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

cs.CVSep 29, 2026

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

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

Organizations: Tsinghua University · LMMs-Lab · Xi’an Jiaotong University

Abstract

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.

Figures & tables

Figure 1: Spatial-OPSD in context. Left: Spatial-OPSD uses tool-enhanced spatial priors to guide a privileged teacher during training; the student infers from the original visual question without GT answers or tools. Right: Schematic comparison of fixed-answer off-policy training, one-round training, and round-wise self-evolution. Within a round, the teacher ( $T$ ) is frozen while the student ( $S$ ) improves; at round boundaries, both roles are initialized from the improved student, while privileged spatial context restores an informative teacher–student asymmetry.

Figure 2: Spatial-OPSD pipeline. Native metadata or external tools produce a scene scaffold. The student receives $(v,q)$ , while the same-checkpoint teacher additionally receives a question-relevant subgraph $z$ . Task answers are excluded from the objective; no scaffold or tool is needed at inference.

Model	Method	SPAR-Bench	MindCube-tiny	MMSI-Bench	ViewSpatial	VSI-Bench	Average
Qwen3-VL-4B ( Bai et al., 2025 )	Base	35.148	24.57	28.0	39.01	55.43	36.432
Qwen3-VL-4B ( Bai et al., 2025 )	Spatial-OPSD	44.788	31.81	29.0	40.70	55.73	40.406
Gemma-3-4B ( Gemma Team, 2025 )	Base	30.640	37.04	27.4	31.90	25.86	30.568
Gemma-3-4B ( Gemma Team, 2025 )	Spatial-OPSD	36.302	40.28	27.9	24.74	25.74	30.992
InternVL3.5-4B ( Wang et al., 2025b )	Base	29.998	35.71	28.2	35.17	54.95	36.806
InternVL3.5-4B ( Wang et al., 2025b )	Spatial-OPSD	39.433	37.04	30.1	35.21	56.92	39.741

Table 1: One-round Spatial-OPSD across 4B-scale VLM families.

Proprietary Models
Model	SPAR-Bench	MindCube-tiny	MMSI-Bench	ViewSpatial	VSI-Bench	Average
Grok-4-2025-07-09 ( xAI, 2025 )	–	63.6	37.8	43.2	47.9	–
GPT-5-2025-08-07 ( OpenAI, 2025 )	49.7	56.3	41.8	45.6	55.0	49.68
Gemini-3-Pro-Preview ( Google DeepMind, 2025 )	48.7	70.9	45.2	50.4	52.5	53.54
Open-Source General Models
BAGEL-7B-MoT ( Deng et al., 2025 )	39.1	34.7	31.0	41.3	31.4	35.50

Table 2: Comparison with proprietary, general open-source, and spatially specialized models. Among open-source models, the best result is bold and the second best is underlined.

Method	Update	Round	SPAR-Bench
Base (Qwen3-VL-4B)	–	0	35.148
Step-wise RSI	Per step	1	0.000
Fixed teacher	None	1	44.788
		2	44.170
		3	43.168
Round-wise RSI (ours)	Per round	1	44.788

Table 3: Ablation of teacher-refresh frequency on SPAR-Bench.

Figure 3: Teacher-refresh ablation on Qwen3-VL-4B. (a,b) Reverse-KL loss and student output entropy with a teacher frozen within the round or refreshed after every step. (c) SPAR-Bench accuracy across three matched rounds for a fixed teacher and for round-wise refresh.

Figure 4: (a) Distillation-loss ablation on five benchmarks for Qwen3-VL-4B. (b) Training-set diagnostic by spatial-prior category.

Figure 5: Effect of numerical noise in privileged spatial priors for Qwen3-VL-4B. Each prior value is multiplied by $1+\epsilon$ , with zero-mean relative error clipped at $\pm 2p$ .

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Model	Method	Use GT Answers	SPAR-Bench	MindCube-tiny	MMSI-Bench	ViewSpatial	VSI-Bench
Qwen3-VL-4B	Base	–	35.148	24.57	28.0	39.01	55.43
	SFT	✓	51.426	32.05	24.0	39.30	51.43
	GRPO	✓	49.068	29.05	28.4	39.51	54.64
	OURS	$\times$	44.788	31.81	29.0	40.70	55.73
Gemma-3-4B	Base	–	30.640	37.04	27.4	31.90	25.86
	SFT	✓	52.898	35.62	25.4	40.53	26.67

Appendix

Table 4: Full results of all models and methods.

Hyperparameter	Value
Optimizer	AdamW
Learning rate	$2\times 10^{-6}$
LR schedule	cosine, $\mathrm{lr}_{\min}=10^{-8}$
Warm-up ratio / weight decay	$0$ / $0$
Adam $\left(\beta_{1},\beta_{2}\right)$	$(0.9,0.98)$
Gradient clipping	$1.0$

Appendix

Table 5: Shared Spatial-OPSD training hyperparameters. “Batch size” is the number of prompts per optimizer update and also the rollout batch size.

Explore similar work

The Art of Interrogation: Consistency Amplifies Factuality in Spatial Reasoning
Jun 10, 2026Theo Uscidda, Marta Tintore Gazulla, Maks Ovsjanikov +2Spatial Reasoning LLM Reasoning Strategies
CREST, ENSAE, Institut Polytechnique de Paris · Google Zurich · Google DeepMind
ProSR: Process-Shaped Spatial Reasoning for Reliable Chain-of-Thought in VLMs
May 25, 2026Jiangyang Li, Cong Wan, Changjie Wu +8Spatial Reasoning Reasoning Trajectory
1Xi’an Jiaotong University · 2Amap, Alibaba Group · 4Shenzhen University +1
Reinforcing Dual-Path Reasoning in Spatial Vision Language Models
Jun 16, 2026Yatai Ji, An-Chieh Cheng, Yang Fu +13Spatial Reasoning Indoor Localization
The University of Hong Kong · NVIDIA · University of California, San Diego

Jun 10, 2026, cs.AIJ/K move · Enter open · S save

The Art of Interrogation: Consistency Amplifies Factuality in Spatial Reasoning

Theo Uscidda, Marta Tintore Gazulla, Maks Ovsjanikov, Federico Tombari+1

CREST, ENSAE, Institut Polytechnique de Paris · Google Zurich · Google DeepMind

Spatial Reasoning LLM Reasoning Strategies Ground Truth Art

Open paper AskPDF arXiv

Current Large Reasoning Models (LRMs) exhibit remarkable general capabilities but significantly underperform in spatial reasoning tasks. Existing approaches treat this gap as a knowledge deficit, relying on supervised fine-tuning (SFT) to ingest labeled spatial data from external vision sources or synthetic engines. In contrast, we argue that for many tasks, spatial reasoning capabilities are already present in pre-trained LRMs but require alignment through logical coherence under geometric 2D and 3D constraints. In this work, we propose a self-supervised reinforcement learning (RL) framework that targets the internal reasoning process without requiring ground-truth annotations. By formalizing the notion of consistency verifiers -- reward functions that check for geometric and semantic consistency under transformations -- we demonstrate that models can improve their spatial reasoning abilities. We use both image transformations, like flipping, and textual transformations, like swapping the order of objects in the question, and propose a new optimal transport-based RL strategy, OT-GRPO, which is a minimal-matching variant of group relative policy optimization tailored to pairwise verifiers. We show that this label-free consistency training approaches the accuracy of models trained with ground-truth supervision and achieves similar generalization across diverse tasks and data domains.

Abstract

Explore similar work

The Art of Interrogation: Consistency Amplifies Factuality in Spatial Reasoning

ProSR: Process-Shaped Spatial Reasoning for Reliable Chain-of-Thought in VLMs

Reinforcing Dual-Path Reasoning in Spatial Vision Language Models