ⟨⋅⟩t · _t averages over the response mask, and the privileged-view gap gt(v)g_t(v) is treated as constant in the backward pass. The operator N normalizes the weights to unit mean, letting λ redistribute supervision without changing its total. The weighting reuses log-probabilities that (1) already computes and requires no additional box signal, auxiliary scorer or forward pass beyond the crop-conditioned teacher. We refer to it as regional-advantage (RA) weighting, since it scales each token’s supervision by its privileged-view gap gtg_t. The two dimensions are coupled because wt(v)w_t(v) is evaluated under the sampled view. When the privileged-view gap is small, the weighting is less selective. As p⁡(τ)p(τ) shifts probability mass toward later, more deployment-aligned views, larger gaps concentrate transfer on tokens with a greater teacher advantage. Progressive view sampling therefore shapes token-level supervision throughout training, and the ablation in Section 3.3 isolates the gain of the schedule. We impose two conditions on the schedule. Order the views v1,…,vMv_1,…,v_M from the teacher’s crop to the deployment image, v1=xbv_1=x_b and vM=xv_M=x, and let p⁡(τ)=(p1(τ),…,pM(τ))p(τ)=(p_1(τ),…,p_M(τ)) be piecewise constant on R stages with boundaries 0=τ0<⋯<τR=10= _0<…< _R=1. Monotone progression: ∑k≤jpk(τ) _k≤ jp_k(τ) is non-increasing in τ for every j<Mj<M, so mass moves toward later views. Terminal alignment: pMp_M dominates the last stage, so the final phase samples and scores predominantly under the deployment view. The teacher’s conditioning is never scheduled. We use M=3M=3 (crop, aspect-preserving padded crop, full image) and R=3R=3. A direct crop-to-full-image transition changes both token-grid geometry and visual content, including the region’s relative scale. We therefore insert the aspect-preserving, white-canvas padded crop as an intermediate view. Given source-image dimensions (W,H)(W,H) and crop dimensions (Wb,Hb)(W_b,H_b), we resize the crop by min⁡(W/Wb,H/Hb) (W/W_b,H/H_b) with aspect ratio preserved (using Lanczos interpolation), and paste the result at the center of a (W,H)(W,H) white canvas. The resized crop therefore spans the canvas in at least one dimension, and any remaining margins are white, so no pixels outside the crop are retained. The crop and padded crop contain the same regional content, while the padded crop and full image share the same canvas dimensions and visual-token grid. The intermediate view therefore aligns token-grid geometry while preserving crop-only content. The full-image view then introduces the surrounding context and restores the region’s relative scale at deployment. Fig. 1 illustrates how PVD works, from the progressive view schedule and view-conditioned teacher–student matching to deployment on the full image. 2.3 A metric interpretation of PVD Training only at the fixed deployment view, as Vision-OPD does, exposes the student to the full crop-to-image discrepancy from the outset. The annotated region covers a small fraction of the image, so after the vision encoder’s resizing much of the evidence the teacher conditions on is severely under-resolved in the student’s input. For a full-distribution metric view of (1), let πϕvπ^v_φ denote the next-token distribution and d(⋅,⋅)=JSD(⋅∥⋅)1/2d(·,·)=JSD(·\,\|\,·)^1/2, which is a metric on distributions [3]. For any student view v the triangle inequality gives d⁡(πTxb,πθx)⏟deployment discrepancy≤d⁡(πTxb,πθv)⏟metric surrogate+d⁡(πθv,πθx)⏟δX(v):deployment slack, d (π^x_b_T,\,π^x_θ )_deployment discrepancy\;≤\; d (π^x_b_T,\,π^v_θ )_metric surrogate\;+\; d (π^v_θ,\,π^x_θ )_ _X(v):\ deployment slack, (6) To identify how the view changes this surrogate, define two student-side distances that vanish at opposite ends of the view order: δT(v)=d⁡(πθxb,πθv),δX(v)=d⁡(πθv,πθx). _T(v)=d (π^x_b_θ,\,π^v_θ ), _X(v)=d (π^v_θ,\,π^x_θ ). (7) The crop-to-view distance δT _T measures how far the student’s distribution moves as its input construction shifts from the teacher’s crop to the sampled view. It captures changes in both token-grid geometry and visual content through their effect on the student’s distribution and serves as a proxy for surrogate difficulty. The deployment slack δX _X is the gap between what is optimized and what is deployed. At v=xbv=x_b, visual inputs match and δT=0 _T=0, so the metric surrogate contains only the EMA parameter mismatch while deployment slack remains. At v=xv=x, δX=0 _X=0 and the bound is tight: the metric surrogate equals the deployment discrepancy and includes the full crop-to-image discrepancy. The crop endpoint aligns the visual inputs, whereas the full-image endpoint aligns training with deployment. The decomposition thus exposes a trade-off between matching the teacher’s visual input and matching the deployment input. For fixed parameters and a common response prefix, if the candidate views satisfy δX(v1)≥⋯≥δX(vM)=0 _X(v_1)≥…≥ _X(v_M)=0, shifting probability mass toward later views reduces the expected deployment slack, while a larger δT _T typically makes the surrogate harder and can induce more selective token weighting. This motivates a schedule that begins with substantial crop exposure and ends predominantly on the deployment view, shifting training from matched-input imitation toward the deployment objective. The decomposition provides an interpretation of the schedule, and Section 3 evaluates it empirically. The token allocation admits an exact decomposition. For a fixed sampled response, let ⟨⋅⟩t · _t average over its valid tokens. Since ⟨w⟩t=1 w _t=1, ⟨wℓ⟩t=⟨ℓ⟩t+Covt⁡(w,ℓ). w _t= _t+Cov_t(w, ). (8) Indeed, expanding ⟨(w−1)(ℓ−⟨ℓ⟩t)⟩t (w-1)( - _t) _t gives the second term. When weight clipping is inactive, wt=1+λg¯tw_t=1+λ g_t, so this correction is λCovt(g¯,ℓ) _t( g, ). Thus RA redistributes a unit-mean supervision budget, emphasizing divergence on tokens where the privileged-view teacher holds a larger advantage over the student. Progressive view sampling determines the inputs and rollouts on which this allocation operates. Setting λ=0λ=0 retains the progressive objective with uniform weights, and additionally fixing v=xv=x recovers Vision-OPD. 2.4 Joint training with task reward PVD supervises the student toward the teacher’s distribution without checking whether its final answer is correct, while a binary task reward checks only the answer and says nothing about which tokens to change. The two signals therefore carry different information. We combine them in a single per-token objective, ℒ=ℒPVD+βℒPG,L=L_PVD+β\,L_PG, (9) where ℒPGL_PG is a group-relative policy-gradient loss [11] on the binary answer reward. Both terms apply to every token of every rollout, so the signals are superposed rather than partitioned. We further investigate whether the two signals remain complementary when applied together, examining the training rollouts in Section 3.5. Table 1: Accuracy (%) on nine benchmarks in three task families. Backbone: Qwen3.5-4B. V-OPD abbreviates Vision-OPD. Post-trained rows report mean ± SD over three seeds and share one training configuration and a 20482048-token evaluation budget. Static-view distill matches the curriculum’s expected view exposure but removes its ordering. Best means are bold, and family averages are reported in the text. Perception & spatial understanding Visual math General & diagram QA Method ZoomB. HR-4K HR-8K CV-B. MVista MVerse MMStar MMMU AI2D All Qwen3.5-4B 48.76 83.88 80.62 88.10 78.50 67.61 73.07 66.00 80.73 74.14 GRPO 57.51± ±.59 84.63± ±.63 80.25± ±.38 87.81± ±.16 76.70± ±.60 63.10± ±.19 72.02± ±.57 63.59± ±.61 85.11± ±.31 74.53± ±.30 V-OPD [20] 57.99± ±.71 81.92± ±.81 78.92± ±.44 86.47± ±.23 77.37± ±.75 68.02± ±.28 75.13± ±.70 67.85± ±.72 85.82± ±.42 75.50± ±.31 Static-view distill 56.96± ±.60 81.83± ±.69 79.79± ±.51 85.97± ±.19 78.20± ±.80 69.35± ±.27 75.07± ±.64 67.78± ±.78 86.03± ±.37 75.67± ±.28 PVD-distill w/o RA 57.71± ±.65 83.42± ±.56 80.79± ±.31 86.57± ±.18 78.73± ±.55 70.95± ±.24 75.33± ±.67 67.22± ±.67 86.29± ±.28 76.34± ±.29 PVD-distill 57.40± ±.83 83.75± ±.75 81.00± ±.50 87.50± ±.21 79.73± ±.85 70.71± ±.18 75.53± ±.53 67.04± ±.83 87.32± ±.44 76.66± ±.30 V-OPD w/ GRPO 58.26± ±.53 83.00± ±.88 81.13± ±.45 87.41± ±.15 79.30± ±.70 70.87± ±.29 75.16± ±.77 67.22± ±.56 86.22± ±.34 76.51± ±.30 PVD-full 57.16± ±.78 84.13± ±.70 81.21± ±.56 88.32± ±.24 81.13± ±.65 72.00± ±.23 76.38± ±.60 69.33± ±.73 87.94± ±.39 77.51± ±.26 3 EXPERIMENTS 3.1 Setup Training. All post-training runs are initialized from the same Qwen3.5-4B checkpoint [10] and trained for 6565 steps on the public Vision-OPD-6K set [20]. We use 9696 prompts per step with 88 rollouts each, learning rate ×10−62\!×\!10^-6 with 1010 warmup steps, prompt and response budgets of 81928192 and 10241024 tokens. Training and evaluation ran on 2 servers with 88 NVIDIA A800 GPUs each, using FSDP and vLLM rollouts [13]. The teacher is an exponential-moving average of the policy, θT←(1−α)θT+αθ _T←(1-α)\, _T+α\,θ with α=0.05α=0.05 applied every optimizer step, and K=100K=100 in (1). All post-trained rows of Table 1 share this configuration, and each ablation pair isolates one component (scheduling, then RA). Training data. Vision-OPD-6K provides region-grounded perception questions over high-resolution natural photographs, 6,2406,240 examples, 99.98%99.98\% four-option multiple choice. Over a random sample of 400400, the teacher’s crop covers a median 7.10%7.10\% of the image area (IQR 1.901.90–20.30%20.30\%), so cropping presents the relevant evidence at a much larger effective scale than the full image. On all examples the first view v1v_1 is the teacher’s crop, so the δT=0 _T=0 endpoint is realized exactly and gt(v)g_t(v) reduces to a parametric teacher–student advantage under identical visual inputs. Hyperparameters and why. For (4)–(5) we use λ=0.5λ=0.5, gmax=2g_ =2 and [wmin,wmax]=[0.5,2][w_ ,w_ ]=[0.5,2], bounding the ratio between the most and least weighted token at 44 so no single token dominates. The stage boundaries are τ1=0.2 _1=0.2, τ2=0.6 _2=0.6 with probabilities (0.7,0.2,0.1)(0.7,0.2,0.1), (0.3,0.4,0.3)(0.3,0.4,0.3), (0.0,0.2,0.8)(0.0,0.2,0.8) over (crop, padded crop, full image). The first boundary sits just after the 1010-step warmup, so the crop-heavy stage covers the least stable part of training, and the last stage spans 40%40\% of the run to let the policy adapt to the deployment view. Every stage keeps mass on at least two views, so exposure to later views increases in increments rather than by a hard switch. We set β=1β=1 in (9). Evaluation. We report accuracy on benchmarks across three families: perception and spatial understanding (ZoomBench [17], HR-Bench 4K and 8K [15], CV-Bench [14]), visual mathematical reasoning (MathVista [9], MathVerse [22]), and general multimodal and diagram QA (MMStar [2], MMMU [21], AI2D [5]). Every row uses the same protocol, namely greedy decoding with a 20482048-token budget, rule-based answer extraction, and a single locally served Qwen3-30B-A3B-Instruct-2507 judge [19] at temperature 00 with one fixed prompt per benchmark, scoring the extracted answer against the official answer key. The judge only maps a free-form response onto that key. It never sees the model identity or competing predictions, and the same judge is applied to every row. The all-benchmark average weights the nine benchmarks equally. Compared systems. Vision-OPD (V-OPD) [20] uses no task reward. GRPO uses task reward alone, and V-OPD w/ GRPO adds the same reward to that baseline, giving a reward-matched control. Static-view distill samples the same three views throughout with the time-averaged curriculum probabilities (0.26,0.28,0.46)(0.26,0.28,0.46), matching expected exposure but removing the ordering. PVD-distill w/o RA restores the schedule, and PVD-distill additionally uses the regional-advantage token weighting of (5). These three are reward-free. PVD-full combines schedule, RA and reward. 3.2 Main results PVD-full reaches 77.51±0.2677.51± 0.26 overall in Table 1, improving on V-OPD by 2.012.01 points and on its reward-matched counterpart V-OPD with GRPO by 1.001.00 point. The improvement over both holds on all three task families, and PVD-full obtains the best mean on 77 of the 99 individual benchmarks. Relative to V-OPD, PVD-full improves 88 of 99 benchmarks, with family-level gains of +1.38+1.38 (perception), +3.87+3.87 (visual math) and +1.62+1.62 (general QA). Per-benchmark gains reach MathVerse +3.98+3.98, MathVista +3.76+3.76, HR-8K +2.29+2.29 and AI2D +2.12+2.12. Against the reward-matched control, PVD-full is better on 88 of 99 benchmarks. Removing reward from both sides preserves the ordering. PVD-distill improves 77 of 99 benchmarks and gains 1.161.16 points over V-OPD. PVD-full also has the lowest overall SD among post-trained methods (0.260.26 versus 0.280.28–0.310.31). 3.3 Ablation: schedule, exposure and token allocation Progressive scheduling improves over exposure-matched static mixing. Static-view distill sees each view as often as the curriculum does in expectation and differs from PVD-distill without RA only in when each view is sampled. It reaches 75.67±0.2875.67± 0.28, only 0.170.17 points above V-OPD, whereas the progressive schedule reaches 76.34±0.2976.34± 0.29, 0.840.84 points above V-OPD. This 0.670.67-point margin over the static mixture accounts for approximately 80%80\% of the schedule’s 0.840.84-point gain over V-OPD. Family-level results sharpen this contrast. Static mixing captures much of the visual-math gain (+1.08+1.08) but loses perception (−0.19-0.19), which the schedule recovers (+0.99+0.99 over the static mixture). Crop exposure alone is therefore insufficient to explain the perception gains. This control measures the full stagewise schedule, including its stronger emphasis on the full image near the end, rather than an isolated easy-to-hard ordering effect. Token allocation is a complementary refinement. Adding RA to the progressive objective raises the average from 76.3476.34 to 76.66±0.3076.66± 0.30, so roughly 72%72\% of the 1.161.16-point reward-free improvement over V-OPD comes from the view curriculum. RA improves all three family averages and the overall accuracy on each of the three matched seeds (+0.33+0.33, +0.31+0.31, +0.34+0.34). These gains span only 0.030.03 points across 3 seeds, supporting a small but repeatable effect. As (8) suggests, RA weighting refines a transfer path already effective with uniform supervision. RA thus provides a modest but consistent additional gain over the progressive-view curriculum, which remains the primary driver of the reward-free improvement. 3.4 Progressive view sampling shapes token supervision Table 2: Stage diagnostics from the reward-free run. We report the mean gap ⟨g⟩ g , the fraction of high-gap tokens with gt>0.10g_t>0.10, the mean unweighted JSD ⟨ℓ⟩ , and the min–max range of normalized RA weights. Stage ⟨g⟩ g (10−210^-2) high-gap ⟨ℓ⟩ (10−310^-3) weights 1 2.4 5.9% 4.4 [0.97,1.88][0.97,1.88] 2 5.2 12.5% 12.2 [0.90,1.98][0.90,1.98] 3 4.6 12.0% 10.2 [0.90,1.98][0.90,1.98] Table 2 tracks the teacher–student gap and divergence as the schedule shifts toward later, more deployment-aligned view mixtures. The mean privileged-view gap is 2.42.4 in the crop-heavy first stage and 5.25.2 and 4.64.6 in Stages 2 and 3, in units of 10−210^-2. Likewise, the high-gap token fraction changes from 5.9%5.9\% to 12.5%12.5\% and 12.0%12.0\%, while the unweighted JSD of (1) changes from 4.44.4 to 12.212.2 and 10.210.2 in units of 10−310^-3. The later-stage mixtures, which include the grid-aligned padded crop and increasing full-image exposure, are therefore associated with a harder surrogate than the first stage. The RA weights widen from [0.97,1.88][0.97,1.88] to [0.90,1.98][0.90,1.98], making token-level emphasis more selective under the same weighting rule. The lower gap in Stage 3 than Stage 2 is consistent with reduced teacher–student disagreement as training progresses. 3.5 Complementarity with task reward Adding task reward raises PVD-distill by 0.850.85 points to 77.51±0.2677.51± 0.26 and raises V-OPD by 1.011.01 points. Reward-only GRPO and reward-free PVD-distill reach 74.5374.53 and 76.6676.66, respectively, both below PVD-full, so the two signals remain complementary. Table 3: Rollout-group composition averaged over the last 1010 training steps. Only disagreeing groups produce a GRPO gradient. Objective all correct all wrong disagree zero PG grad. GRPO 43.1% 23.8% 33.1% 66.9% V-OPD w/ GRPO 42.4% 13.5% 44.1% 55.9% PVD-full 41.0% 12.7% 46.3% 53.7% Table 3 examines the rollout groups that supply the GRPO signal. Each prompt produces 88 rollouts, and the group-relative advantage is zero when all are correct or all are wrong. Reward-only GRPO leaves 66.9%66.9\% of groups with zero gradient, including 23.8%23.8\% in which every rollout is wrong. Adding distillation cuts the all-wrong fraction to 13.5%13.5\% for V-OPD with GRPO and 12.7%12.7\% for PVD-full, raising the reward-gradient-producing share to 44.1%44.1\% and 46.3%46.3\%. The dense per-token distillation loss built from (1) does not require a correct rollout, providing supervision where reward supplies no within-group gradient; the jointly trained policies also yield more groups with nonzero reward gradients. 3.6 Generalization beyond the training format Training uses only region-grounded perception questions over natural photographs, yet the gains are larger on visual math and general QA than on the perception family that the training data resemble. The pattern holds against the reward-matched V-OPD with GRPO, with gains of +0.26+0.26 on perception, +1.48+1.48 on visual math and +1.68+1.68 on general QA. The gains therefore extend to questions and imagery beyond the training format, consistent with transfer of improved fine-detail sensitivity. 4 CONCLUSION We presented PVD, coupling a stagewise regional-to-global view schedule through a token-grid-aligned padded crop with teacher-gap-based token reweighting. The padded crop preserves regional content while aligning token geometry, and the schedule accounts for most of the reward-free gain. Combined with task reward, PVD-full reaches 77.51±0.2677.51± 0.26, exceeding reward-free and reward-matched baselines by 2.012.01 and 1.001.00 points, respectively. Deployment requires neither region annotations nor inference-time search. 5 COMPLIANCE WITH ETHICAL STANDARDS This work did not involve human participants or animals, and no ethical approval was required. No new data were collected, and all experiments use publicly released model weights, a publicly released training set and publicly released multimodal evaluation benchmarks intended for research use. 6 ACKNOWLEDGMENT This work was conducted at Baidu Inc. ChatGPT was used for language editing and figure refinement of the manuscript and limited assistance in debugging experimental code. All AI-assisted edits and code changes were reviewed and validated by the authors, who take full responsibility for the content of this work. The authors declare no relevant financial or non-financial interests. References [1] R. Agarwal et al. (2024) On-policy distillation of language models: learning from self-generated mistakes. In International Conference on Learning Representations, Cited by: §1. [2] L. Chen et al. (2024) Are we on the right way for evaluating large vision-language models?. Advances in Neural Information Processing Systems 37, p. 27056–27087. Cited by: §3.1. [3] D. M. Endres and J. 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