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Spatial-OPSD: Self-Improving Spatial Reasoning via Label-Free Self-Distillation

Zhenyu Liu, Zhangquan Chen, Keyi Chen, Mingze Sun, Xiang An, Haodong Jing, Ruqi Huang

arXiv:2609.37055v1cs.CV

TL;DR

Spatial-reasoning improvements often depend on answer labels, answer-derived rewards, or other task-specific supervision. Spatial-OPSD uses spatial priors to distill teacher feedback on student-generated trajectories, and repeated rounds improve an already spatially specialized model. Its current training implementation obtains privileged scaffolds from external perception and reconstruction tools.

  • Problem

    Improving spatial reasoning commonly relies on ground-truth answers, answer-derived rewards, or other task-specific supervision, despite the availability of spatial structure in perception and reconstruction.

    Source: §1 · p. 1

  • Method

    Spatial-OPSD uses a same-checkpoint teacher with automatically obtained spatial priors to supervise student-generated trajectories, then refreshes both roles from the improved student between rounds.

    Source: §1 · p. 2, §3.2 · p. 4

  • Results

    Across four VLM families, one round consistently improves the five-benchmark average, while three rounds yield the highest average among compared open-source models and the best results on three of five benchmarks.

    Source: §1 · p. 2

  • Takeaways & Limitations

    The results show that intrinsic spatial supervision remains reusable across generations, including for a model that has already undergone strong spatial specialization.

    Source: §4.3 · p. 6

    The current implementation obtains privileged spatial scaffolds from external perception and reconstruction tools during training.

    Source: §5 · p. 9

Abstract

from arXiv · show

Vision-language models (VLMs) increasingly operate in embodied and spatially grounded settings, where accurate understanding of depth, viewpoint, and three-dimensional relations is essential. However, improving spatial reasoning typically relies on ground-truth answers, answer-derived rewards, or other forms of task-specific supervision. We introduce Spatial-OPSD, a label-free self-improvement framework that instead exploits spatial structure naturally available from perception and reconstruction tools. During training, a privileged teacher receives automatically obtainable spatial priors, such as depth, reconstructed 3D relations, and camera geometry, while the student observes only the original visual-language input. On trajectories sampled by the student itself, the teacher provides dense token-level supervision, allowing the student to internalize spatial knowledge without ground-truth answer labels or privileged information at inference time. To extend this supervision beyond a single round, we adopt a round-wise recursive training scheme: the teacher remains frozen within each round to provide a stable learning target, and the improved student initializes both teacher and student in the next round, where privileged spatial priors re-establish an informative teacher--student asymmetry. This enables repeated self-improvement while avoiding a rapidly moving teacher during optimization. Across four VLM families, a single round of Spatial-OPSD consistently improves the five-benchmark average, while three rounds further push a strong spatially specialized model to the open-source frontier, achieving the highest average among the open models and the best results on three of five spatial reasoning benchmarks. Our code is available at https://github.com/vermouth599/Spatial-OPSD.

1 INTRODUCTION

Spatial-OPSD addresses the reliance of spatial-reasoning training on fixed targets and task-specific supervision by using automatically obtained spatial structure as privileged teacher context. It supports recursive self-improvement, with consistent single-round gains across four VLM families and stronger multi-round results for a spatially specialized model.

1 INTRODUCTION

  • Spatial reasoning requires VLMs to understand depth, relative position, viewpoint, and three-dimensional relations, beyond recognizing objects.The paper identifies these capabilities as important in embodied and spatially grounded environments.Source: §1 · p. 1
  • Existing approaches commonly rely on ground-truth or pseudo-labeled answers or geometric cues as fixed, task-specific training targets.The paper frames reusable spatial structure as an alternative to treating it as one-time training data.Source: §1 · p. 1
  • Spatial-OPSD gives a teacher automatically obtained spatial priors and trains it to supervise student-generated trajectories without ground-truth answer labels.The student receives only the original visual-language input; at round boundaries, the improved student initializes both roles and spatial context restores their information asymmetry.Source: §1 · p. 2
  • Three rounds achieve the highest average among compared open-source models and the best results on three of five spatial reasoning benchmarks.Across four VLM families, a single round consistently improves the five-benchmark average.Source: §1 · p. 2
  • The paper’s contributions include label-free privileged supervision, round-wise recursive self-improvement, and evaluations across four VLM families and five spatial reasoning benchmarks.The recursive scheme refreshes the teacher between rounds rather than continually during a round.Source: §1 · p. 2

2 RELATED WORK

The related work connects Spatial-OPSD to on-policy distillation, geometric approaches to spatial understanding, and recursive self-improvement. It distinguishes the method through question-relevant geometry as privileged context and weight updates without task-answer labels.

2.1 ON-POLICY SELF-DISTILLATION

  • Spatial-OPSD uses student-generated trajectories and gives the same-model teacher question-relevant geometry rather than a task answer.The student receives neither that geometry nor an answer-derived training signal.Source: §2.1 · p. 3

2.2 SPATIAL UNDERSTANDING

  • Prior spatial work uses geometric estimates and reconstruction outputs as informative supervision, while Spatial-OPSD supplies question-relevant structure to the teacher during training.The student retains the original visual input as its only information source at inference.Source: §2.2 · p. 3

2.3 RECURSIVE SELF-IMPROVEMENT

  • Unlike cited recursive approaches using answer-selected rationales or code-based scaffolds, Spatial-OPSD updates VLM weights through privileged on-policy distillation without task-answer labels.The improved student initializes both roles after each round; the teacher stays frozen within a round and refreshes between rounds.Source: §2.3 · p. 3

3 METHODOLOGY

Spatial-OPSD excludes task answers and answer-derived rewards from optimization, using automatically derived geometry as privileged teacher context instead. Its pipeline builds and retrieves spatial scaffolds, distills teacher feedback on student-sampled responses, and initializes later rounds from the improved student.

3.1 PROBLEM SETTING AND SUPERVISION SCOPE

  • Spatial-OPSD excludes task answers and answer-derived rewards from optimization, while automatically obtained geometric structure serves as privileged teacher context.The paper calls this setting answer-label-free optimization.Source: §3.1 · p. 3

3.2 OVERVIEW

  • A geometry builder creates a reusable scene scaffold and a retriever selects a question-relevant subgraph for the same-checkpoint teacher, while the student receives only the visual input and question.Training builds object- and camera-centric scaffolds, queries the teacher along student-sampled responses, and initializes the next round from the improved student.Source: §3.2 · pp. 3–4, Figure 2 · p. 4
  • The teacher’s advantage comes from privileged geometry, not greater model capacity, and the deployed student uses only the original input.No scaffold or tool is needed at inference.Source: §3.2 · p. 4, Figure 2 · p. 4

3.3 CONSTRUCTING PRIVILEGED SPATIAL INFORMATION

Spatial-OPSD builds spatial priors from available native geometry or pseudo-geometry, organizes scene information into reusable question-relevant subgraphs, and filters uncertain geometry. Metric values are retained only when scale is reliable.

3.3.1 SOURCE-ADAPTIVE GEOMETRY ACQUISITION

  • Geometry acquisition preserves native data when available and uses perception and reconstruction tools to produce pseudo-geometry for some RGB-only or video samples.Sources include SPAR-7M-RGBD, VSI-590K, and SenseNova-SI-8M; when scale is unreliable, the scaffold uses ordinal or normalized geometry instead of metric values.Source: §3.3.1 · pp. 4–5

3.3.2 REUSABLE SPATIAL SCAFFOLD

  • The reusable scene graph stores object- and camera-centric geometry, and question-based retrieval returns a deterministic text subgraph for the teacher.The teacher must still ground references, select a coordinate frame, compose relations, and generate the response; its token distribution, not the dataset answer, defines the target.Source: §3.3.2 · p. 5

3.3.3 QUALITY CONTROL

  • Quality control filters pseudo-geometry using detection, visibility, point-count, point-map-confidence, and cross-view reprojection checks.The method also discards boundary-dominated masks, duplicates, extreme camera poses, and uncertain relations; these checks reduce noise inherited from external tools.Source: §3.3.3 · p. 5

3.4 ON-POLICY SPATIAL SELF-DISTILLATION

Spatial-OPSD evaluates teacher feedback on trajectories sampled by the student, using the same response prefixes but different contexts. The teacher receives privileged geometric context, and training uses pure distillation without answer cross-entropy or answer-derived rewards.

3.4 ON-POLICY SPATIAL SELF-DISTILLATION

  • On-policy distillation evaluates teacher feedback on student-generated trajectories, unlike fixed-reference trajectories whose prefixes may differ.At each response position, teacher and student consume the sampled prefix but receive different contexts.Source: §3.4 · p. 5
  • Training uses pure distillation, with prompt and padding positions masked and no answer cross-entropy or answer-derived rewards.Gradients are stopped through the teacher.Source: §3.4 · p. 5
  • Teacher and student share architecture and initialization, but the teacher receives privileged geometric context and remains frozen within the round.The rollout engine is synchronized with the student after each optimizer update.Source: §3.4 · p. 5

3.5 ROUND-WISE SELF-EVOLUTION

Spatial-OPSD refreshes the teacher at round boundaries: it stays fixed while the student improves, and the resulting checkpoint initializes both roles in the next round. The privileged supervision gap may narrow within a round but need not change monotonically after refresh.

3.5 ROUND-WISE SELF-EVOLUTION

  • Spatial-OPSD refreshes the teacher only at round boundaries, avoiding both a permanently frozen teacher and a continually moving target.The authors note that a permanently frozen teacher cannot inherit student gains, while step-wise updates move the target continually.Source: §3.5 · p. 5
  • The improved student checkpoint initializes both teacher and student in the next round, so teacher capability changes only between rounds.Within each round, the privileged target is stationary while the student receives on-policy updates.Source: §3.5 · p. 5
  • Table 1 covers one-round Spatial-OPSD across 4B-scale VLM families.Source: Table 1 · p. 6
  • The privileged supervision gap may narrow within a round but need not change monotonically after teacher refresh.Source: §3.5 · p. 6

4 EXPERIMENTS

Across four VLM families, Spatial-OPSD improves five-benchmark averages, and three recursive rounds further improve a strong spatial model. Ablations indicate that round-wise teacher refresh, reverse-KL distillation, and varied spatial priors support these results, which persist under noisy priors.

4.1 EXPERIMENTAL SETUP

  • The evaluation reports accuracy on five spatial reasoning benchmarks and uses ground-truth answers only for evaluation, not optimization.The benchmarks are SPAR-Bench, MindCube-tiny, MMSI-Bench, ViewSpatial-Bench, and VSI-Bench.Source: §4.1 · p. 6

4.2 EFFECTIVENESS ACROSS MODEL FAMILIES

  • One round of Spatial-OPSD improves the five-benchmark average for all four tested VLM families, with particularly consistent gains on SPAR-Bench and MMSI-Bench.The study reports that benchmark-specific regressions remain, while overall improvement holds across substantially different architectures.Source: §4.2 · p. 6

4.3 THREE-ROUND RECURSIVE SELF-IMPROVEMENT

  • Recursive Spatial-OPSD further improves an already strong spatial model on most benchmarks, achieving the highest average among compared open-source models and best open-model performance on three benchmarks.Source: §4.3 · p. 6

4.5 ABLATING THE DISTILLATION LOSS

  • Reverse-KL distillation achieves the strongest overall performance and most balanced transfer across the five benchmarks, although objectives favor different benchmarks.The comparison tests reverse KL, forward KL, and Jensen–Shannon divergence.Source: §4.5 · p. 7, Figure 4 · p. 8

4.4 ABLATING THE TEACHER-REFRESH SCHEDULE

  • Round-wise teacher refresh continues improving across rounds, while step-wise refresh eventually collapses and a permanently fixed teacher cannot sustain improvement.The tested schedule freezes the teacher within each round and refreshes it between rounds.Source: §4.4 · p. 7, Table 3 · p. 7, Figure 3 · p. 8

4.6 TRAINING-SET ANALYSIS OF SPATIAL-PRIOR CATEGORIES

  • Across metric geometry, 3D relations, and cross-view geometry, priors strengthen the privileged teacher, and the distilled student improves over the base model without those priors.The analysis compares the base model, privileged teacher, and distilled student for each spatial-prior category.Source: §4.6 · pp. 7–8

4.7 ROBUSTNESS TO NOISY SPATIAL PRIORS

  • Moderate prior perturbations cause little degradation, and Spatial-OPSD remains stronger than the unadapted model even with substantially noisier priors.The tested relative-noise levels are p ∈ {0.05, 0.10, 0.20}.Source: §4.7 · p. 8, Figure 5 · p. 9

5 CONCLUSION

Spatial-OPSD uses spatial priors for recursive self-improvement and reports sustained gains, while its current training setup relies on external perception and reconstruction tools.

5 CONCLUSION

  • Across four VLM families, one round improves the five-benchmark average, while three rounds achieve the highest average among compared open-source models and best results on three of five benchmarks.Ablations identify round-wise teacher refresh as a key mechanism for sustained improvement and show effectiveness with imperfect spatial priors.Source: §5 · p. 9
  • Current training obtains privileged spatial scaffolds from external perception and reconstruction tools; autonomous tool use and model-generated scaffolds are future work.Source: §5 · p. 9
  • The authors report that AI tools assisted manuscript editing, organization, and presentation and interpretation of results, with all assisted content manually reviewed and verified.Source: AI USE STATEMENT · p. 9
  • The experiments use publicly available, fully anonymized datasets and do not involve human subjects, privacy infringement, or harmful discrimination concerns.Source: ETHICS STATEMENT · p. 9

A FULL RESULTS

Table 4 is identified as presenting full results for all models and methods.

A FULL RESULTS

B EXPERIMENTAL SETUP

The experiments use a shared spatial-reasoning training set and compare Spatial-OPSD across several open-weight VLM backbones. Training uses student-generated trajectories and a frozen privileged teacher within each round, with answer-supervised baselines also evaluated.

B EXPERIMENTAL SETUP

  • The shared 6.2k-example training set combines SPAR-7M-RGBD, VSI-590K, and SenseNova-SI-8M, with teacher-only geometric context and answer annotations excluded from the Spatial-OPSD loss.All compared training objectives use the same examples and visual preprocessing; SFT and GRPO additionally consume answer annotations.Source: B EXPERIMENTAL SETUP · p. 13
  • Spatial-OPSD is evaluated on four approximately 4B open-weight backbones and additionally on SenseNova-SI-Qwen3-VL-8B for recursive improvement of a stronger spatial model.Source: B EXPERIMENTAL SETUP · p. 13
  • For each prompt, a frozen same-initialization teacher receives privileged spatial context and supplies token-level distributions on the current student's response; the teacher is refreshed only between rounds.The method uses reverse KL without auxiliary label cross-entropy, and each round makes one pass over the training set.Source: B EXPERIMENTAL SETUP · p. 13
  • Shared training hyperparameters use AdamW with a cosine schedule, no warm-up, a 10^-8 minimum learning rate, bfloat16, and a 262,144-pixel maximum image budget.The setup also uses FSDP2 and activation checkpointing, with no CPU offloading; optional thinking modes are disabled.Source: B EXPERIMENTAL SETUP · p. 13, Table 5 · p. 14
  • SFT and GRPO are answer-supervised baselines, with GRPO initialized from base models and trained using answer-based rewards.SFT runs one epoch; the supplied GRPO description specifies 300 optimizer steps and eight generations per prompt.Source: B EXPERIMENTAL SETUP · pp. 13–14

B.1 EVALUATION PROTOCOL

Evaluation follows the EASI protocol with deterministic zero-shot decoding and aligned model adapters, processors, settings, and scorers; training uses a single NVIDIA H20 GPU.

B.1 EVALUATION PROTOCOL

  • Evaluation uses EASI v0.2.2 with task-provided prompts, parsers, and aggregation code, and final base-versus-trained comparisons share adapters, processors, decoding settings, and scorers.Evaluation is zero-shot with deterministic decoding at temperature 0, sampling disabled, and batch size one for EASI-aligned results.Source: §B.1 · p. 14
  • Training runs on a single NVIDIA H20 GPU with 96 GB memory and uses the specified Python, PyTorch, CUDA, Transformers, SGLang, Ray, FlashAttention, and lmms-eval stack.Per-example outputs are preserved for auditing benchmark parsers.Source: §B.1 · p. 14

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