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ICCV/2025/R1-Onevision_ Advancing Generalized Multimodal Reasoning through Cross-Modal Formalization/full.md

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+# R1-Onevision: Advancing Generalized Multimodal Reasoning through Cross-Modal Formalization
+
+Yi Yang $^{1*}$  Xiaoxuan He $^{1,3*}$  Hongkun Pan $^{2*}$  Xiyan Jiang $^{1}$  Yan Deng $^{1}$  Xingtao Yang $^{1}$  Haoyu Lu $^{4}$  Dacheng Yin $^{3}$  Fengyun Rao $^{3}$  Minfeng Zhu $^{2\dagger}$  Bo Zhang $^{2\dagger}$  Wei Chen $^{1\dagger}$ $^{1}$  State Key Lab of CAD&CG, Zhejiang University  $^{2}$  Zhejiang University  $^{3}$  WeChat Vision, Tencent Inc.  $^{4}$  Renmin University of China
+
+![](images/a1e23ee67a5e81011a05a2a7150e7042042a32d314a60560e156337167f40452.jpg)  
+?  
+Figure 1. Comparison of baseline models and R1-Onevision. Deepseek-R1 struggles with perception errors due to GPT-4o's incomplete image description and Qwen2.5-VL lacks the necessary reasoning ability to solve the problem. In contrast, R1-Onevision accurately interprets the image, applies structured reasoning, and arrives at the correct solution.
+
+Question: Cynthia paints each region of the figure in a single color: red, blue or yellow. She paints with different colors the regions that touch each other. In how many different ways can Cyntia paint the figure?
+
+![](images/74bca2b42d9e13b122bdc2c76960acc0eb637989755e145b7f002873353ab559.jpg)
+
+# GPT-4o Caption:
+
+The image features a series of concentric circles with varying thicknesses, forming a symmetrical pattern. The outermost circle is the largest, enclosing progressively smaller circles toward the center. Some of the inner circles intersect with each other, creating curved segments that resemble a layered or nested design. The overall composition appears structured and balanced, with smooth, evenly spaced curves contributing to a visually appealing geometric arrangement. The image is monochromatic, utilizing black outlines on a white background.
+
+![](images/8bcf068a006da5acca5f71fe2e43cf51536cc0074a7c220a34e64c142adfbaaf.jpg)
+
+# Deepseek-R1:
+
+Okay, let's tackle this problem step by step... First, I need to visualize the figure described... Since it's concentric circles,... The challenge is to figure out how many regions there are and their adjacency. Let me try to break it down... Let's consider possible common figures of this type... Case 1: A simple target with three concentric circles... Total:  $3^{*}2^{*}2^{*}2 = 24$ . Case 2: Suppose there are two intersecting circles inside... Total:  $3^{*}2^{*}2^{*} = 12$ . However, I recall that in similar problems with a central region and surrounding regions forming a cycle... Assuming the structure forms a chain of outer, middle, and inner annuli, plus four inner regions arranged in a cycle the coloring constraints are:
+
+1. Outer annulus (O): 3 color choices: 2.Middle color: (M) 2.
+
+2. Middle annulus (M): 2 choices (different from O).  
+3. Inner annulus (I): 2 choices (different from M).
+
+4. Four inner regions: Form a cycle, requiring 2 alternating colors
+
+different from 1, yielding 2 colorings.
+
+Total colorings:
+
+3 (O)*2 (M)*2 (I)*2 (inner cycle) = 24. Final answer: 24.
+
+![](images/9a7811c5bfaa9563efeeb9009ecce8482047020b926095a51b0fabfa6f419b7d.jpg)
+
+# Qwen2.5-VL-7B:
+
+To determine the number of different ways Cynthia can paint the figure, we need to consider the constraints given: each region must be painted with a different color from its adjacent regions. Let's analyze the figure step by step.
+
+1. Identify the regions. 2. Coloring the innermost circle3. Coloring the next circle: The next circle must be a different color from the innermost circle. So, there are 2 choices for this circle. 4. Coloring the next circle: The third circle must be a different color from the second circle. So, there are 2 choices for this circle.5. Coloring the next circle6. Coloring the outermost circle - 3 choices for the innermost circle.
+
+- 2 choices for the second circle. 2 choices for the third circle.2 choices for the fourth circle. 2 choices for the outermost circle. The total number of different ways to paint the figure is:  $3^{*}2^{*}2^{*}2^{*}2 = 3^{*}16 = 48$ . Thus, the number of different ways Cynthia can paint the figure is 48
+
+![](images/4de7d7821bad7c3337471c9de946d4dbfb815f1dfe603119b34b4fc235205c06.jpg)
+
+# R1-Onevision:
+
+The image shows a figure with five concentric circles, each touching the next. Cynthia uses three colors: red, blue, and yellow. Each circle must be painted a different color from its neighbors. Since the circles are concentric, each circle touches the next, meaning each circle must be painted a different color.
+
+Let's analyze the coloring:
+
+1. The innermost circle can be any of the three colors (red, blue, or yellow).
+
+2. The next circle must be a different color from the innermost circle.
+
+3. The third circle must be a different color from the second circle.
+
+4. The fourth circle must be a different color from the third circle.
+
+5. The outermost circle must be a different color from the fourth circle.
+
+Given that there are three colors and each circle must be a different color from its neighbors, the number of ways to color the circles is the number of permutations of the three colors. This is calculated as  $3!$  (3 factorial), which is 6. Therefore, the number of different ways Cynthia can paint the figure is 6.
+
+The number of different ways Cynthia can paint the figure is 6.
+
+# Abstract
+
+Large Language Models have demonstrated remarkable reasoning capability in complex textual tasks. However, multimodal reasoning, which requires integrating visual and textual information, remains a significant challenge. Existing visual-language models often struggle to effectively analyze and reason visual content, resulting in suboptimal performance on complex reasoning tasks. Moreover, the absence of comprehensive benchmarks hinders the accurate assessment of multimodal reasoning capabilities. In this paper, we introduce R1-Onevision, a multimodal reasoning model designed to bridge the gap between visual perception and deep reasoning. To achieve this, we propose a cross-modal reasoning pipeline that transforms images into formal textual representations, enabling precise language-based reasoning. Leveraging this pipeline, we construct the R1-Onevision dataset which provides detailed
+
+step-by-step multimodal reasoning annotations across diverse domains. We further develop the R1-Onevision model through supervised fine-tuning and reinforcement learning to cultivate advanced reasoning and robust generalization abilities. To comprehensively evaluate multimodal reasoning performance across different grades, we introduce R1-Onevision-Bench, a benchmark aligned with human educational stages, covering exams from junior high school to university and beyond. Experimental results show that R1-Onevision achieves state-of-the-art performance, outperforming models such as GPT-4o and Qwen2.5-VL on multiple challenging multimodal reasoning benchmarks. Code, dataset and benchmark are available at https://github.com/Fancy-MLLM/R1-Onevision
+
+# 1. Introduction
+
+Recent language reasoning models like Deepseek-R1 [8], chain-of-thought prompting [28], and Cumulative Reasoning [39] have achieved remarkable progress in solving complex problems including coding [3, 7], mathematics [5, 10],
+
+and science [27]. However, multimodal reasoning remains a largely underexplored challenge. Unlike textual reasoning, multimodal reasoning requires the model to iteratively extract, structure, and verify information from images. Existing visual-language models often fail to organize available information and conduct in-depth reasoning processes, leading to failures in visual reasoning tasks.
+
+Current research on visual-language models has increasingly emphasized step-by-step reasoning. Some approaches, such as Llava-CoT [32] and Llama-V-o1 [24], employ a predefined thinking structure to constrain the model's reasoning process, limiting its robustness and creative potential. While such structured templates improve consistency, they often lead to shallow reasoning with limited comprehension. The others, like MAmmoTH-VL [9], rely on direct imitation of curated ground-truth answers, causing models to generate responses directly without a trial-and-error manner. Consequently, these models may fail to generalize beyond their training distributions. An example of these limitations is shown in Fig. 1. DeepseekR1 suffers from perception errors due to incomplete image descriptions from GPT-4o [19], while Qwen2.5-VL [2], despite its strong multimodal capabilities, lacks deep reasoning ability and ultimately fails to solve the problem. These challenges highlight the limitations of current multimodal reasoning approaches, which either impose rigid frameworks that restrict generalization or fail to provide humanlike thinking to accurately process visual information.
+
+In addition, there is a lack of comprehensive benchmarks for evaluating multimodal reasoning capability across a diverse range of tasks. Existing benchmarks used by open-compass [6] mainly focus on mathematical problems, such as MathVision [25], MathVista [17], and WeMath [22]. Although some more challenging datasets, like HumanEvalV [37], Humanity's Last Exam [20], and ZeroBench [23], aim to assess complex diagram understanding or broader knowledge proficiency, these benchmarks remain specialized, covering only limited aspects of reasoning.
+
+In this work, we address these challenges by introducing a cross-modal reasoning pipeline to construct a multimodal reasoning dataset, a post-training strategy to empower reasoning capabilities, and a comprehensive multimodal reasoning benchmark. First, we propose a cross-modal reasoning pipeline that transforms images into visual formal representations and allows language models to process and reason over images precisely. We construct the R1-Onevision dataset to provide a detailed step-by-step multimodal reasoning process over diverse domains, including natural scenes, charts, mathematical expressions, and science. Second, we employ a two-stage post-training strategy to train our R1-Onevision model with advanced reasoning abilities. The supervised finetuning (SFT) stage cultivates coherent thinking patterns and
+
+output structures using our R1-Onevision dataset. The reinforcement learning (RL) stage strengthens both the model's reasoning performance and its generalization across diverse tasks. Third, to evaluate multimodal reasoning models, we introduce R1-Onevision-Bench, a comprehensive benchmark explicitly designed to assess "grade-level" reasoning performance across scientific domains in the human educational system: mathematics, physics, chemistry, biology, and logical deduction. Finally, extensive experiments on several benchmarks, including MathVision [25], MathVerse [38], MathVista [17], WeMath [22] and our R1-Onevision-Bench, demonstrate the superior multimodal reasoning performance of our R1-Onevision model.
+
+Our main contributions are summarized as follows:
+
+- We present a cross-modal reasoning pipeline to construct R1-Onevision Dataset which encompasses a broad spectrum of images, questions and their reasoning process.  
+- We introduce R1-Onevision, a visual language reasoning model designed for complex problem-solving.  
+- We build R1-Onevision-Bench to assess multimodal reasoning performance across different educational levels and subject areas in a course-aware manner.  
+- Extensive experiments show the superiority of R1-Onevision compared to the baseline Qwen2.5-VL model and closed-source models like GPT-4o.
+
+# 2. Related Work
+
+Multimodal Large Language Models. MLLMs have shown significant potential in a wide range of multimodal tasks. [2, 4, 18, 26] achieve excellent visual understanding ability by integrating both visual and textual data. Recently, Multimodal Large Language Models [9, 31] demonstrate the advanced reasoning abilities when interpreting visual tasks. In addition, some studies [24, 31] introduce plan-based CoT prompting to guide models to generate intermediate information for predicting final answers. LLaVA-CoT [31] introduces a novel VLM designed to conduct visual reasoning, demonstrating exceptional performance on tasks that require structured thinking and reasoning. Based on LLaVA-CoT, LlamaV-o1 [24] introduces a multi-step curriculum learning approach, where tasks are progressively organized to facilitate incremental skill acquisition and problem-solving. CoMCTS [33] introduces the concept of collective learning into "tree search" for efficient reasoning-path searching and learning. In this paper, we propose R1-Onevision, which uses supervised fine-tuning and reinforcement learning during the post-training phase to obtain reasoning ability across different tasks.
+
+Large Language Model Reasoning. The development of robust reasoning capabilities in Large Language Models (LLMs) has been a focal point of research [1, 11, 15, 21]. Some LLMs understand and solve questions by learning to
+
+![](images/9b07d336561ddd1264bf97c87600858a87162261a05a9eff00583114ba1865e2.jpg)  
+Figure 2. Overview of our R1-Onevision framework. The cross-modal reasoning pipeline begins with data preparation, integrating visual formal descriptions to enhance reasoning. We employ role-playing strategies to generate the R1-Onevision dataset with high-quality reasoning data. Post-training consists of supervised fine-Tuning to learn reasoning manner, followed by rule-based Reinforcement Learning to improve generalization across multimodal tasks.
+
+create each intermediate step of the reasoning involved till the final answer. For example, Chain-of-Thought (CoT) prompting, where a complex question is decomposed into intermediate reasoning steps, has shown promise in guiding LLMs to structured solutions [29, 34]. Since certain visual tasks, such as solving Sudoku puzzles, urgently require multimodal large language models (MLLMs) to provide step-by-step reasoning capabilities, it is crucial to develop appropriate methods to enhance the performance of multimodal foundational models.
+
+Visual Reasoning Benchmarks. With the advancement of model capabilities in visual reasoning, an increasing number of studies have proposed various benchmarks to evaluate the reasoning abilities of these models [12, 14, 36]. The MATH-Vision (MATH-V) [25] dataset collects 3,040 high-quality mathematical problems with visual contexts sourced from real math competitions. DynaMATH [40] provides a dynamic visual math benchmark specifically designed to evaluate the mathematical reasoning robustness of VLMs. In this paper, we introduce a comprehensive benchmark designed to evaluate "grade-level" reasoning performance across scientific domains in the educational system.
+
+# 3. Method
+
+Multimodal reasoning requires a comprehensive understanding of both visual and textual modalities, yet existing models often fail to understand visual content and struggle with high-level reasoning. To bridge this gap, we introduce a cross-modal reasoning pipeline that transfers reasoning capabilities of language models to visual modality through formal visual representations. Further, we employ a post-training strategy to stabilize reasoning processes and improve generalization across diverse multimodal tasks.
+
+# 3.1. Cross-Modal Reasoning Pipeline
+
+Our cross-modal reasoning pipeline is designed to bridge the gap between language reasoning models and vision models by integrating visual formal representations. Formal language is a structured system with strict syntactic and semantic constraints that eliminate ambiguity, ensuring logical consistency. With formal description of visual content, language reasoning models are able to see and reason over image elements. We use DeepSeek-R1 [8] to generate reasoning processes on LLaVA-OneVision [16] and collect these data into the R1-Onevision dataset. Figure 2 illustrates the cross-modal reasoning process. Examples of the generated data are provided in the supplementary.
+
+Data Curation and Filtering. For visual reasoning, we aggregate diverse multimodal datasets covering natural images, OCR-based text extraction, charts, mathematical expressions, and scientific reasoning problems, selecting only those that support structured reasoning. The final dataset incorporates components from the LLaVA-OneVision dataset [16], augmented with domain-specific datasets tailored for complex inference tasks.
+
+Image Formal Description. A key feature of our pipeline lies in its use of formal language-based annotations. To achieve this, we leverage a combination of GPT-40, Grounding DINO, and EasyOCR to translate visual image content into formal textual description. We outline the annotation process below and provide details of the prompt design in the Appendix ??
+
+- Charts & Diagrams: We prompt GPT-4o to generate structured representations, such as SPICE for circuit schematics, PlantUML or Mermaid.js for flowcharts, HTML for UI layouts, CSV/JSON for tables, and Matplotlib for annotated charts.  
+- Natural Scenes: We enhance images with fine-grained spatial description by leveraging Grounding DINO to extract bounding box annotations of key elements and GPT-4o to generate descriptive captions.  
+- Text-only Images: When dealing with images containing printed or handwritten text, we employ EasyOCR to extract text with positions and use GPT-4o to reconstruct the original document.  
+- Images with Visual and Textual Content: We integrate GPT-4o-generated captions, Grounding DINO bounding boxes, and EasyOCR-extracted text to ensure both textual and visual elements are accurately captured.  
+- Mathematical Images: For images containing mathematical content, we employ GPT-4o to propose reasoning strategies to guide the inference process.
+
+Reasoning Process Generation. Given an image, we prompt language reasoning model with its dense captions and questions to construct cross-modal Chain-of-Thought (CoT) data. While the original Chain-of-Thought (CoT) approach offered a structured reasoning path based on textual captions, it inherently lacked the essential visual component—the ability to directly “see” and interpret the image. To address this limitation, we propose a Role-Playing strategy that emulates human-like visual comprehension. This method involves iteratively revisiting the image, refining its understanding, and enhancing the fidelity of the reasoning process. This process improves multimodal coherence and ensures a contextually rich reasoning process.
+
+Quality Assurance. To ensure the reliability of generated reasoning process, we employ GPT-4o to remove inaccurate, irrelevant, or inconsistent CoT steps. This step guarantees a high-quality dataset for multimodal reasoning.
+
+![](images/cae5599dcd930057f32874bbc8f87dedbfcdf71abf1733cf51ddd4bcabaf2272.jpg)  
+R1-Onevision Dataset  
+Figure 3. The data distribution of R1-Onevision dataset. R1-Onevision consists of  $155\mathrm{k}$  data, including Science, Math, General and Doc/Chart/Screen.
+
+R1-Onevision Dataset. Finally, as shown in the Figure 3, the R1-Onevision dataset is a carefully crafted tool designed to push the boundaries of multimodal reasoning. R1-Onevision encompasses a wide range of domains, including science, mathematics, chart data, and general real-world scenarios, totaling over  $155\mathrm{k}$  carefully curated samples. R1-Onevision serves as a rich resource for developing visual reasoning model.
+
+# 3.2. Post-Training Strategy
+
+To enhance multimodal reasoning capabilities, we introduce a two-stage post-training strategy consisting of Supervised Fine-Tuning (SFT) and rule-based Reinforcement Learning (RL). SFT stabilizes the model's reasoning process and standardizes its output format, while RL further improves generalization across diverse multimodal tasks.
+
+# 3.2.1. Supervised Fine-Tuning
+
+Leveraging the R1-Onevision dataset, we enhance the reasoning capabilities of visual language models through SFT. SFT stabilizes the model output format and cultivates a more sophisticated reasoning process in the large-scale model. This approach not only standardizes the output but also lays a solid foundation, enabling subsequent RL to achieve significant performance gains.
+
+# 3.2.2. Reinforcement Learning on the SFT Model
+
+Building upon the SFT-trained model, we employ rule-based reinforcement learning (RL) to optimize structured reasoning and ensure output validity. Specifically, we define two reward rules inspired by R1 and update the model using Group Relative Policy Optimization (GRPO). The RL stage further encourages the model to generate reliable outputs and enhances the generalizability of the model.
+
+Rule-Based Rewards. As illustrated in the Reinforcement Learning part of Figure 2, we define two reward rules that assess the generated answers from two perspectives:
+
+- Format Reward: In order to ensure the existence of the reasoning process, the format reward rule requires that the response must follow a strict format where the model's reasoning is enclosed between <think> and </think>. A regular expression ensures the presence and correct ordering of these reasoning markers.  
+- Accuracy Reward: The accuracy reward requires the answer to be enclosed within <answer> and </answer> so that it can be extracted via a regular expression and compared against the ground truth to measure correctness. For deterministic tasks such as math problems, the final answer must be provided in a specified format (e.g., within a box) to enable reliable rule-based verification. In cases like object detection, the reward is determined by Intersection over Union (IoU) score with ground truth.
+
+Group Relative Policy Optimization. We employ GRPO to achieve balanced integration of consistent policy updates and robust reward signals in a controlled manner. For each token in the generated answer, GRPO first computes the log probabilities under both the new policy  $(\pi(\theta))$  and a reference policy. GRPO then calculates a ratio of these probabilities and clip it to the range  $[1 - \epsilon, 1 + \epsilon]$  to prevent overly large updates. The normalized reward (serving as the advantage) is used in a PPO-style loss:
+
+$$
+\mathcal {L} _ {\mathrm {c l i p}} = - \mathbb {E} \left[ \min  \left(\operatorname {r a t i o} _ {t} \cdot \operatorname {A d v} _ {t}, \operatorname {c l i p p e d} \operatorname {r a t i o} _ {t} \cdot \operatorname {A d v} _ {t}\right) \right].
+$$
+
+Here,  $\mathrm{Adv}_t$  denotes the advantage function, capturing how much better (or worse) a particular action is compared to a baseline policy value.
+
+To further maintain closeness to the reference distribution, a KL divergence penalty (weighted by  $\beta$ ) is added, yielding the overall loss:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\mathrm {G R P O}} (\theta) = - \mathbb {E} \left[ \min  \left(\operatorname {r a t i o} _ {t} \cdot \operatorname {A d v} _ {t}, \operatorname {c l i p p e d} _ {t} \operatorname {r a t i o} _ {t} \cdot \operatorname {A d v} _ {t}\right) \right. \\ \left. - \beta \cdot \operatorname {K L} \left(\pi_ {\theta} (y \mid x), \pi_ {\text {r e f}} (y \mid x)\right) \right]. \\ \end{array}
+$$
+
+Compared to other methods, the GRPO clipping mechanism prevents extreme policy shifts, while the KL regularization keeps the updated policy aligned with the baseline. This combination ensures that our model integrates rule-based rewards efficiently without compromising training stability.
+
+# 4. Multimodal Reasoning Benchmark
+
+To assess the reasoning capabilities of our R1-Onevision model, we introduce a dedicated multimodal reasoning benchmark—R1-Onevision-Bench. This benchmark is designed to comprehensively evaluate the model's performance across a wide spectrum of reasoning tasks, spanning multiple domains such as mathematics, physics, chemistry, biology, and logical deduction.
+
+<table><tr><td>Statistic</td><td>Number</td></tr><tr><td>Total questions</td><td>942</td></tr><tr><td>- Multiple-choice questions</td><td>783 (83.1%)</td></tr><tr><td>- Free-form questions</td><td>159 (16.9%)</td></tr><tr><td>- Newly collected questions</td><td>942 (100.0%)</td></tr><tr><td>Grades/Categories/Subcategories</td><td>4/5/38</td></tr><tr><td>Number of unique images</td><td>938 (99.6%)</td></tr><tr><td>Number of unique questions</td><td>942 (100.0%)</td></tr><tr><td>Number of unique answers</td><td>152 (16.1%)</td></tr><tr><td>Maximum question length</td><td>390</td></tr><tr><td>Maximum answer length</td><td>54</td></tr><tr><td>Average question length</td><td>127.2</td></tr><tr><td>Average answer length</td><td>2.1</td></tr></table>
+
+Table 1. Key statistics of R1-Onevision-Bench.
+
+Inspired by human educational progression, R1-Onevision-Bench is structured to reflect graded levels of complexity. It includes real-world reasoning tests at the middle school, high school, and university levels, alongside a social test. Table 1 and Figure 4 present detailed information and structure about our benchmark. Notably, all questions in our benchmark are newly collected from publicly available international competitions, university exams, and standardized tests. Our benchmark is entirely independent of the existing benchmarks mentioned in Section 5.1, with no data overlap. This design not only mirrors the stages of cognitive development but also ensures that the evaluation covers both academic and practical reasoning skills.
+
+By integrating diverse problem types and difficulty levels, R1-Onevision-Bench provides a rigorous framework for benchmarking multimodal reasoning. This enables us to better evaluate the grade at which multimodal language models exhibit reasoning capabilities and identify which aspects of knowledge and experience require supplementation to further enhance their performance.
+
+Moreover, our benchmark further subdivides each category into specific subcategories. Figure 5 presents the distribution of tasks across categories, subcategories, and grade levels, along with examples from multiple domains.
+
+# 5. Experiment
+
+In this section, we first introduce the Experimental Setup of R1-Onevision in Section 5.1. Then, we present the main results in Section 5.2. Section 5.3 conducts a detailed evaluation of various models on the R1-Onevision benchmark. Finally, Section 5.4 conducts a systematic analysis to evaluate the importance of various components during training.
+
+# 5.1. Experimental Setup
+
+We evaluate R1-Onevision on several multimodal reasoning benchmarks, including MathVista [17], MathVision [25],
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">MathVision</td><td colspan="2">MathVerse</td><td rowspan="2">MathVista</td><td rowspan="2">WeMath</td></tr><tr><td>ALL</td><td>Vision Only</td></tr><tr><td>Base Model</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Qwen2.5-VL-7B [2]</td><td>25.4</td><td>43.6</td><td>38.2</td><td>63.7</td><td>61.0</td></tr><tr><td>Our Models</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>R1-Onevision-7B</td><td>29.9</td><td>46.4</td><td>40.0</td><td>64.1</td><td>61.8</td></tr><tr><td>Closed-source Models</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GPT-4o [19]</td><td>30.6</td><td>41.2</td><td>34.5</td><td>60.0</td><td>69.0</td></tr><tr><td>Other Models</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>InternVL2.5-8B [4]</td><td>17.1</td><td>35.6</td><td>22.8</td><td>64.5</td><td>53.8</td></tr><tr><td>Qwen2-VL-7B [26]</td><td>21.7</td><td>30.2</td><td>25.4</td><td>61.6</td><td>50.5</td></tr><tr><td>LLaVA-CoT-11B [32]</td><td>-</td><td>-</td><td>22.6</td><td>52.5</td><td>-</td></tr></table>
+
+Table 2. Experimental results on mathematical reasoning benchmarks. Except for LLaVA-CoT-11B, all reported results are based on our reproduced experiments. The highest accuracy is marked in blue.  
+
+<table><tr><td>Method</td><td>Hallusion</td><td>MMStar</td><td>MMVet</td><td>MathVision</td><td>R1-Onevision Bench</td><td>MathVerse Vision Only</td><td>MathVista</td></tr><tr><td>LLaVA-CoT-11B</td><td>47.80</td><td>57.60</td><td>60.30</td><td>19.9</td><td>27.71</td><td>22.6</td><td>52.5</td></tr><tr><td>LlamaV-o1-11B</td><td>63.51</td><td>59.53</td><td>65.40</td><td>14.47</td><td>28.34</td><td>23.48</td><td>54.40</td></tr><tr><td>R1-Onevision-7B</td><td>66.18</td><td>59.76</td><td>68.58</td><td>29.9</td><td>36.2</td><td>40.0</td><td>64.1</td></tr></table>
+
+![](images/7f03f74e137204ca4bc769654d5ca5b64ed8bd6471c44a8ea04cd928ce50aa91.jpg)  
+Figure 4. Overview of R1-Onevision-Bench. This benchmark comprises 38 subcategories organized into 5 domains. The tasks are categorized into four difficulty levels, from 'Junior High School' to 'Social Test' challenges, ensuring comprehensive evaluation of model capabilities across varying complexities.
+
+MathVerse [38] and WeMath [22]. The performance of all models is derived from VLMEvalKit's testing results [6].
+
+We adopt Qwen2.5-VL series as baseline models, and conduct experiments on baselines 3B and 7B to examine the effectiveness of our method. The SFT experiments are conducted with a batch size of 128, a learning rate of 1e-5, and training for one epoch. Then, we perform RL on the CLEVR dataset [13]. We experiment with training subsets of  $10\mathrm{k}$  for a single epoch each. SFT and RL training took 14 hours and 16 hours respectively on 8 NVIDIA A800 GPUs. More details about the dataset construction, training and benchmark are provided in the supplementary.
+
+Table 3. Comparison with previous multimodal large language models for reasoning. We compare our model R1-Onevision-7B with LLaVA-CoT and LlamaV-o1 on both general benchmarks and reasoning benchmarks.  
+
+<table><tr><td>Benchmark</td><td>MathVision</td><td>WeMath</td><td>MathVerse
+(Vision Only)</td><td>R1-Onevision
+Bench</td></tr><tr><td>Reflection times</td><td>1.22</td><td>1.26</td><td>0.91</td><td>1.51</td></tr></table>
+
+Table 4. Results on the reflection capability of R1-Onevision.
+
+# 5.2. Main Results
+
+Table 2 summarizes the quantitative results, showcasing that R1-Onevision consistently outperforms state-of-the-art (SoTA) multimodal methods across the majority of benchmarks. R1-Onevision achieved significant accuracy improvements on MathVerse and MathVision, showing that fine-grained visual-textual alignment and coherent chain-of-thought reasoning effectively enhance performance. It surpasses GPT-4o by  $5.2\%$  on MathVerse ALL,  $5.5\%$  on MathVerse (Vision Only), and  $4.1\%$  on MathVista. On MathVision it reaches  $29.9\%$  accuracy, matching GPT-4o
+
+![](images/7e0824b326e3cf4b0f0fb6ad951dd807e10ba1f7d0111d26c3dabbb6cd631919.jpg)  
+Figure 5. Samples across each category from R1-Onevision-Bench. R1-Onevision-Bench comprises multi-modal questions and answers in math, physics, chemistry, biology and deduction across multiple educational grades that require deep thinking and reasoning.
+
+![](images/80d94795b037fe25870fe5e5c4afe8cc1b8883dfc9860a8dfcb59fd3684b96ba.jpg)
+
+![](images/bc208749b809209e019fd4c65f169cbe9b78e27abf2348e90f037cff515e7629.jpg)
+
+![](images/8e91e40d5371a2f6e739a934bab026b680a58c76f67df2e8ed94c6412532e7d2.jpg)
+
+![](images/396b78a59f9552b27364bac16ce35e19b6af39832b3d08685be169c12870e80b.jpg)
+
+and underscoring its strong competitiveness.
+
+In Table 3, we compare our method with LLaVA-CoT and LlamaV-o1 on three general benchmarks and four reasoning benchmarks. Notably, MM Vet comprises complex multimodal tasks that require free-form answers. The results show that ours outperforms previous multimodal reasoning models on both general and reasoning benchmarks.
+
+Furthermore, we investigate the reflection capability of our model, as shown in Table 4. Following DeepSeekR1, we count reflection terms in CoT to calculate reflection times. The results demonstrate that our model is capable of self-reflection and self-correction during reasoning process.
+
+# 5.3. Benchmark Analysis
+
+We evaluate the performance of two sets of models in the R1-Onevision benchmark, which categorize into four levels of difficulty (ranging from 'Junior High School' to 'Social Test') and five distinct academic disciplines. The two model groups consist of closed-source VLMs and open-source VLMs, respectively. We deploy VLMEvalkit package to infer in various models. As for scoring in R1-Onevision-Bench, we use GPT-4o-mini to extract the answer and score. The detailed prompt is shown in the supplementary.
+
+<table><tr><td>Benchmark</td><td>SFT+RL</td><td>RL</td></tr><tr><td>MathVision</td><td>29.9</td><td>28.0</td></tr></table>
+
+Table 6. Comparison of MathVision performance between SFT+RL and RL. The best results are marked in blue.
+
+Overall Results on Average Accuracy. Table 5 summarizes the average performance of both closed-source and open-source models. Overall, closed-source systems maintain a clear lead. Gemini-2.0-Flash achieves the highest mean accuracy, exceeding GPT-4o by approximately  $10\%$  and surpassing the  $50\%$  threshold on most tasks. While all models perform well on middle- and high-school
+
+questions, their accuracy declines on university-level and professional-certification exams. Deduction problems remain particularly challenging, with no system exceeding  $40\%$  accuracy. On the open-source side, Qwen2.5-VL-72B has markedly narrowed the gap, achieving an average accuracy of  $52\%$ , which matches the closed-source Claude-3.5 and ranks second only to Gemini-2.0-Flash. Among models with 4B-10B parameters, R1-Onevision, developed based on Qwen2.5-VL, has delivered outstanding results, ranking just behind the top closed-source models.
+
+# 5.4. Ablation Study
+
+# 5.4.1. Analysis of Training Strategy
+
+To evaluate the effectiveness of our training data, we compare two training strategies: (1) Supervised Fine-Tuning (SFT) on our dataset and (2) SFT followed by Reinforcement Learning (RL). As shown in Table 6, RL alone brings limited improvement, demonstrating that prior SFT establishes a robust foundation by aligning the model with high-quality reasoning patterns. Furthermore, as Table 7 shows, SFT alone markedly improves accuracy on MathVision and MathVerse (Vision Only) and achieves comparable performance on MathVerse All, suggesting that our data cultivates systematic reasoning skills. Adding RL stage to the SFT-trained model provides further improvement, guiding the model toward deeper, more deductive reasoning and enabling it to tackle harder, more nuanced problems.
+
+To further validate the effectiveness of formal descriptions and role playing in our dataset construction pipeline, we conduct additional ablation studies. Table 8 shows the SFT performance of CoT data generated from GPT-4o-labeled captions versus formal descriptions. The results demonstrate the superiority of formal description, and adding the role-playing step further improves performance.
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">Avg</td><td colspan="4">Grade</td><td colspan="5">Category</td></tr><tr><td>Junior High School</td><td>High School</td><td>College</td><td>Social Test</td><td>Math</td><td>Physics</td><td>Chemistry</td><td>Biology</td><td>Deduction</td></tr><tr><td colspan="11">Closed-source</td></tr><tr><td>GPT-4o</td><td>49.6</td><td>51.3</td><td>56.2</td><td>45.3</td><td>26.5</td><td>41.3</td><td>52.5</td><td>71.4</td><td>63.4</td><td>26.5</td></tr><tr><td>Gemini-2.0-Flash</td><td>59.1</td><td>56.0</td><td>65.9</td><td>61.2</td><td>39.8</td><td>52.3</td><td>64.4</td><td>74.3</td><td>67.2</td><td>39.8</td></tr><tr><td>Claude-3.5</td><td>52.1</td><td>56.0</td><td>55.9</td><td>49.4</td><td>30.6</td><td>46.5</td><td>54.3</td><td>66.7</td><td>65.7</td><td>30.6</td></tr><tr><td colspan="11">Open-source</td></tr><tr><td>MiniCPM-o-2.6 [35]</td><td>30.4</td><td>33.4</td><td>31.7</td><td>21.2</td><td>31.6</td><td>24.2</td><td>31.7</td><td>30.5</td><td>41.8</td><td>31.6</td></tr><tr><td>InternVL2.5-8B [4]</td><td>29.5</td><td>33.1</td><td>30.6</td><td>21.8</td><td>27.6</td><td>26.3</td><td>24.8</td><td>32.4</td><td>46.3</td><td>27.6</td></tr><tr><td>InternVL2.5-8B-MPO [4]</td><td>32.5</td><td>37.4</td><td>33.6</td><td>24.7</td><td>26.5</td><td>28.7</td><td>29.9</td><td>41.0</td><td>44.8</td><td>26.5</td></tr><tr><td>Qwen2-VL-7B [26]</td><td>30.0</td><td>35.4</td><td>28.5</td><td>25.9</td><td>26.5</td><td>26.3</td><td>28.1</td><td>30.5</td><td>45.5</td><td>26.5</td></tr><tr><td>Qwen2.5-VL-7B [2]</td><td>32.1</td><td>33.8</td><td>37.1</td><td>25.3</td><td>19.4</td><td>31.5</td><td>27.3</td><td>39.0</td><td>47.0</td><td>19.4</td></tr><tr><td>DeepSeek-VL2 [30]</td><td>29.8</td><td>34.4</td><td>30.9</td><td>18.8</td><td>30.6</td><td>23.5</td><td>28.4</td><td>29.5</td><td>47.8</td><td>30.6</td></tr><tr><td>R1-Onevision-7B</td><td>36.2</td><td>40.1</td><td>39.5</td><td>27.6</td><td>26.5</td><td>33.0</td><td>30.2</td><td>49.5</td><td>53.0</td><td>26.5</td></tr><tr><td>Qwen2.5-VL-72B [2]</td><td>52.0</td><td>54.3</td><td>56.7</td><td>54.1</td><td>23.5</td><td>48.9</td><td>55.8</td><td>63.8</td><td>63.4</td><td>23.5</td></tr></table>
+
+Table 5. Evaluation results of closed-source and open-source multimodal models on R1-Onevision benchmark. We divide the benchmark into four grades ('Junior High School', 'High School', 'College', 'Social Test') and five categories ('Math', 'Physics', 'Chemistry', 'Biology', 'Deduction'). The highest accuracy for closed-source and open-source LMMs are marked in green and blue, respectively.  
+
+<table><tr><td>Model</td><td>MathVision</td><td>MathVerse</td><td>MathVerse
+(Vision Only)</td></tr><tr><td>Qwen2.5-VL-7B</td><td>25.4</td><td>43.6</td><td>38.2</td></tr><tr><td>SFT</td><td>26.3</td><td>43.4</td><td>39.7</td></tr><tr><td>SFT+RL</td><td>29.9</td><td>46.4</td><td>40.0</td></tr></table>
+
+Table 7. Ablation study on training strategies.  
+
+<table><tr><td>Formal Description</td><td>Role Playing</td><td>Mathvision</td><td>MathVerse (Vision Only)</td><td>Mathverse</td></tr><tr><td></td><td></td><td>10.86</td><td>31.98</td><td>29.39</td></tr><tr><td>✓</td><td></td><td>21.05</td><td>36.29</td><td>40.43</td></tr><tr><td>✓</td><td>✓</td><td>26.32</td><td>39.72</td><td>43.38</td></tr></table>
+
+Table 8. Ablation study for formal description and role playing  
+
+<table><tr><td>Model</td><td>MathVision</td><td>MathVerse</td><td>MathVerse
+(Vision Only)</td></tr><tr><td>Qwen2.5-VL-3B</td><td>21.7</td><td>34.7</td><td>31.2</td></tr><tr><td>R1-Onevision-3B</td><td>23.7</td><td>38.6</td><td>35.5</td></tr></table>
+
+Table 9. Evaluation of our method using Qwen2.5-VL-3B base model on MathVision, MathVerse and MathVerse (Vision Only).
+
+# 5.4.2. Ablation Study on Model Parameters Variants
+
+To demonstrate the effectiveness of our approach across models of different parameter sizes, we conducted a series of ablation experiments using Qwen2.5-VL-3B as a smaller base model. Specifically, we applied both Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL) to the Qwen2.5-VL-3B model and evaluated its performance. Table 9 shows that R1-Onevision-3B outperforms the Qwen2.5-VL-3B by  $2.0\%$  on MathVision,  $3.9\%$
+
+on MathVerse ALL, and  $4.3\%$  on MathVerse (Vision Only).
+
+These findings highlight the scalability and adaptability of our method across different model sizes.
+
+# 6. Conclusion
+
+In this paper, we introduce a comprehensive framework for multimodal reasoning, built upon a cross-modal formalization approach that unifies data construction, model training, and evaluation. Our framework is designed to address the inherent challenges of integrating visual and textual modalities, enabling models to reason effectively across these domains. The cross-modal reasoning pipeline at the core of this framework bridges the gap between vision and language by leveraging fine-grained alignment mechanisms and structured reasoning pathways. This framework has led to the creation of the R1-Onevision dataset, a rich resource featuring detailed step-by-step reasoning annotations designed to enhance model training and evaluation. The R1-Onevision model, trained using this framework, demonstrates strong multimodal reasoning capabilities and exhibits robust generalization across diverse tasks, from visual question answering to complex problem-solving scenarios. To further support the evaluation of multimodal reasoning, we introduce R1-Onevision-Bench, a comprehensive benchmark that assesses model performance across various dimensions of reasoning in a rigorous and structured manner. Extensive experiments validate the effectiveness of our approach, showing significant improvements over state-of-the-art open-source models.
+
+# Acknowledgment
+
+This work was supported by the National Natural Science Foundation of China (No. 62132017, No. 62302435 and No. 62402434). This work was also funded by Zhejiang Provincial Natural Science Foundation of China (No. LD24F020011 and No. LQ24F020006).
+
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+# R1-VL: Learning to Reason with Multimodal Large Language Models via Step-wise Group Relative Policy Optimization
+
+Jingyi Zhang Jiaxing Huang Huanjin Yao Shunyu Liu Xikun Zhang Shijian Lu Dacheng Tao Nanyang Technological University, Singapore
+
+# Abstract
+
+Recent studies generally enhance MLLMs' reasoning capabilities via supervised fine-tuning on high-quality chain-of-thought reasoning data, which often leads models to merely imitate successful reasoning paths without understanding what the wrong reasoning paths are. In this work, we aim to enhance the MLLMs' reasoning ability beyond passively imitating positive reasoning paths. To this end, we design Step-wise Group Relative Policy Optimization (StepGRPO), a new online reinforcement learning framework that enables MLLMs to self-improve reasoning ability via simple, effective and dense step-wise rewarding. Specifically, StepGRPO introduces two novel rule-based reasoning rewards: Step-wise Reasoning Accuracy Reward (StepRAR) and Step-wise Reasoning Validity Reward (StepRVR). StepRAR rewards the reasoning paths that contain necessary intermediate reasoning steps via a soft key-step matching technique, while StepRAR rewards reasoning paths that follow a well-structured and logically consistent reasoning process through a reasoning completeness and logic evaluation strategy. With the proposed StepGRPO, we introduce R1-VL, a series of MLLMs with outstanding capabilities in step-by-step reasoning. Extensive experiments over 8 benchmarks demonstrate the superiority of our methods. Code is available at link.
+
+# 1. Introduction
+
+Multimodal large language models (MLLMs) have achieved significant progress in vision-language understanding [1, 8, 15, 18, 21, 38, 43, 51]. Recent efforts generally enhance MLLMs' reasoning capabilities by employing supervised fine-tuning (SFT) on high-quality chain-of-thought (CoT) reasoning data generated by powerful models (e.g., GPT4) [37, 44, 46, 54]. For example, Mulberry [46] introduces CoMCTS, which utilizes multiple
+
+![](images/045db299069a7eb8bc9928c4e2c7b9e5de383f4bb1cbcaccdacb79e165ca5aa5.jpg)  
+Figure 1. For MLLMs, online reinforcement learning with outcome-level reward, like in Deepseek-R1's GRPO [34], often suffers from sparse reward issues, where only a few reasoning paths can receive positive/high rewards during training, ultimately leading to poor exploration efficiency and unstable learning process. To tackle this, we propose a novel online reinforcement learning framework that incorporates step-wise reasoning rewards in addition to outcome-level rewards, encouraging MLLMs to iteratively refine their reasoning with dense rewards and resulting in a more stable training process and improved reasoning capability. The experiments are conducted on Qwen2-VL-7b over MathVista.
+
+models to collectively search and identify effective reasoning paths, followed by SFT on the collected reasoning data. However, SFT approaches focus solely on positive reasoning paths (i.e., those leading to correct answers), while the negative reasoning paths are largely neglected. This limitation may cause the model to merely imitate successful reasoning paths without understanding what the flawed and wrong reasoning paths are.
+
+In this work, we aim to enhance the MLLMs' reasoning ability beyond passively imitating positive reasoning paths. Recent advancements in NLP, such as Deepseek-R1 [13] and Kimi-K1.5 [36], have shown great potential in incentivizing the reasoning capability of LLMs via actively selfexploring. The core design of these advances (e.g., GRPO in Deepseek-R1) lies in online reinforcement learning without the need for reward models, which encourages an LLM
+
+to generate a group of reasoning paths and iteratively refine its reasoning process by rewarding the generated reasoning paths based on a rule-based reward function. Typically, an outcome-level reward strategy is used: reasoning paths leading to correct answers receive higher rewards, while those leading to incorrect answers receive lower ones.
+
+An intuitive idea is to directly apply these simple and effective LLM online reinforcement learning methods for MLLMs. However, relying solely on outcome-level rewards, like in Deepseek-R1's GRPO, often suffers from sparse reward issues on MLLM reasoning learning, resulting in suboptimal performance. Specifically, most MLLMs, especially smaller ones, exhibit very limited capability in long-chain reasoning accuracy and validity, whereas only a few MLLM-generated reasoning paths can receive positive/high rewards. This lack of positive reward signals reduces exploration efficiency and leads to an unstable learning process, as illustrated in Fig. 1.
+
+We propose to tackle this sparse reward issue by introducing dense step-wise reasoning rewards in addition to sparse outcome-level rewards. To this end, we design Stepwise Group Relative Policy Optimization (StepGRPO), a new online reinforcement learning framework that enables MLLMs to self-improve reasoning ability via simple, effective and dense step-wise rewarding while using no additional process reward models. Specifically, StepGRPO introduces two novel rule-based reasoning reward mechanisms: Step-wise Reasoning Accuracy Reward (StepRAR) and Step-wise Reasoning Validity Reward (StepRVR).
+
+StepRAR rewards the reasoning path using a soft key-step matching technique that evaluates whether the reasoning path contains key intermediate reasoning steps (i.e., the necessary steps to reach the correct final solution). StepRVR rewards the reasoning path based on a reasoning completeness and logic evaluation method, which assesses whether the reasoning process is well-structured and logically consistent. In this way, StepRAR and StepRVR help mitigate the sparse reward issue by providing informative rewards, even when the reasoning path does not produce the correct final answer – as long as it includes key intermediate reasoning steps or follows a structured and logical reasoning process. With StepRAR and StepRVR, StepGRPO takes the average step-wise reasoning rewards of a group of sampled reasoning paths as a baseline to estimate the advantage for policy optimization. Using the proposed StepGRPO, we develop R1-VL, a series of MLLMs with R1-like step-by-step reasoning capabilities.
+
+The proposed StepGRPO offers two key advantages. 1) Effectiveness. StepGRPO introduces two step-wise reasoning reward mechanisms with group relative optimization, which provide rich and fine-grained step-wise reasoning rewards along the whole reasoning trajectory beyond the final answer. This mitigates the sparse reward issue and encour
+
+ages more structured, logically consistent reasoning trajectories. 2) Efficiency. StepGRPO achieves step-wise reasoning rewarding in a rule-based manner, which provides step-wise reasoning rewards while eliminating the need of process reward models. This significantly reduces computational overhead while maintaining fine-grained step-wise supervisions.
+
+The main contributions of this work are threefold. First, we propose StepGRPO, a new online reinforcement learning framework that enables MLLMs to self-improve reasoning ability via a simple, effective and dense step-wise rewarding. Second, we design two novel rule-based reasoning reward mechanisms, i.e., step-wise reasoning accuracy reward and step-wise reasoning validity reward, which effectively mitigate the sparse reward issue for MLLMs without the need of process reward models. Third, with the proposed StepGRPO, we develop R1-VL, a series MLLMs that have superior reasoning capabilities. Forth, extensive experiments over multiple benchmarks show that R1-VL achieves superior performance compared with state-of-the-art MLLMs.
+
+# 2. Related Work
+
+# 2.1. Multimodal Large Language Model
+
+Multimodal Large Language Models (MLLMs) [1, 8, 15, 18, 21, 38, 43, 51, 52] have shown remarkable advancements across a wide range of vision-language understanding tasks, demonstrating their capabilities in comprehending and analyzing visual contents across various application domains. Early research on MLLMs primarily focuses on text generation based on text prompts and input multiple modalities such as images [20, 21], videos [9, 35]. Recent advancements further enhance the capabilities of MLLMs from various aspects. For example, recent models [25, 42] incorporate multimodal inputs and outputs such as video, audio, and point cloud inputs beyond text and images. In addition, some efforts attempt to adapt MLLMs for domain-specific tasks, such as medical image understanding [17, 19, 55] and document analysis [22, 49]. In this work, we focus on enhancing the reasoning ability of MLLMs in tackling complex reasoning tasks and introduce R1-VL, a series of MLLMs that have superior reasoning capability.
+
+# 2.2. MLLM Reasoning
+
+Inspired by the advances in NLP that show great potential in learning to reason and tackling complex language tasks [29], recent studies attempt to enhance the reasoning capability of MLLM. Generally, current MLLM reasoning methods improve the reasoning capability of MLLM by generating high-quality chain-of-thoughts (CoT) data using powerful model (e.g., GPT-4) and performing supervised
+
+fine-tuning with the collected data [10, 37, 44, 46, 54]. For example, Mulberry [46] introduces Collective Monte Carlo Tree Search (MCTS) into MLLM and proposes CoMCTS which leverages complementary knowledge from multiple models to collaboratively search and identify effective reasoning paths. In addition, recent works [14, 27, 30, 47] attempt to explore online reinforcement learning to improve the MLLMs' reasoning ability. Different from these works, we design StepGRPO that enables MLLM to self-improve the reasoning ability with step-wise reward signals.
+
+# 2.3. Reinforcement Learning
+
+Reinforcement Learning (RL) [16] is a fundamental approach in machine learning, where an agent learns to interact with an environment by taking actions, receiving rewards, and updating its policy to maximize the long-term return. With the rise of large language models (LLMs) [4, 28, 31], Reinforcement Learning with Human Feedback (RLHF) [3] has emerged as a key technique for fine-tuning models using human preference data. RLHF leverages algorithms like Proximal Policy Optimization (PPO) [33] and Direct Preference Optimization (DPO) [32] to guide model behavior for improving the alignment, coherence and helpfulness in response generation.
+
+Recently, RL is increasingly adopted to enhance LLMs' reasoning capabilities [5, 7, 13, 24, 36, 50], especially for mathematical problem solving. The core is to adopt an appropriate reward function or model that evaluates and reinforces high-quality reasoning paths while penalizing low-quality ones, guiding the model's optimization towards more structured and coherent reasoning trajectories using the RL algorithm. For example, ReST-MCTS* [50] trains a process reward model (PRM) for determining the correctness of each reasoning step within reasoning paths. Recent methods have found that using a simple outcome-level rule-based reward function (i.e., the reasoning trajectories leading to correct answer are rewarded with higher score) can already provide an effective and reliable reward signal during the RL process [13, 24, 36]. For example, DeepSeek-R1 [13] demonstrates that group relative policy optimization (GRPO) [34] with outcome-level reward effectively enhances the reasoning capability of LLMs. In this work, we aim for improving the reasoning capability of MLLMs through reinforcement learning and propose StepGRPO, which effectively tackles the sparse reward issue in MLLMs, leading to stable training process and better reasoning capability.
+
+# 3. Method
+
+This section first presents the task formulation, and then introduces the proposed Step-wise Group Relative Policy Optimization (StepGRPO). More details to be elaborated in the ensuing subsections.
+
+# 3.1. Task Formulation
+
+In this paper, we consider a pre-trained MLLM and denote it as a policy model  $\pi_{\theta}$ . Given a multimodal question  $Q$  consisting of an image and a textual task instruction, i.e.,  $Q = \{\text{text}, \text{image}\}$ , the policy model  $\pi$  generates response  $\mathbf{c}$  with a step-by-step reasoning trajectory. Generally, this process can be formulated as a sequence of next token prediction actions, i.e.,  $\mathbf{c} = (a_1, a_2, \dots, a_t, \dots, a_T)$ , where each action  $a_t$  is sampled from the policy model  $\pi_{\theta}$  and  $T$  represents the maximum sequence length. After each action, the new state  $s_{t+1}$  is determined by updating the current state  $s_t$  with the newly generated action  $a_t$ , i.e.,  $s_{t+1} = (s_t, a_t)$ ,  $1 \leq t \leq T$ .
+
+Considering this formulation, the objective of our task is to optimize the policy model  $\pi_{\theta}$  such that it can select better actions based on the previous states, thereby improving reasoning quality. In the context of reinforcement learning (RL), the policy model is generally optimized by maximizing the cumulative reward, where the reward for taking action  $a_{t}$  at state  $s_t$  is denoted as  $r(s_t,a_t,s_{t + 1})$ . Following prior studies [46], we define an action in this paper as generating a reasoning step, which consists of one or more sentences containing multiple word tokens.
+
+# 3.2. Step-wise Group Relative Policy Optimization
+
+We propose Step-wise Group Relative Policy Optimization (StepGRPO), a novel online reinforcement fine-tuning framework that mitigates the sparse reward issue for MLLMs and encourages self-improvement in reasoning ability through simple, effective and dense step-wise reward mechanisms. As illustrated in Fig. 2, StepGRPO consists of two phases: (1) a policy warm-up phase and (2) a step-wise online policy optimization phase. The overall algorithm is shown in Algorithm 1.
+
+# 3.2.1. Policy Warm-up
+
+This phase equips the policy model with fundamental reasoning capabilities, ensuring it can generate proper stepwise reasoning paths before reinforcement learning. During the warm-up phase, the policy model is fine-tuned using a multimodal dataset  $D_{s}$  with Chain-of-Thought (CoT) reasoning path, where each data consists of a multimodal question  $Q$  and a step-by-step reasoning path  $\tau$ , i.e.,  $D_{s} = \{Q^{n}, \tau^{n}\}_{n=1}^{N}$ :
+
+$$
+\mathcal {L} _ {\text {w a r m - u p}} = - \mathbb {E} _ {\tau \sim D _ {s}} [ \sum_ {t = 1} ^ {T} \log (\pi_ {\theta} (a _ {t} | s _ {t})) ]. \tag {1}
+$$
+
+# 3.2.2. Step-wise Online Policy Optimization
+
+This phase enables MLLMs to self-improve their reasoning ability via online reinforcement learning, mitigating the sparse reward issue through step-wise reasoning rewards. As illustrated in Fig. 2, for each question  $Q \in D_{s}$ ,
+
+![](images/63b7d9c10823788b7fca5a6efb71f874524cb97c2b342c5721d0f68e6864f343.jpg)  
+Question: In the given diagram, triangle ABC has AD as its median and point E is the midpoint of AD. If the area of triangle ABC is 12, what is the area of triangle ABE?
+
+![](images/35a83766051badbf8ccf7672900d5d5649543e4300c4b88813f9239a33b4893f.jpg)  
+Answer: Step 1: Since AD is a median, it divides triangle ABC into two equal areas: ABD and ACD. Step 2: Segment AE is half of AD, splitting triangle ABD into two triangles of equal area: ABE and BED. Step 3: The area of triangle ABD is half of triangle ABC, which is  $\frac{\text{frac}}{12} \times \frac{1}{2} = 6$ . Step 4: Since E is the midpoint of AD, triangle ABE is half of triangle ABD. Therefore, the area of triangle ABE is  $\frac{\text{frac}}{6} \times \frac{1}{2} = 3$ . The final answer is 3.  
+(a) Step-wise Reasoning Accuracy Reward  
+Figure 2. Overview of the proposed StepGRPO. StepGRPO consists of two phases: a policy warm-up phase and a step-wise online policy optimization phase. After the warm-up, the policy model  $\pi_{\theta}$  generates a group of reasoning paths  $\{\mathbf{c}^i\}_{i=1}^M$  and assigns step-wise rewards using two proposed mechanisms: Step-wise Reasoning Accuracy Reward (StepRAR) and Step-wise Reasoning Validity Reward (StepRVR). StepRAR rewards reasoning paths that contain key intermediate steps, identified using a soft key-step matching technique. StepRVR rewards reasoning paths based on completeness and logical consistency, ensuring they are well-structured. StepGRPO then estimates the advantage  $\hat{A}$  for policy optimization by using the average step-wise reasoning reward of a group of sampled reasoning paths as a baseline. Examples for StepRAR and StepRVR are illustrated in (a) and (b), respectively.
+
+# Pre-extracted key steps with Augmentations:
+
+1. AD is a median; median is  $AD$  
+2. equal area; ...  
+3. AE is half of AD;  $AE = 1 / 2AD$  
+4. frac{12}{2} {2} = 6;  $\underline{12 / 2} = 6,\dots$  
+5. E is the midpoint; ..  
+6. frac{6}{2} = 3; 6/2 = 3. ...
+
+# Soft key-step matching :
+
+Description: The image shows ...; #Rationale: The question asks for the area...; #Step1: ... we find AD is a median of ...; #Step2: ... AE splits triangle ABD ...; #Step3: ... The area of triangle ABD is  $12/2 = 6$ , ..., and the area of triangle ABE is frac{6}{2} = 3. #The final answer is: 3. Step-wise Matching score: 3/6
+
+# (b) Step-wise Reasoning Validity Reward
+
+Description  $\rightarrow$  #Rationale  $\rightarrow$  # Step1  $\rightarrow$  ...  $\rightarrow$  #Step  $N\rightarrow$  #Answer.
+
+i. Reasoning completeness
+
+Description  $\rightarrow$  #Rationale  $\rightarrow$  #Answer. Missing reasoning steps
+
+Description  $\rightarrow$  # Step1  $\rightarrow$  ...  $\rightarrow$  #Step  $N\rightarrow$  #Answer. Missing rationale
+
+ii. Reasoning logic
+
+Description  $\rightarrow$  #Rationale  $\rightarrow$  #Answer  $\rightarrow$  #Step1...  $\rightarrow$  #Step N.  
+#Description  $\rightarrow$  #Step3  $\rightarrow$  #Rationale  $\rightarrow$  ...  $\rightarrow$  #Step 1  $\rightarrow$  #Answer
+
+the policy model  $\pi_{\theta}$  first generates a group of  $M$  reasoning trajectories via multiple rollouts, i.e.,  $\{\mathbf{c}^i\}_{i=1}^M$ , where  $\mathbf{c}^i = (a_1^i, a_2^i, \ldots, a_t^i, \ldots, a_T^i)$ . After obtaining a group of  $M$  reasoning trajectories, we employ our proposed step-wise reasoning rewards to evaluate and reward each generated reasoning trajectory. Specifically, we introduce two types of rule-based step-wise rewards, i.e., step-wise reasoning accuracy (StepRAR) reward and step-wise reasoning validity reward (StepRVR).
+
+Step-wise reasoning accuracy reward (StepRAR) reduces the effect of learning from sparse reward by additionally rewarding reasoning paths that contain correct intermediate reasoning steps contributing to the final solution. Specifically, for each question  $Q$ , we pre-extract a set of key reasoning steps  $\mathbf{v} = \{v_{1}, v_{2}, \ldots\}$  from the corresponding reasoning path  $\tau$  in dataset  $D_{s}$ . We define key steps as the essential variables and equations that directly contribute to the final solution, and prompt GPT-4 to extract several key steps from the reasoning path for each question. To ensure efficient reward assignment, we refine the extracted steps by removing redundant content and retaining only the core few words necessary for reasoning. Furthermore, we
+
+augment each extracted key step into multiple equivalent formats to allow more flexible and accurate matching, preventing missed matches due to math-related formatting differences. For example, a mathematical expression such as " $\frac{6}{3} = 2$ " is augmented to "  $6 / 3 = 2$  " or "6 divided by 3 equals 2".
+
+With the extracted key reasoning steps  $\mathbf{v} = \{v_{1}, v_{2}, \ldots\}$  and such soft marching mechanism, we calculate a match score for each generated reasoning path based on the ratio of matched key steps, i.e.,  $k^{i} = |\mathbf{v}_{\text{match}}| / |\mathbf{v}|$ . Then, StepRAR for  $1 \leq t \leq T$  is defined as:
+
+$$
+r _ {a u c} ^ {i} \left(s _ {t}, a _ {t}, s _ {t + 1}\right) = \left\{ \begin{array}{l l} 1 + \alpha k ^ {i}, & \operatorname {a n s} \left(s _ {t + 1}\right) = y, \\ \alpha k ^ {i}, & \operatorname {a n s} \left(s _ {t + 1}\right) \neq \text {n u l l}, \neq y, \\ 0, & \operatorname {a n s} \left(s _ {t + 1}\right) = \text {n u l l}, \end{array} \right. \tag {2}
+$$
+
+where  $y$  is the ground-truth answer extracted from CoT reasoning path.
+
+By leveraging pre-extracted key reasoning steps, StepRAR efficiently provides additional supervision with a simple soft matching mechanism, ensuring the model learns meaningful reasoning processes instead of guessing
+
+answers randomly.
+
+Step-wise reasoning validity reward (StepRVR) aims for ensuring the generated paths adhere to a logically structured and coherent progression beyond the reasoning accuracy. Prior studies [44, 46] have demonstrated structural reasoning, such as problem decomposition and progressive reasoning, facilitates more accurate and interpretable reasoning processes, as they encourage models to break down complex problems into multiple intermediate steps rather than direct answer generation.
+
+Inspired by these findings, we incorporate step-wise reasoning validity to reinforce well-organized reasoning paths that follow an expected logical flow. Specifically, we define StepRVR using two key criteria: reasoning completeness  $\delta^c$  and reasoning logic  $\delta^l$ . Reasoning completeness requires the response to include three essential components, i.e., a background analysis involving image description and rationale analysis to establish context, a step-by-step reasoning process and a final answer. In addition to the reasoning completeness, reasoning logic ensures the reasoning path to follow a logical progression, where the background analysis must come before solution steps and the final answer should only appear after reasoning steps are complete.
+
+With these two criteria, we define StepRVR as
+
+$$
+r _ {v a l} ^ {i} \left(s _ {t}, a _ {t}, s _ {t + 1}\right) = \left\{ \begin{array}{l l} 1, & \mathbb {I} \left(\delta^ {c} \left(s _ {t + 1}\right)\right) \cdot \mathbb {I} \left(\delta^ {l} \left(s _ {t + 1}\right)\right) = 1, \\ 0, & \text {o t h e r w i s e ,} \end{array} \right. \tag {3}
+$$
+
+where the reasoning trajectory is rewarded only if it satisfies both completeness and logical coherence. By enforcing this, StepRVR helps the model produce structured, interpretable and logically sound reasoning trajectories, enhancing both the quality and reliability of generated responses.
+
+Optimization with the step-wise rewards. After obtaining two types of step-wise rewards, we compute the overall reward for each reasoning path as  $r^i = r_{auc}^i + r_{val}^i$ , and repeatedly compute the rewards for all generated reasoning paths, i.e.,  $\{r^1, r^2, \dots, r^M\}$ .
+
+To estimate the advantage of each reasoning trajectory, we normalize its reward relative to the group as follow:
+
+$$
+\hat {A} ^ {i} = \frac {r ^ {i} - \operatorname {m e a n} \left(\left\{r ^ {1} , r ^ {2} , \dots , r ^ {M} \right\}\right)}{\operatorname {s t d} \left(\left\{r ^ {1} , r ^ {2} , \dots , r ^ {M} \right\}\right)}, \tag {4}
+$$
+
+where the mean group reward serves as the baseline, and  $\hat{A}_i$  measures how much better or worse  $r_i$  is compared to other reasoning trajectories within the group. Following this, we optimize the policy model with the loss defined as:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\text {S t e p R L}} = - \underset {Q \in D _ {s}} {\mathbb {E}} \left[ \frac {1}{M} \sum_ {i = 1} ^ {M} \left(\frac {\pi_ {\theta} \left(\mathbf {c} ^ {i} \mid Q\right)}{\left[ \pi_ {\theta} \left(\mathbf {c} ^ {i} \mid Q\right) \right] _ {\text {n o g r a d}}} \hat {A} ^ {i} \right. \right. \tag {5} \\ - \beta D _ {K L} \left(\pi_ {\theta} | | \pi_ {r e f}\right) ], \\ \end{array}
+$$
+
+Algorithm 1 Step-wise Group Relative Policy Optimization  
+Input: Policy model  $\pi_{\theta}$  initialized by a pre-trained  
+MLLM; a multimodal dataset  $D_{s} = \{Q^{n},\tau^{n}\}_{n = 1}^{N}$    
+Output: Trained policy model  $\pi_{\theta}$    
+Policy warm-up:  
+for iter  $= 1$  to  $N$  do Sample  $\{Q,\tau \} \in D_s$  Optimize policy model  $\pi_{\theta}$  by Eq. 1  
+end for  
+Step-wise online policy optimization:  
+for iter  $= 1$  to  $N$  do Sample  $\{Q,\tau \} \in D_s$  Generate a group of reasoning paths  $\{\mathbf{c}^i\}_{i = 1}^M\sim \pi_\theta$  Obtain step-wise rewards  $\{r^i\}_{i = 1}^M$  by Eqs. 2-3 Obtain relative advantages  $\{\hat{A}^i\}_{i = 1}^M$  by Eq. 4 Optimize policy model  $\pi_{\theta}$  by Eqs. 5-6  
+end for  
+return policy model  $\pi_{\theta}$
+
+where KL divergence is adopted to regularize the policy model, preventing excessive deviation from the reference model. The reference model is typically initialized as the same model as the policy model but remains frozen during RL training. The KL divergence between the policy model and the reference model is estimated as in [34]:
+
+$$
+D _ {K L} \left(\pi_ {\theta} \right\| \pi_ {r e f} = \frac {\pi_ {r e f} \left(\mathbf {c} ^ {i} \mid Q\right)}{\pi_ {\theta} \left(\mathbf {c} ^ {i} \mid Q\right)} - \log \frac {\pi_ {r e f} \left(\mathbf {c} ^ {i} \mid Q\right)}{\pi_ {\theta} \left(\mathbf {c} ^ {i} \mid Q\right)} - 1. \tag {6}
+$$
+
+# 4. Experiment
+
+This section presents experiments including datasets and implementation details, main experimental results, ablation studies and discussion, respectively. More details are to be described in the ensuing subsections.
+
+# 4.1. Datasets
+
+For policy warm-up, we adopt Mulberry-260k [46] for supervised fine-tuning. For step-wise online policy optimization, we randomly sample 10K data from Mulberry-260k as our training data. For evaluation, we adopt 8 widely-used multimodal benchmarks for comprehensively evaluating our proposed StepGRPO, including MathVista [23], MMStar [6], Math-Vision [40], ChartQA [26], DynaMath [56], HallusionBench [12], MathVerse [53], MME [11] and MM-Reason [45]. These multimodal benchmarks cover a wide range of tasks from mathematical reasoning, chart understanding, visual hallucination and general visual understanding.
+
+# 4.2. Implementation Details
+
+Our proposed StepGRPO is generally applicable to different MLLMs. In our experiments, we adopt two state-of-the-art
+
+<table><tr><td>Method</td><td>MathVista</td><td>MMStar</td><td>Math-V</td><td>ChartQA</td><td>DynaMath</td><td>HallBench</td><td>MathVerse</td><td>MMEsum</td><td>MMReason</td><td>AVG</td></tr><tr><td colspan="11">Closed-Source Model</td></tr><tr><td>GPT-4o [15]</td><td>63.8</td><td>63.9</td><td>30.3</td><td>85.7</td><td>63.7</td><td>55.0</td><td>39.4</td><td>2329</td><td>21.1</td><td>56.2</td></tr><tr><td>Claude-3.5 Sonnet [1]</td><td>67.7</td><td>62.2</td><td>-</td><td>90.8</td><td>64.8</td><td>55.0</td><td>-</td><td>1920</td><td>-</td><td>-</td></tr><tr><td colspan="11">Open-Source Model</td></tr><tr><td>Cambrain-1-8B [38]</td><td>49.0</td><td>-</td><td>-</td><td>73.3</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>MM-1.5-7B [51]</td><td>47.6</td><td>-</td><td>-</td><td>78.6</td><td>-</td><td>-</td><td>-</td><td>1861</td><td>-</td><td>-</td></tr><tr><td>Idefics3-LLaMA3-8B [18]</td><td>58.4</td><td>55.9</td><td>-</td><td>74.8</td><td>-</td><td>-</td><td>-</td><td>1937</td><td>-</td><td>-</td></tr><tr><td>InternVL2-8B [8]</td><td>58.3</td><td>61.5</td><td>-</td><td>83.3</td><td>39.7</td><td>-</td><td>-</td><td>2210</td><td>-</td><td>-</td></tr><tr><td>MiniCPM-V-2.6-8B [48]</td><td>60.6</td><td>57.5</td><td>-</td><td>-</td><td>-</td><td>48.1</td><td>-</td><td>2348</td><td>-</td><td>-</td></tr><tr><td>DeepSeek-VL2-MOE-4.5B [43]</td><td>62.8</td><td>61.3</td><td>-</td><td>86.0</td><td>-</td><td>-</td><td>-</td><td>2253</td><td>11.5</td><td>-</td></tr><tr><td colspan="11">Reasoning Model</td></tr><tr><td>LLaVA-CoT-11B [44]</td><td>54.8</td><td>57.6</td><td>-</td><td>-</td><td>-</td><td>47.8</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>LLaVA-Reasoner-8B [54]</td><td>50.6</td><td>54.0</td><td>-</td><td>83.0</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Insight-V-8B [10]</td><td>49.8</td><td>57.4</td><td>-</td><td>77.4</td><td>-</td><td>-</td><td>-</td><td>2069</td><td>-</td><td>-</td></tr><tr><td>Mulberry-7B [46]</td><td>63.1</td><td>61.3</td><td>-</td><td>83.9</td><td>45.1</td><td>54.1</td><td>-</td><td>2396</td><td>11.8</td><td>-</td></tr><tr><td>LlamaV-o1-11B [37]</td><td>54.4</td><td>59.4</td><td>-</td><td>-</td><td>-</td><td>63.5</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Vision-R1-7B [14]</td><td>73.5</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>52.4</td><td>-</td><td>-</td><td>-</td></tr><tr><td>LMM-R1 [30]</td><td>63.2</td><td>58.0</td><td>26.3</td><td>-</td><td>-</td><td>-</td><td>41.5</td><td>-</td><td>-</td><td>-</td></tr><tr><td>R1-ShareVL-7B [47]</td><td>75.4</td><td>67.0</td><td>29.5</td><td>-</td><td>-</td><td>-</td><td>52.8</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Qwen2-VL-2B [41]</td><td>43.0</td><td>48.0</td><td>12.4</td><td>73.5</td><td>24.9</td><td>41.7</td><td>19.7</td><td>1872</td><td>7.7</td><td>37.5</td></tr><tr><td>R1-VL-2B (Ours)</td><td>52.1</td><td>49.8</td><td>17.1</td><td>75.2</td><td>29.4</td><td>44.0</td><td>26.2</td><td>2048</td><td>8.3</td><td>41.6</td></tr><tr><td>Qwen2-VL-7B [41]</td><td>58.2</td><td>60.7</td><td>16.3</td><td>83.0</td><td>42.1</td><td>50.6</td><td>32.5</td><td>2327</td><td>11.9</td><td>48.7</td></tr><tr><td>R1-VL-7B (Ours)</td><td>63.5</td><td>60.0</td><td>24.7</td><td>83.9</td><td>45.2</td><td>54.7</td><td>40.0</td><td>2376</td><td>12.5</td><td>52.1</td></tr><tr><td>Qwen2.5-VL-7B [2]</td><td>68.2</td><td>63.9</td><td>25.1</td><td>87.3</td><td>53.2</td><td>52.1</td><td>49.2</td><td>2347</td><td>17.3</td><td>55.5</td></tr><tr><td>R1-VL-7B* (Ours)</td><td>74.3</td><td>66.2</td><td>28.2</td><td>87.7</td><td>56.5</td><td>57.2</td><td>52.2</td><td>2395</td><td>17.9</td><td>58.4</td></tr></table>
+
+Table 1. Main experimental results. To comprehensively examine the proposed StepGRPO, we conduct extensive experiments with two baseline models on eight benchmarks, and compare StepGRPO with various state-of-the-art MLLMs.* indicates that the model is trained using Qwen2.5-VL-7B as the base model with the data from [47].  
+
+<table><tr><td rowspan="2">Warm-up</td><td colspan="2">Step-wise reasoning rewards</td><td rowspan="2">MathVista</td></tr><tr><td>StepRAR</td><td>StepRVR</td></tr><tr><td rowspan="2">✓</td><td></td><td></td><td>58.2</td></tr><tr><td></td><td></td><td>61.2</td></tr><tr><td>✓</td><td>✓</td><td></td><td>62.4</td></tr><tr><td>✓</td><td></td><td>✓</td><td>61.9</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>63.5</td></tr></table>
+
+Table 2. Ablation study of StepGRPO over Qwen2-VL-7B.
+
+open-source MLLMs, i.e., Qwen2-VL-2B and Qwen2-VL-7B [41]. For the policy warm-up phase, we set the training batch size to 128. Following prior work [46], we use a learning rate of  $1\mathrm{e}^{-5}$  for Qwen2-VL-2B and  $5\mathrm{e}^{-6}$  for Qwen2-VL-7B, respectively.
+
+For the step-wise online policy optimization phase, we perform 4 rollouts per question  $(M = 4)$  and set the sampling temperature to 1.2 to encourage diverse reasoning paths. The maximum sequence length is set to  $L = 1024$ , ensuring that the model can generate complete reasoning paths. Both the policy model and reference model are ini
+
+tialized from the model after the warm-up, with the reference model frozen during RL training. The policy model's learning rate is  $1\mathrm{e}^{-6}$ , and we set the batch size to 4. We set the coefficient of match score  $\alpha$  to 0.1 to balance its effect. Following [39], the KL divergence coefficient  $\beta$  in Eq. 5 is set to 0.04 by default. All experiments are conducted on 4 H100-80GB GPUs.
+
+# 4.3. Main Experimental Results
+
+We conduct a comprehensive evaluation of R1-VL across eight widely used benchmarks, comparing it with various state-of-the-art MLLMs, as shown in Table 1.
+
+We first compare R1-VL with its baseline models, Qwen2-VL-2B and Qwen2-VL-7B. The baseline models exhibit limited reasoning capability, leading to very few reasoning paths receiving rewards, which negatively impacts the reasoning capability. In contrast, R1-VL with our proposed StepGRPO consistently improves the baseline models by significant margins, achieving  $4.6\%$  improvement over Qwen2-VL-2B and  $3.8\%$  over Qwen2-VL-7B. This improvement is largely attributed to that StepGRPO introduces step-wise reasoning accuracy and validity rewards,
+
+<table><tr><td></td><td colspan="5">Number of generations M per question</td></tr><tr><td>Method</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td></tr><tr><td>R1-VL-7B</td><td>62.5</td><td>62.8</td><td>63.5</td><td>63.2</td><td>63.7</td></tr></table>
+
+which provide rich and informative supervision at each reasoning step, effectively mitigating the sparse reward issue for MLLMs.
+
+In addition, we compare R1-VL with existing state-of-the-art reasoning MLLMs. As shown in Table 1, R1-VL achieves better performance on most benchmarks, particularly in mathematical reasoning tasks. For example, R1-VL-7B surpasses Mulberry-7B and LlamaV-o1-11B by  $0.6\%$  and  $9.3\%$  respectively on the reasoning-intensive benchmark MathVista. Notably, R1-VL-2B even outperforms larger MLLMs. For instance, R1-VL-2B largely outperforms LLaVA-Reasoner-8B and LLaVA-CoT-11B by  $13.1\%$  and  $9.3\%$  on MathVista, respectively. This superior performance demonstrates that StepGRPO effectively enhances MLLMs' reasoning abilities by encouraging self-improvement via step-wise online reinforcement learning, rather than merely imitating positive reasoning paths.
+
+Additionally, we benchmark R1-VL against general MLLMs, including closed-source models such as GPT-4o and Claude-3.5 Sonnet, as well as open-source models like Cambrain-1-8B and DeepSeek-VL2-MOE-4.5B. We observe that R1-VL outperforms most open-source MLLMs and achieves competitive results against closed-source models. For example, R1-VL-7B achieves 63.7 accuracy on MathVista, closely matching GPT-4o's accuracy of 63.8. These results further validate StepGRPO's effectiveness in enhancing the reasoning capabilities of MLLMs.
+
+# 4.4. Ablation Study
+
+We conduct ablation studies for StepGRPO on Qwen2-VL-7B over MathVista benchmark for examining the effect of step-wise reasoning rewards including step-wise reasoning accuracy reward (StepRAR) and step-wise reasoning validity reward (StepRVR), as well as the role of the warm-up phase. As shown in Table 2, involving a warm-up stage improves baseline model to  $61.2\%$ , allowing the model to learn basic reasoning knowledge before reinforcement learning. In addition, including either StepRAR or StepRVR into the online reinforcement learning process outperforms the model with warm-up by large margins, demonstrating that both two types of step-wise rewards contribute to enhancing step-by-step reasoning capabilities. The best performance (i.e.,  $63.7\%$ ) is achieved when both StepRAR and StepRVR are applied together. This shows that StepGRPO effectively improves complex
+
+Table 3. Parameter analysis of  $M$ . The experiments are conducted on Qwen2-VL-7B over MathVista.  
+
+<table><tr><td>Method</td><td>MathVista</td></tr><tr><td>Warm-up</td><td>61.7</td></tr><tr><td>Warm-up + Outcome-level reward</td><td>62.3</td></tr><tr><td>Warm-up + Step-wise reward (Ours)</td><td>63.5</td></tr></table>
+
+Table 4. Effectiveness of the step-wise reasoning rewards. The experiments are conducted on Qwen2-VL-7B over MathVista.
+
+![](images/2e1796fe5e6bd68fae3af1f0b2f358055373843d2e6690a753256a884f36a39f.jpg)  
+Figure 3. Comparison between StepGRPO and SFT. The experiments are conducted on Qwen2-VL-7B over MathVista.
+
+reasoning tasks by reinforcing both the correctness of intermediate steps and the overall logical structure of the reasoning process.
+
+# 4.5. Discussion
+
+Parameter analysis. We conduct the parameter analysis on the number of generations  $M$  in a group with Qwen2-VL7B over benchmark MathVista, analyzing its impact on reasoning performance. As described in Section 3,  $M$  controls the number of generated reasoning trajectories per question during the RL phase. Table 3 shows that a larger  $M$  generally leads to better performance. This is because, in group relative optimization, the baseline reward is estimated as the average reward of all generated reasoning paths. A larger  $M$  results in a more stable and accurate baseline estimation, whereas a small  $M$  may lead to high variance in baseline estimation, making the optimization process less reliable. However, increasing  $M$  also introduces higher computational costs. Therefore, we set  $M = 4$  as the default to balance performance and computational efficiency.
+
+Effectiveness of the step-wise reward. Our proposed stepwise reward mechanism plays a crucial role in mitigating the sparse reward issue by providing fine-grained supervision at each reasoning step. To further validate its effectiveness, we conduct an experiment comparing outcome-level reward against our step-wise reward. Specifically, we evaluate three settings: (1) Warm-up only; (2) Warm-up + Outcome-level Reward, where the model is optimized with outcome-level reward; and (3) Warm-up + Step-wise Re
+
+![](images/47edfcbc925bdd982646d33fc08105899593eafceb9024b31c2f10007f61ac98.jpg)  
+Question: Subtract all red things.  
+Subtract all tiny matte balls. How many objects are left?  
+Correct answer: 5
+
+Qwen2-VL-7B:
+
+First, identify the red objects in the image. There is 1 red object, which is a small red sphere. Incorrect reasoning
+
+Then, subtract the red object from the total number of objects. There are 7 objects in total and subtracting the 1 red object leaves 6 objects. Identify the tiny matte balls in the image. There are 2 tiny matte balls, which are the small green cylinder and the cyan sphere. Subtract the tiny matte balls from the remaining objects.
+
+After subtracting the red object, there are 6 objects left. Subtracting the 2 tiny matte balls leaves 4 objects. Answer: 4
+
+# Mulberry-7B:
+
+Image Description: The image shows several 3D objects on a flat surface. There are two red objects: a small red sphere and a larger green cylinder. Other objects include a yellow cube, a green cylinder, a blue cylinder, a purple cylinder, and a teal sphere.
+
+Rationales: The question asks to subtract all red things and all tiny matte balls. We need to identify these objects in the image and count the remaining ones.
+
+Let's think step by step.
+
+Step 1: Identify and count all red objects. There is one red sphere. Incorrect reasoning Step 2: Identify and count all tiny matte balls. There is one teal sphere, which is not red, so it is not subtracted.
+
+Step 3: Subtract the red objects and tiny matte balls from the total number of objects:  $7 - 1 = 6$
+
+The final answer is: 6
+
+# StepGRPO (Ours):
+
+Image Description:
+
+The image shows a collection of 3D geometric objects on a flat surface. There are various colored shapes, including a red sphere, a yellow cube, a green cylinder, a blue cylinder, a purple cylinder, and a cyan sphere.
+
+Rationales:
+
+The question asks to subtract all red things and all tiny matte balls, then determine how many objects are left. This involves identifying and counting specific objects based on their color and size.
+
+Let's think step by step.
+
+Step 1:
+
+Identify and count all objects in the image. There are seven objects: a yellow cube, a green cylinder, a blue cylinder, a purple cylinder, a red sphere, and a cyan sphere.
+
+Step 2:
+
+Subtract all red things. There is one red sphere.
+
+![](images/427ae8a94d1d79342341c97de9ce9f2ebbacb58f150c21c9ed38e7fc5d3b756b.jpg)
+
+Step 3:
+
+Subtract all tiny matte balls from the remaining objects. There is one cyan sphere, which is matte and small.
+
+Step 4:
+
+Count the remaining objects after removing the red sphere and the cyan sphere.
+
+The final answer is: 5
+
+![](images/366b9a391d6df3169d49060204f2bcb3a08049f149364a189b7477110792c573.jpg)  
+Figure 4. Qualitative comparison.
+
+ward, where the model is optimized with our proposed stepwise reasoning reward. As shown in Table 4, both outcome-level reward and our step-wise reward improve the warm-up model's performance, while our step-wise reward achieves better performance. This further demonstrates that stepwise rewards are more effective in enhancing MLLMs' reasoning capabilities, as they provide more fine-grained supervision and largely mitigate the sparse reward issue.
+
+Comparison to supervised fine-tuning (SFT). As discussed before, StepGRPO encourages MLLM to self-improve the reasoning ability with step-wise reward signals rather than merely imitating the successful reasoning paths. Here, we conduct experiments to further compare StepGRPO with SFT. Specifically, we start with the model after the warm-up and conduct the experiments with Qwen2-VL-7B over MathVista. As shown in Fig. 3, under the same number of training steps, StepGRPO consistently outperforms SFT, demonstrating the effectiveness of step-wise reinforcement learning. This is largely attributed to StepGRPO's ability to refine reasoning trajectories through self-exploration and reward-guided optimization, rather than solely relying on passive imitation of reasoning paths. By leveraging step-wise reasoning rewards, StepGRPO provides more rich and informative supervision, leading to better reasoning processes compared to SFT.
+
+Qualitative comparison. We provide qualitative comparison of Qwen2VL-7B, Mulberry-7B and our R1-VL-7B. As shown in Fig. 4, Qwen2-VL-7B generates relatively short responses, lacking a thorough reasoning process. While Mulberry-7B generates detailed reasoning paths, its intermediate steps contain errors, leading to incorrect final an
+
+svers. In contrast, R1-VL-7B enables more accurate step-by-step reasoning process.
+
+We provide more discussions, experimental results and qualitative analysis in the appendix.
+
+# 5. Conclusion
+
+This paper presents StepGRPO, a new online reinforcement learning framework that enables MLLMs to self-improve reasoning ability via simple, effective and dense step-wise reward mechanism. Specifically, StepGRPO introduces two rule-based reasoning reward mechanisms, i.e., Step-wise Reasoning Accuracy Reward that rewards the intermediate reasoning steps based on a soft key-step matching technique and Step-wise Reasoning Validity Reward that rewards the reasoning path's reasoning structure and logical consistency though a reasoning completeness and logic evaluation method. In this way, StepGRPO enables to effectively mitigate the sparse reward issue for MLLMs without the need of process reward models and encourages more structured and logically consistent reasoning process. With the proposed StepGRPO, we develop R1-VL, a series of MLLMs with superior reasoning capability. Extensive experiments over eight benchmarks demonstrate the superiority of the proposed StepGRPO compared with the state-of-the-art MLLMs.
+
+Acknowledgement. This research is supported by the RIE2025 Industry Alignment Fund - Industry Collaboration Projects (IAF-ICP) (Award I2301E0026), administered by A\*STAR, as well as supported by Alibaba Group and NTU Singapore through Alibaba-NTU Global e-Sustainability CorpLab (ANGEL).
+
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+# RA-BUSSeg: Relation-aware Semi-supervised Breast Ultrasound Image Segmentation via Adjacent Propagation and Cross-layer Alignment
+
+Wanting Zhang $^{1}$ , Zhenhui Ding $^{1}$ , Guilian Chen $^{1}$ , Huisi Wu $^{1*}$ , Jing Qin $^{2}$
+
+<sup>1</sup> College of Computer Science and Software Engineering, Shenzhen University
+
+2 Centre for Smart Health, School of Nursing, The Hong Kong Polytechnic University
+
+2310273079@email.szu.edu.cn, hswu@szu.edu.cn
+
+# Abstract
+
+Accurate breast ultrasound (BUS) image segmentation is critical for diagnosis and surgical planning, but faces challenges due to limited labeled images. Semi-supervised methods show promise by leveraging pseudo-labels to mitigate reliance on large-scale annotations. However, their performance is highly dependent on the quality of pseudolabels, which is difficult to guarantee in BUS images due to inherent complexities such as low contrast, speckle noise, and artifacts. Previous studies primarily focus on refining pseudo-labels in one way or the other, or introducing auxiliary supervision; yet they overlook the potential of harnessing intrinsic and inherent pixel relations to enhance the robustness of semi-supervised segmentation. In this paper, we present a novel relation-aware semi-supervised model for BUS image segmentation, which is composed of two innovative components: an adjacent relation propagation (ARP) module and a cross-layer relation alignment (CRA) module, for comprehensively explore pixel relations to improve segmentation performance. The ARP propagates relations among adjacent pixels to reinforce the collaborative prediction of correlated pixels and enhance the model's awareness of local semantic consistency. The CRA aligns cross-layer pixel relations, employing deep-layer guidance to rectify erroneous correlations in shallow layers for noise suppression, while integrating multi-scale contexts to enable robust segmentation of lesions with varying sizes. Extensive experiments on two representative BUS datasets under various labeling conditions demonstrate the superiority of our method to the SOTAs. Codes are available at https://github.com/dodooo1/RA-BUSSeg.
+
+# 1. Introduction
+
+Breast cancer poses a significant global health challenge, with the Global Cancer Observatory reporting that it ac
+
+![](images/0f5cbce5195e023838b1ef576e6cabb3b5e926345768037d9580df3d5a96826c.jpg)  
+(a)
+
+![](images/17ef3a6073224cf927f18d66b409e10d91cb93047878539fd6d46a6a8dcda135.jpg)  
+(b)
+
+![](images/38a1a75f582ab72ddb9bf037f913033d9df501dbee64bacef548e7fa57d0f890.jpg)  
+(c)  
+Figure 1. Challenges of breast ultrasound image segmentation: (a) low contrast between breast masses and background, (b) blurring boundaries caused by speckle noise and severe artifacts, and (c) lesions with varying scales. The yellow boxes indicate the locations of the lesions and the red regions represent ground truth.
+
+counts for  $24.5\%$  of all female cancer cases [3]. Evidence has demonstrated that early screening plays a pivotal role in reducing breast cancer mortality [5]. Breast ultrasound (BUS) is widely used in current screening procedures, given its portability, cost-effectiveness, non-invasiveness, and superior performance in detecting dense breasts versus mammography [2, 10]. Computer-assisted BUS analysis systems can enhance diagnosis accuracy and support precise surgical planning, while alleviating doctors' workload in large-scale screening scenarios. To the end, many recent studies [4, 16, 29, 34] are devoted to developing deep learning models for automatic segmentation of breast lesions from BUS images to facilitate the construction of these systems.
+
+To ensure segmentation model accuracy, large-scale pixel-level annotations are typically required for training. However, publicly available labeled BUS images are scarce, while manual annotation is costly and expertise-intensive. In this regard, semi-supervised learning (SSL) approaches are widely harnessed to reduce reliance on annotated data. Pseudo-labeling is a prevalent SSL paradigm that generates pseudo-labels for unlabeled data and uses them alongside labeled data for training [31, 43]. The learning objective is to minimize pixel-wise divergence between predictions and pseudo-labels, making training performance highly depen
+
+dent on pseudo-label quality. In BUS image segmentation, pseudo-label quality is, however, often degraded by low contrast, speckle noise, and imaging artifacts (see Fig. 1).
+
+Serveral approaches have been proposed to enhance pseudo-label quality to facilitate robust training [18, 25]. Some methods [31] discard low-confidence pseudo-labels based on predicted class entropy, but such post-prediction filtering fails to address the root issue. Sun et al. [26] refine pseudo-labels via global pixel pairwise relationships modeling and label propagation. However, modeling global pixel relationships in BUS images may incorrectly associate lesions with noise and artifact regions. Some recent studies employ contrastive learning to introduce complementary global supervision, enabling the acquisition of rich semantic context and alleviating the limitations of pixel-level constraints [30, 35]. Yet, in contrastive learning, the inaccurate sampling of positive/negative pair caused by suboptimal pseudo-labels can exacerbate confirmation bias. Mai et al. [20] analyze the bottlenecks of contrastive learning and propose rank-aware correlation consistency as a more robust supervision signal, which is constructed from pixel correlations modeled by representative agents. We argue that single-layer pixel relation modeling captures limited context and lacks multi-scale semantic integration, thereby weakening the model's capability in handling lesions of varying scales while suppressing speckle noise and artifacts.
+
+In this paper, we propose a novel semi-supervised model for BUS segmentation by sufficiently exploring pixel relations; we call the model  $RA$ -BUSSeg. Our model consists of two innovative components: an adjacent relation propagation (ARP) module and a cross-layer relation alignment (CRA) module. In ARP, we model relations among adjacent pixels and leverage relation propagation to extract information from neighboring semantically similar pixels to facilitate prediction. This propagation enables the mutual reinforcement of predictions for correlated pixels within neighborhoods and enhances the model's perception of local semantic consistency. On the other hand, in CRA, we construct an auxiliary supervision signal based on the pixel relations among different feature layers to maintain the semantic consistency across layers. To mitigate the interference of speckle noise and low contrast in global pixel relation modeling, we model the relations in each layer by sampling representative points (called proxies) with spatial correspondence in each layer as semantic anchors, and comparing their correlations with each pixel. In principle, pixel relations in shallow layers retain richer detailed contrasts between pixels, while relations derived in abstract deep features have potential to reduce the impact of irrelevant noise and artifacts on segmentation. We align relations in shallow pixels with those in deep layers to enforce cross-layer consistency, where top-down semantic guidance corrects false correlations in low-level features, and thus effectively
+
+suppressing noise propagation. In addition, the aggregation of multi-scale contexts enhances the model's robustness in segmenting lesions of different sizes. We perform extensive experiments on two representative public breast ultrasound datasets, BUSI [1] and UDIAT [40], to validate the effectiveness of the proposed model; experimental results demonstrate that our RA-BUSSeg outperforms SOTA methods by a considerable margin under different semi-supervised settings.
+
+Our contributions can be summarized as follows:
+
+- We propose a novel relation-aware network for BUS image segmentation (RA-BUSSeg) that explores rich pixel relations to precisely delineate lesions under strong noise and artifacts, and thus boost the robustness of semi-supervised BUS segmentation.  
+- We propose an ARP module to reinforce connections between adjacent correlated pixels through relation propagation, enhancing the awareness of local semantic consistency, and a CRA module to leverage pixel relations extracted from high-level features to correct false correlations derived from shallow layers, thereby suppressing the impacts of noise and improve segmentation accuracy.  
+- We conduct extensive experiments on two representative BUS datasets under various labeling conditions to highlight the effectiveness and superiority of our method.
+
+# 2. Related Work
+
+# 2.1. Breast Ultrasound Image Segmentation
+
+In recent years, the fully-supervised paradigm based on CNN [21, 24, 41, 44] and Transformer [12, 22, 28, 37] has achieved remarkable outcomes in breast ultrasound (BUS) image segmentation. BCT-Net [36] integrates CNN and Transformer, introducing a dual-level attention mechanism and a hybrid objective loss function for breast ultrasound image segmentation. However, the accurate annotation of BUS images requires expertise and is costly, which hinders the applicability of fully-supervised segmentation methods. Some studies explore the potential of semi-supervised learning to reduce the dependence on labeled data. Mainstream semi-supervised learning methods are primarily classified into pseudo-labeling and consistency regularization. The pseudo-labeling paradigm [15, 23, 38] generates pseudo-labels for unlabeled data based on model predictions and uses them alongside labeled data for training. On the other hand, the consistency regularization-based methods [9, 17, 39, 42] learn from unlabeled data by encouraging consistency between the original predictions and their perturbed counterparts (including perturbations to inputs, features, and the network). For semi-supervised segmentation in breast tumor, UA-RC [33] improves the segmentation performance by calibrating the representations of uncertain predictions. PH-Net [13] proposes an adaptive
+
+![](images/d3ea9054b77371177586dbf6a2c793d73896186b69e00307aed98fd310617206.jpg)  
+Figure 2. Overview of RA-BUSSeg, which consists of an adjacent relation propagation (ARP) module and a cross-layer relation alignment (CRA) module. Our ARP strengthens connections between adjacent correlated pixels with similar semantic via relation propagation, enhancing the model's perception of local semantic consistency. Meanwhile, CRA utilizes pixel relations from deep features to rectify false correlations derived from shallower layers, effectively suppressing the impact of noise and improving segmentation accuracy.
+
+patch augmentation and a hard-patch contrastive learning to achieve better performance on hard cases.
+
+# 2.2. Inter-pixel Relation
+
+In semi-supervised semantic segmentation, the pseudolabeling paradigm assigns a category pseudo-label to each pixel and leverage individual pixel-wise consistency as a supervision signal to guide model training. However, this process heavily relies on the accuracy of pseudo-label, and relying solely on individual pixel-wise consistency fails to fully explore the information embedded in unlabeled data. IpixMatch [32] proposes an extra inter-pixel loss to mine the neglected but valuable inter-pixel information for semi-supervised learning. RankMatch [19] constructs representative proxies to model inter-pixel correlations and utilizes rank-aware correlation consistency as a more effective supervision signal to achieve robust semi-supervised learning. Given the spatial continuity and structural similarity of lesions in breast ultrasound images, modeling the relation of adjacent pixel effectively aggregates intra-neighborhood information, thereby enhancing the accurate of pseudo-label assignment. Modeling global pixel relationships further enables the model to capture comprehensive contextual information in long-range dependencies, which is particularly important for segmentation tasks. Additionally, the coordination between shallow features providing fine-grained details and deep features containing high-level semantics allows the model to preserve a simultaneous understanding of contextual semantics across multi-scale feature layers. These insights drive our exploration of pixel relation within
+
+adjacent regions and across feature layers, aiming to break the bottleneck of pixel-wise constraints.
+
+# 3. Method
+
+# 3.1. Overview
+
+The overview of our semi-supervised breast ultrasound (BUS) image segmentation model,  $RA$ -BUSSeg, is shown in Fig. 2. Our network follows the basic teacher-student framework, where both teacher and student networks share the same structure. Initially, our model is pre-trained on limited labeled images  $B^{l} = \{(x_{i}^{l},y_{i}^{l})\}$ , where  $y_{i}^{l}$  denotes the label for each image.  $\mathcal{L}_s$  is employed for supervised learning on labeled set  $B^{l}$ , which minimizes the divergence between the prediction from student network  $\mathcal{P}^s (x_i^l)$  and  $y_{i}^{l}$ .
+
+$$
+\mathcal {L} _ {s} = \frac {1}{| B ^ {l} |} \sum_ {i = 1} ^ {| B ^ {l} |} \frac {1}{| H W |} \sum_ {j = 1} ^ {H W} \ell_ {c e} \left(\mathcal {P} ^ {s} \left(x _ {i j} ^ {l}\right), y _ {i j} ^ {l}\right), \tag {1}
+$$
+
+where the subscript  $ij$  represents the  $j$ -th pixel in the  $i$ -th image, and  $|B^l|$  denotes the number of labeled samples.  $\ell_{ce}$  is the standard cross-entropy loss. Subsequently, unlabeled images  $B^u = \{x_i^u\}$  are also used for training, where the pseudo-labels generated from the predictions of teacher network. For unsupervised learning on unlabeled set,  $\mathcal{L}_u$  is applied to enforce consistency between the prediction from student network  $\mathcal{P}^s(x_i^u)$  and the pseudo-label  $\hat{y}_i^u$ .
+
+$$
+\mathcal {L} _ {u} = \frac {1}{| B ^ {u} |} \sum_ {i = 1} ^ {| B ^ {u} |} \frac {1}{| H W |} \sum_ {j = 1} ^ {H W} \ell_ {c e} \left(\mathcal {P} ^ {s} \left(x _ {i j} ^ {u}\right), \hat {y} _ {i j} ^ {u}\right), \tag {2}
+$$
+
+![](images/4a927e97a4a50a0c45e7ee206dbc64d7dc403efaf5fd8716a47fc4b42ff4d304.jpg)  
+Figure 3. Illustration of adjacent relation propagation (ARP). The ARP spreads adjacent relations into predictions, aiming to mutually reinforce the prediction of semantically similar pixels and enhance the perception of local semantic consistency.
+
+where the  $|B^u|$  denotes the number of unlabeled samples.
+
+However, in low-contrast BUS images with speckle noise and severe artifacts, the generated pseudo-labels often suffer from poor quality, hindering the effective learning from unlabeled data. We explore robust semi-supervised learning from pixel relations to break the bottleneck of pixel-wise constraints from pseudo-labels. To this end, we develop two innovative components: an adjacent relation propagation (ARP) module and a cross-layer relation alignment (CRA) module. Our proposed ARP module propagates the relations between adjacent pixels into the prediction, refining the prediction with information extracted from neighboring semantically similar pixels. It strengthens the connection between adjacent correlated pixels and promotes the model's perception of local semantic consistency. Our CRA module further models pixel relations through representative proxies in different feature layers and enforces consistency on shallow-to-deep relations to align multi-scale semantics. It utilizes high-level semantic to rectify the erroneous pixel relations derived from shallow features, aiming to mitigate noise propagation. In addition, the aggregation of multi-scale context promotes the model's robust segmentation of lesions with varying scales.
+
+# 3.2. Adjacent Relation Propagation
+
+Most semi-supervised methods employ the entropy of predicted class probabilities to filter out low-confidence pixel pseudo-labels. However, this filtering strategy, as a post-processing method, fails to actually enhance the quality of the pseudo-labels. We realize that the relations between adjacent pixels can provide valuable insights for more accurate prediction. To this end, we propose an adjacent relation propagation (ARP) module to strengthen the model's attention to adjacent pixel relations, which involves the generation of relation maps and the subsequent propagation.
+
+As shown in Fig. 3, we first generate the adjacent relation map based on the features  $\mathcal{F} \in \mathbb{R}^{HW \times C}$  extracted by the encoder, where  $C$  denotes the channel dimension, and
+
+$H$  and  $W$  are the height and width, respectively. Specifically, we employ a sliding window to capture features within the adjacent region and use the dot product to quantify the correlations between adjacent points and the center point. For clarity, we illustrate the process on a single pixel  $p_j$  and utilize  $\mathcal{N}_j = \{p_{k,l} \mid -\frac{n}{2} \leq k \leq \frac{n}{2}, -\frac{n}{2} \leq l \leq \frac{n}{2}\}$  to represent the set of pixels in the  $n \times n$  sliding window centered on  $p_j$ . The adjacent relation map  $\mathcal{M}_j$  of  $p_j$  can be expressed as follows:
+
+$$
+\mathcal {M} _ {j} = \operatorname {S o f t m a x} \left(\mathcal {F} _ {j} \mathcal {F} _ {\mathcal {N} _ {j}} ^ {\top} / \sqrt {C}\right), \tag {3}
+$$
+
+where  $\mathcal{F}_j\in \mathbb{R}^{1\times C}$  is the feature of  $p_j$ ,  $\mathcal{F}_{\mathcal{N}_j}\in \mathbb{R}^{nn\times C}$  denotes the features of the pixels in  $\mathcal{N}_j$ , and  $\top$  represents the matrix transpose operation. Subsequently, we propagate the relation map into the predictions (logit outputs) of student network by matrix multiplication, obtaining a new output that considers the pixel relation within adjacency compared to the original output. The new output of  $p_j$  is calculated as:
+
+$$
+\tilde {\mathcal {P}} ^ {s} (p _ {j}) = \sum \mathcal {P} ^ {s} (\mathcal {N} _ {j}) \odot \mathcal {M} _ {j}, \tag {4}
+$$
+
+where  $\mathcal{P}^s (\mathcal{N}_j)$  is the original logits output of pixels in  $\mathcal{N}_j$  and  $\odot$  denotes the Hadamard product. We minimize the discrepancy between the new output and the pseudo-label using the loss  $\mathcal{L}_{ARP}^u$  to enhance the model's awareness of local semantic consistency, formulated as follows:
+
+$$
+\mathcal {L} _ {A R P} ^ {u} = \frac {1}{| B ^ {u} |} \sum_ {i = 1} ^ {| B ^ {u} |} \frac {1}{| H W |} \sum_ {j = 1} ^ {H W} \ell_ {c e} (\tilde {\mathcal {P}} ^ {s} (x _ {i j} ^ {u}), \hat {y} _ {i j} ^ {u}), \quad (5)
+$$
+
+where  $\tilde{\mathcal{P}}^s (x_{ij}^u)$  denotes the new output of the  $j$ -th pixel in an unlabeled image  $x_{i}^{u}$  generated by Eq. (4). Moreover, this process is also applied to labeled images, using the  $\tilde{\mathcal{P}}^s (x_i^l)$  and the label  $y_{i}^{l}$  to construct the loss  $\mathcal{L}_{ARP}^l$ . The loss introduced by ARP module,  $\mathcal{L}_{ARP} = \mathcal{L}_{ARP}^l +\mathcal{L}_{ARP}^u$ , serves as an additional supervision signal for model optimization. In addition to focusing on classification accuracy, this optimization objective models the relations between adjacent pixels, facilitating mutual reinforcement of predictions for similar neighboring pixels to capture the overall structure of lesions and enhancing the model's awareness of local semantic consistency.
+
+# 3.3. Cross-layer Relation Alignment
+
+Modeling pixel relations in a single feature layer captures only limited contextual information at a fixed scale, failing to encompass multi-scale semantics. This limitation weakens the model's ability to distinguish noise and compromises its robustness in handling scale-varying lesions. To this end, we propose a cross-layer relation alignment (CRA) module, which involves modeling pixel relations through proxies and optimizing the model by enforcing consistency in cross-layer pixel relations.
+
+![](images/8fa0785e27637fc2f4f1ce46a58faef495db05c3def7a6ce1f9610f446774063.jpg)  
+Figure 4. Illustration of cross-layer relation alignment (CRA). The CRA leverages high-level semantic information to rectify false correlations in noise-prone shallow layers, facilitating noise suppression and improving segmentation precision.
+
+As shown in Fig. 4, we first adopt a greedy strategy to select a set of representative points, referred to as proxies. We employ proxies as semantic anchors to model pixel relations, decreasing computational complexity while reducing noise in pixel relations that could interfere with model optimization. Specifically, we first randomly select a pixel in the lesion area as the first proxy  $P_{1}$ , and compute its correlations with other points via the dot product of their features. The second proxy  $P_{2}$  is the pixel with the lowest correlation with  $P_{1}$ . To prevent the third proxy from being localized around  $P_{1}$ , we select the pixel with the lowest correlation with both  $P_{1}$  and  $P_{2}$ , rather than comparing only with  $P_{2}$ .
+
+$$
+\begin{array}{l} \mathcal {C} _ {P _ {1}} = \operatorname {S o f t m a x} \left(\mathcal {F} _ {P _ {1}} \mathcal {F} ^ {\top} / \sqrt {C}\right), \tag {6} \\ P _ {2} = \arg \min  \left(\mathcal {C} _ {P _ {1}}\right), \\ \end{array}
+$$
+
+$$
+\begin{array}{l} \mathcal {C} _ {P _ {2}} = \operatorname {S o f t m a x} \left(\mathcal {F} _ {P _ {2}} \mathcal {F} ^ {\top} / \sqrt {C}\right), \tag {7} \\ P _ {3} = \arg \min  \left(\mathcal {C} _ {P _ {1}} + \mathcal {C} _ {P _ {2}}\right), \\ \end{array}
+$$
+
+where  $\mathcal{C}_{P_k} \in \mathbb{R}^{1 \times HW}$  represents the correlation of the  $k$ -th proxy with all pixels, and  $\arg \min$  denotes the operation of selecting the index corresponding to the minimum value in  $\mathcal{C}_{P_k}$ . Following this strategy, the pixel with the weakest correlation to the selected proxies is sampled as a new proxy each time. These proxies, characterized by distinct features, preserve comprehensive semantic cues in original image. The relations between each pixel  $p_j$  and proxies exhibit diverse contrastive descriptions within an image, which can be quantified through the dot product:
+
+$$
+\mathcal {R} _ {p _ {j}} = \mathcal {F} _ {p _ {j}} \cdot \mathcal {F} _ {P _ {k}}, \quad \forall k \in \{1, 2, \dots , N \}, \tag {8}
+$$
+
+where  $N$  is the number of proxy. The modeling of pixel relations within a single feature layer confines contextual information to a fixed receptive field, limiting the model's ability to consistently understand the relationship between multi-scale features. The shallow layers emphasize fine-grained local details of the lesion, such as texture and sharp
+
+edges, while deep features offer high-level global semantics, like the overall morphology and structure. All of them are essential for perceiving the structure of the lesions and accurately delineating their details. Therefore, we utilize bilinear interpolation to match the spatial resolution of feature maps from deeper layers to shallower layers, and map the proxies to their corresponding positions for modeling pixel relations in multiple layers. To achieve semantic alignment across layers and ensure consistent understanding of multiscale features, we employ Kullback-Leibler (KL) divergence to align shallow pixel relations with those in deeper layers. Specifically, we minimize the divergence of proxy-level relations across layers, which is formulated as follows:
+
+$$
+\begin{array}{l} \mathcal {L} _ {C R A} = \frac {1}{| B |} \sum_ {i = 1} ^ {| B |} \frac {1}{| H W |} \sum_ {j = 1} ^ {H W} \left(\ell_ {k l} \left(R _ {p _ {i j}} ^ {1}, R _ {p _ {i j}} ^ {2}\right) \right. \tag {9} \\ + \ldots + \ell_ {k l} (R _ {p _ {i j}} ^ {L - 1}, R _ {p _ {i j}} ^ {L})), \\ \end{array}
+$$
+
+where  $|B|$  is the length of labeled and unlabeled set, and  $L$  denotes the  $L$ -th feature layer. Speckle noise, due to its random brightness and position, causes high-frequency variations in shallow features, while deeper layers smooth these changes by focusing on global semantics. Under this optimization objective, the model effectively captures pixel relations across different scales and leverages high-level semantic guidance to rectify erroneous relations derived from shallow layers. This process mitigates noise propagations, thereby improving the model's segmentation performance for breast lesions in the presence of severe noise. In addition, when encountering breast lesions of varying scales, the aggregation of multi-scale contextual information enhances the model's robustness in addressing this challenge.
+
+# 3.4. Loss Function
+
+The overall loss function is formulated as a weighted combination of  $\mathcal{L}_s$  in Eq. (1),  $\mathcal{L}_u$  in Eq. (2) and the losses introduced by the proposed ARP and CRA modules, which can be expressed as follows:
+
+$$
+\mathcal {L} = \mathcal {L} _ {s} + \lambda_ {u} \mathcal {L} _ {u} + \lambda_ {1} \mathcal {L} _ {A R P} + \lambda_ {2} \mathcal {L} _ {C R A}, \tag {10}
+$$
+
+where  $\lambda_{u},\lambda_{1}$  , and  $\lambda_{2}$  denote the weights for the respective losses, all set to 1.
+
+# 4. Experiments
+
+# 4.1. Experimental Setup
+
+# 4.1.1. Datasets and evaluation metrics
+
+We validate the effectiveness of our method on two public breast ultrasound (BUS) datasets, BUSI [1] and UDIAT [40]. The BUSI dataset comprises 780 annotated images, including 437 benign, 210 malignant, and 133 normal cases, derived from 600 female aged 25 to 75 years. We conduct
+
+![](images/0b548187a2b4813a3d216beea8667900394cf3f5e03ba6d023e9e7a55b36c07d.jpg)  
+Figure 5. Visual comparison with state-of-the-art methods on the 1/4 partition protocol of two famous breast ultrasound datasets: UDIAT and BUSI. Red, green and yellow regions represent ground truth, prediction and their overlapping regions, respectively.
+
+experiments on both benign and malignant cases containing lesions to evaluate the performance of our approach in breast tumor segmentation. The UDIAT dataset, collected from the UDIAT Diagnostic Center, contains 163 annotated BUS images (110 benign and 53 malignant cases). We employ five-fold cross-validation under different labeling scenarios, including  $1/2$ ,  $1/4$  and  $1/8$  partition protocols. The partition protocols represent the proportion of labeled data within the entire dataset. We employ the dice coefficient (Dice), intersection over union (IoU) and Hausdorff Distance (HD) to evaluate the segmentation performance, and compute the mean value and the standard deviation across five folds.
+
+# 4.1.2. Implementation details
+
+Our method is implemented in PyTorch and runs on a single NVIDIA GeForce RTX 3090 with 24 GB of memory. We adopt ResNet-50 [11] pre-trained on ImageNet [8] as the backbone, while DeepLabv3+ [6] serves as the decoder. The student network is optimized using a stochastic gradient descent (SGD) optimizer with a momentum of 0.9 and a weight decay of 0.0005. The learning rate starts at 0.003, which is decayed by a polynomial strategy  $lr = 0.003 \times \left(1 - \frac{\text{iter}_{\text{curr}}}{\text{iter}_{\text{total}}}\right)^{0.9}$ . To update the teacher model, we apply exponential moving averaging (EMA) to the student network's parameters. The training lasts for 200 epochs, with the first 10 dedicated to pre-training. The batch-size is set to 2. During each epoch, we unify the image resolution to  $512 \times 512$  and apply weak data augmentation, including random scaling, random cropping and random horizontal flipping, to both labeled and unlabeled samples.
+
+# 4.2. Comparison with State-of-the-art Methods
+
+We compare our method with several state-of-the-art (SOTA) approaches, including seven semi-supervised segmentation methods for natural and medical images and
+
+three specific methods for breast ultrasound (BUS) datasets. The selected methods can be categorized as follows: (1) Classic semi-supervised methods:  $\mathrm{U}^2\mathrm{PL}$  [31] and CSS [27]; (2) Contrastive learning-based methods: DGCL [30] and PRCL [35]; (3) Correlation-based methods: CorrMatch [26] and RankMatch [20], which have exhibited competitive performance in natural image segmentation through inter-pixel correlation analysis; (4) Medical-specific methods: ABD [7], a SOTA semi-supervised model for medical images, and BUS-specific frameworks UA-RC [33] and PH-Net [14]. All methods adopt ResNet-50 as the backbone and are implemented under the same experimental conditions as our approach. Fig. 5 visualizes the predictions of our model alongside those of selected methods, which intuitively highlight the superiority of our approach. We deliberately show challenging cases with lesions of varying scales, irregular shapes, and surrounded by noise and artifacts to demonstrate our method's precise tumor segmentation capability in complex scenarios.
+
+The quantitative results presented in Tab. 1 conclusively demonstrates the superior performance of our proposed model across all comparative approaches. The improvements over correlation-based methods demonstrate the efficacy of our proposed modules in tackling task-specific challenges unique to breast ultrasound imaging—particularly inherent noise, severe artifacts, and lesions of varying sizes. Specifically, the adjacent relation propagation mechanism enhances local semantic consistency and spatial continuity in segmentation predictions, while the cross-layer relation alignment facilitates noise suppression and improves robustness to lesion size variations. Notably, our method outperforms the SOTA model ABD by  $1.46\%$ ,  $1.65\%$ , and  $1.35\%$  in Dice coefficient under  $1/2$ ,  $1/4$ , and  $1/8$  labeled data partitions on the BUSI dataset, respectively, while also achieving superior performance over BUS-specific frameworks across all evaluation protocols. Even compared to
+
+<table><tr><td rowspan="3">Method</td><td rowspan="3">Year</td><td colspan="8">UDIAT</td><td colspan="7">BUSI</td><td></td><td></td><td></td></tr><tr><td colspan="3">1/2</td><td colspan="3">1/4</td><td colspan="2">1/8</td><td colspan="3">1/2</td><td colspan="3">1/8</td><td></td><td></td><td></td><td></td></tr><tr><td>Dice±std (%)</td><td>IoU±std (%)</td><td>HD</td><td>Dice±std (%)</td><td>IoU±std (%)</td><td>HD</td><td>Dice±std (%)</td><td>IoU±std (%)</td><td>HD</td><td>Dice±std (%)</td><td>IoU±std (%)</td><td>HD</td><td>Dice±std (%)</td><td>IoU±std (%)</td><td>HD</td><td></td><td></td><td></td></tr><tr><td>\( U^2PL [31] \)</td><td>2022</td><td>81.39±3.23</td><td>73.11±3.52</td><td>6.88</td><td>78.20±3.14</td><td>69.99±2.79</td><td>7.14</td><td>73.44±2.67</td><td>64.92±3.03</td><td>8.25</td><td>75.72±2.74</td><td>66.96±3.03</td><td>7.95</td><td>73.06±2.76</td><td>64.85±2.44</td><td>9.27</td><td>70.53±3.15</td><td>61.96±3.63</td><td>9.56</td></tr><tr><td>CSS [27]</td><td>2023</td><td>82.15±3.07</td><td>73.20±3.34</td><td>6.41</td><td>78.67±3.08</td><td>69.92±3.17</td><td>6.97</td><td>74.25±2.37</td><td>65.97±2.13</td><td>7.96</td><td>76.02±2.67</td><td>67.36±2.65</td><td>8.03</td><td>73.74±2.60</td><td>64.69±2.15</td><td>9.01</td><td>71.19±2.98</td><td>62.43±3.22</td><td>9.29</td></tr><tr><td>DGCL [30]</td><td>2023</td><td>82.97±2.87</td><td>73.39±2.94</td><td>6.00</td><td>80.25±3.07</td><td>72.05±3.01</td><td>6.30</td><td>75.91±3.14</td><td>66.88±3.28</td><td>7.73</td><td>76.88±2.22</td><td>67.50±1.95</td><td>7.66</td><td>75.75±2.37</td><td>67.30±2.06</td><td>8.30</td><td>72.85±2.68</td><td>63.22±2.12</td><td>8.74</td></tr><tr><td>PRCL [35]</td><td>2024</td><td>82.78±2.94</td><td>74.12±3.00</td><td>6.25</td><td>79.82±3.12</td><td>70.84±3.29</td><td>6.56</td><td>75.68±2.94</td><td>66.55±2.51</td><td>7.93</td><td>76.54±2.48</td><td>68.05±2.62</td><td>7.82</td><td>75.21±2.57</td><td>66.06±2.69</td><td>9.02</td><td>72.60±2.63</td><td>64.03±3.39</td><td>9.02</td></tr><tr><td>CorrMatch [26]</td><td>2024</td><td>82.61±2.65</td><td>73.88±2.94</td><td>6.09</td><td>79.43±2.88</td><td>70.46±3.19</td><td>6.54</td><td>74.49±2.36</td><td>65.32±2.48</td><td>8.06</td><td>76.18±2.02</td><td>67.57±2.75</td><td>7.99</td><td>75.03±1.97</td><td>66.38±2.36</td><td>8.94</td><td>72.22±2.08</td><td>63.79±1.76</td><td>9.02</td></tr><tr><td>RankMatch [20]</td><td>2024</td><td>83.18±2.83</td><td>73.73±3.10</td><td>6.07</td><td>80.77±3.08</td><td>71.95±3.12</td><td>6.31</td><td>76.40±2.22</td><td>67.53±2.19</td><td>7.37</td><td>77.10±2.16</td><td>68.79±1.84</td><td>7.00</td><td>75.76±2.42</td><td>67.05±2.11</td><td>8.26</td><td>73.20±2.43</td><td>64.66±2.10</td><td>8.65</td></tr><tr><td>ABD [7]</td><td>2024</td><td>83.75±2.17</td><td>74.57±2.66</td><td>5.72</td><td>81.69±2.16</td><td>72.54±2.38</td><td>6.00</td><td>77.94±2.80</td><td>68.27±2.92</td><td>6.73</td><td>77.65±1.77</td><td>69.15±1.52</td><td>6.63</td><td>76.30±2.02</td><td>67.72±1.87</td><td>8.24</td><td>73.71±2.23</td><td>65.03±2.34</td><td>8.62</td></tr><tr><td>UA-RC [33]</td><td>2024</td><td>83.40±2.54</td><td>75.05±2.10</td><td>5.62</td><td>81.29±3.02</td><td>72.91±3.46</td><td>6.22</td><td>77.22±2.23</td><td>68.28±2.15</td><td>7.02</td><td>77.47±1.98</td><td>68.72±1.85</td><td>6.82</td><td>76.09±2.24</td><td>67.47±2.01</td><td>8.18</td><td>73.66±2.47</td><td>65.00±2.91</td><td>8.27</td></tr><tr><td>PH-Net [14]</td><td>2024</td><td>84.06±2.29</td><td>75.70±2.63</td><td>5.28</td><td>81.80±2.50</td><td>72.02±2.86</td><td>5.84</td><td>78.40±3.35</td><td>69.87±3.69</td><td>6.54</td><td>78.02±1.99</td><td>69.81±2.75</td><td>6.40</td><td>76.81±1.75</td><td>68.38±2.37</td><td>8.21</td><td>74.09±2.10</td><td>65.53±2.33</td><td>8.01</td></tr><tr><td>BCT-Net [36]</td><td>2025</td><td>80.07±3.06</td><td>71.20±3.16</td><td>8.11</td><td>76.42±3.55</td><td>67.89±3.26</td><td>7.03</td><td>73.00±2.61</td><td>64.32±2.90</td><td>7.83</td><td>74.96±2.61</td><td>66.98±2.48</td><td>8.73</td><td>72.52±2.56</td><td>64.17±2.61</td><td>9.10</td><td>69.99±1.86</td><td>61.29±2.05</td><td>9.89</td></tr><tr><td>SupOnly</td><td>-</td><td>78.51±1.34</td><td>69.55±1.46</td><td>7.93</td><td>75.11±2.37</td><td>66.44±2.38</td><td>7.01</td><td>72.24±4.13</td><td>63.27±4.21</td><td>8.82</td><td>74.17±2.39</td><td>65.60±2.51</td><td>8.62</td><td>71.62±2.01</td><td>62.78±2.17</td><td>9.33</td><td>68.96±1.86</td><td>60.28±1.81</td><td>9.94</td></tr><tr><td>Ours</td><td>-</td><td>84.77±2.43</td><td>76.40±2.26</td><td>5.28</td><td>82.55±2.21</td><td>74.21±1.80</td><td>5.73</td><td>79.76±2.79</td><td>71.24±2.68</td><td>6.50</td><td>79.11±1.89</td><td>70.30±2.06</td><td>6.17</td><td>77.95±1.84</td><td>69.30±1.64</td><td>8.00</td><td>75.06±2.19</td><td>66.41±2.35</td><td>8.13</td></tr></table>
+
+Table 1. Quantitative comparison with state-of-the-art methods on two famous breast ultrasound datasets: UDIAT and BUSI.  
+
+<table><tr><td colspan="2">Method</td><td colspan="2">UDIAT</td><td colspan="2">BUSI</td></tr><tr><td>ARP</td><td>CRA</td><td>Dice±std (%)</td><td>IoU±std (%)</td><td>Dice±std (%)</td><td>IoU±std (%)</td></tr><tr><td></td><td></td><td>75.11±2.37</td><td>66.44±2.38</td><td>71.62±2.01</td><td>62.78±2.17</td></tr><tr><td>✓</td><td></td><td>80.79±2.29</td><td>71.91±2.18</td><td>76.31±2.24</td><td>67.67±1.84</td></tr><tr><td></td><td>✓</td><td>81.21±1.91</td><td>72.42±2.11</td><td>76.42±2.51</td><td>67.84±2.60</td></tr><tr><td>✓</td><td>✓</td><td>82.55±2.21</td><td>74.21±1.80</td><td>77.95±1.84</td><td>69.30±1.64</td></tr></table>
+
+Table 2. Ablation studies of proposed ARP and CRA components on 1/4 partition protocol of UDIAT and BUSI datasets.
+
+![](images/be1d834f43ba53302a5aedd3deba68159eff3d9d7f56f4d9dd054855eb5318d9.jpg)  
+Figure 6. Comparison of predicted lesion boundaries without relation propagation, with adjacent and with global propagation. The red and yellow contours represent ground truth and prediction with our adjacent relation propagation, respectively. The green contours (top) and the blue contours (bottom) show predicted edges without propagation and with global propagation, respectively.
+
+the fully supervised BCT-Net [36], our method shows competitive performance, highlighting the efficacy of leveraging unlabeled data under limited annotations.
+
+# 4.3. Ablation Studies
+
+# 4.3.1. Effectiveness of ARP and CRA
+
+We conduct component-wise ablation analysis to evaluate the adjacent relation propagation (ARP) module and the cross-layer relation alignment (CRA) module. In Tab. 2, we present the quantitative results on the UDIAT and BUSI datasets under the 1/4 partition protocol (results under other protocols are provided in the supplementary material). SupOnly, which is only trained on labeled images, serves as the baseline with Dice coefficient of  $75.11\%$  and  $71.62\%$  on the UDIAT and BUSI datasets, respectively.
+
+![](images/bec4d452b0917e16cd3e41cf656c09956f2c93f68081d32a4af02ad8aa1fb652.jpg)  
+Figure 7. Visual comparison of feature maps in combination of ARP and CRA on 1/4 partition protocol of UDIAT and BUSI datasets. (a) Image. (b) GT. (c) SupOnly. (d) w/ ARP. (e) w/ CRA. (f) Ours.
+
+The combination of the ARP module achieves significant Dice improvements of  $+5.68\%$  and  $+4.69\%$  on the UDIAT and BUSI datasets, respectively. As illustrated in Fig. 7, the feature map comparison reveals that relation propagation guarantees local semantic consistency and enhances the overall continuity of the segmented breast masses. In addition, we visualize the comparison of predicted lesion boundaries with and without adjacent propagation, as shown at the top of Fig. 6. It indicates that ARP enables to refine boundary with the semantic assistance of adjacent similar pixels, ensuring that local semantic consistency is taken into account during prediction. The comparative visualization between adjacent propagation and global propagation, presented in the bottom of Fig. 6, highlights the constraining of propagation range effectively mitigates noise-induced false associations while maintaining spatial coherence in segmentation targets.
+
+Additionally, when integrated with the CRA module, our method attains Dice enhancements reaching  $6.10\%$  and  $4.80\%$  on the UDIAT and BUSI datasets, respectively. Fig. 7 intuitively reveals that the CRA enables precise local-
+
+![](images/306af7b47764c5ee71a39312dd34367338a11a48b918b8c43a692d602e3eae58.jpg)  
+Figure 8. Ablation studies in the range of propagation on  $1/4$  partition protocol of UDIAT and BUSI datasets.
+
+![](images/41c106eb2b450133d5df26f14a470d8f74b28f0f39b1ea1aa9d166df4d2e414c.jpg)  
+Figure 9. Ablation studies in the number of proxy on 1/4 partition protocol of UDIAT and BUSI datasets.
+
+ization and robust delineation of lesion regions across varying scales. The Dice coefficient of the complete framework reaches  $82.55\%$  (UDIAT) and  $77.95\%$  (BUSI), verifying the importance of our proposed relation-aware architecture in achieving accurate segmentation of BUS images.
+
+Compared to the baseline, the training time increases slightly (96→139 s/epoch on BUSI under 1/4 partition), but the added complexity from relation construction notably improves segmentation accuracy. Notably, relation map construction and our modules operate solely during training, adding no inference-time overhead.
+
+# 4.3.2. Impact of propagation range
+
+We conduct an ablation study on the range of propagation in the adjacent relation propagation (ARP) module on the 1/4 partition protocol of the UDIAT and BUSI datasets, as shown in Fig. 8. By modulating the sliding window dimensions to regulate the number of feature vectors captured in the adjacent region, our model achieves optimal performance with a  $3 \times 3$  sliding window configuration. The performance degrades as the window expands, which may be attributed to excessive propagation ranges inducing erroneous lesion-background correlations. Conversely, constrained range exploits the inherent spatial continuity of lesion structures, enforcing connections between adjacent pixels to enhance the model's awareness on local semantic consistency.
+
+![](images/b896ba80dae6f23115c643e1e65d90e0e87add838d47f284111e0bc6da8e16c8.jpg)  
+Figure 10. Failure cases. Green, red and yellow regions represent prediction, ground truth and their overlapping areas.
+
+# 4.3.3. Impact of the number of proxy
+
+We conduct an ablation analysis on the 1/4 partition protocol of the UDIAT and BUSI datasets to investigate the impact of proxies in the cross-layer relation alignment (CRA) module (see Fig. 9). Quantitative analysis reveals peak performance is achieved with 64 proxies. Insufficient proxies fail to preserve diverse semantic cues in the original feature maps, which may limit the acquisition of rich contrastive information for modeling pixel relations. However, an excessive number of proxies increases computational complexity and have potential to introduce noise into the correlation processes, negatively impacting the model's optimization.
+
+# 4.4. Discussions and Limitations
+
+Although we only conduct experiments on the breast ultrasound (BUS) datasets, our approach is tailored to the specific challenges of the BUS tasks, and we believe it can be generalized to other tasks with similar challenges. Additionally, our method still has limitations. As shown in Fig. 10, our method may misclassify regular artifacts in ultrasound images as lesions while separating true lesions. In addition, the segmentation results may be incomplete when light and dark boundaries exist within the lesions.
+
+# 5. Conclusion
+
+We propose a novel relation-aware semi-supervised segmentation network for breast lesions in ultrasound image, named RA-BUSSeg, which consists of an adjacent relation propagation (ARP) module and a cross-layer relation alignment (CRA) module. Our proposed ARP captures and propagates pixel relations within adjacent regions, allowing mutual reinforcement between semantically similar pixels and enhancing the model's perception of local semantic consistency. The developed CRA models pixel relations by proxies and aligns shallow-to-deep relations, harnessing high-level semantics to rectify erroneous correlations in shallow layers for noise suppression. CRA also facilitates robust segmentation of lesions with diverse scales by aggregating context in multi-scale feature layers. Extensive experiments on two BUS datasets validate our approach's superiority.
+
+# Acknowledgments
+
+This work was supported partly by the National Natural Science Foundation of China (No. 62273241), the Natural Science Foundation of Guangdong Province, China (No. 2024A1515011946), and the Hong Kong RGC Collaborative Research Fund (project no C5055-24G).
+
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+# RAGD: Regional-Aware Diffusion Model for Text-to-Image Generation
+
+Zhennan Chen $^{1\star}$  Yajie Li $^{1\star}$  Haofan Wang $^{2,3}$  Zhibo Chen $^{3}$  Zhengkai Jiang $^{4}$  Jun Li $^{1}$  Qian Wang $^{5\boxtimes}$  Jian Yang $^{1}$  Ying Tai $^{1\boxtimes}$ $^{1}$ Nanjing University  $^{2}$ InstantX Team  $^{3}$ Liblib AI  $^{4}$ HKUST  $^{5}$ China Mobile https://github.com/NJU-PCALab/RAG-Diffusion
+
+![](images/f33c8637cdc7061bd4c78125c3f2aca00e982bd6f07eb694798301f078cd5be5.jpg)  
+On the left, Einstein is painting the Mona Lisa; in the center, Elon Reeve Musk is participating in the U.S. presidential election; on the right, Trump is hosting a Tesla product launch.
+
+![](images/e4f779350f69a5f746e00941e5b4cd5d56f2284ae95a37a6244b0af3655bffef.jpg)  
+Seven ceramic mugs in different colors are placed on a wooden table, with numbers from 1 to 7 written on the cups, and a bunch of white roses on the left.  
+Figure 1. RAGD decouples a raw prompt into regional prompts, processes different regions separately and strengthens the interaction between adjacent regions. It enables precise control over object relationship, action and attributes, achieving more harmonious and consistent complex compositional generation compared to competing models like Flux and RPG.
+
+![](images/0eb409e727db389586ae7c77aa9c86c3c4757ae0b68132ce59f4d21f8e1dbd10.jpg)  
+A cylindrical glass, obscuring the right half of the apple behind it.
+
+# Abstract
+
+Regional prompting, or compositional generation, which enables fine-grained spatial control, has gained increasing attention for its practicality in real-world applications. However, previous methods either introduce additional trainable modules, thus only applicable to specific models, or manipulate on score maps within attention layers using attention masks, resulting in limited control strength when the number of regions increases. To handle these limitations, we present RAGD, a Regional-Aware text-to-image Generation method conditioned on regional descriptions for precise layout composition. RAGD decouples the multi-region generation into two sub-tasks,
+
+the construction of individual region (Regional Hard Binding) that ensures the regional prompt is properly executed, and the overall detail refinement (Regional Soft Refinement) over regions that dismiss the visual boundaries and enhance adjacent interactions. Furthermore, RAGD novelly makes repairing feasible, where users can modify specific unsatisfied regions in the last generation while keeping all other regions unchanged, without relying on additional inpainting models. Our approach is tuning-free and applicable to other frameworks as an enhancement to the prompt following property. Quantitative and qualitative experiments demonstrate that RAGD achieves superior performance over attribute binding and object relationship than previous methods.
+
+# 1. Introduction
+
+Recent advancements in diffusion models [5, 14, 20, 25, 28, 32, 35, 36, 38-40, 43, 47, 48, 50-56] have substantially enhanced the aesthetic appeal and prompt adherence in text-to-image synthesis. The prevailing trend sees the denoising architecture shifting from UNet [31] to the Diffusion Transformer (DiT) [25], which excels in scaling with large datasets. Transformer-based diffusion models like PixArt $\alpha$  [4], Stable Diffusion 3/3.5 [9], and Flux.1 [2] have set a new benchmark, surpassing the quality of earlier UNet-based models such as Stable Diffusion 1.5 [30] and SDXL [26]. Furthermore, employing more robust text encoders, including T5-XXL [27], has demonstrated the ability to render visual text and significantly enhance prompt adherence. Some innovative studies even leverage large language models (LLMs) for text representation, with examples like KColors [37] utilizing GLM [7] and Playground V3 [23] employing Llama3-8B [8]. Despite this significant progress in generating high-quality images from prompts, achieving precise fine-grained spatial control remains elusive. In essence, current generative models still struggle with comprehending the quantity and spatial arrangement of objects.
+
+To address these limitations, the concept of regional prompting, also known as regional control, regional grounding, or composition generation, has emerged. Unlike providing a single global description, achieving fine-grained region-controllable generation requires users to supply not only the spatial location (e.g., a segmentation mask or bounding box) but also a corresponding description for each region. Several approaches have been proposed under this setting, broadly falling into two categories: tuning-based and tuning-free. For tuning-based methods, they often necessitate the training of an additional module to handle explicit conditions like bounding boxes. For example, GLIGEN [21] integrates regional inputs into new trainable layers through a gated mechanism, where each grounding token is a combination of the semantics of the grounded entity and its spatial location. Similarly, InstanceDiffusion [41] and Ms-diffusion [42] also incorporate learnable blocks to handle per-instance conditioning. These methods generally deliver strong performance in precise regional control but are limited to specific base models due to the introduction of extra trainable components. On the other hand, tuning-free methods, such as Multidiffusion [1], RPG [45], and Omost [24], operate on the denoised latent space or attention score map with a mask for each region. They frequently employ a split-and-merge strategy but face challenges in maintaining precise control as the number of regions increases.
+
+In this paper, we adopt a tuning-free manner and aim to improve its control strength and coherence when dealing with multiple regions. Specifically, we present RAGD, a novel Regional-Aware text-to-image Generation method for precise regional control, which is composed of two sub
+
+tasks, Regional Hard Binding and Regional Soft Refinement. First, we implement region-aware hard binding at the beginning of the denoising process to ensure that each regional prompt is executed accurately. This step breaks down the input prompt into several regional prompts, each with its respective spatial position, and then merges the individually denoised regional latents into the original image latent. Second, to dismiss the visual boundaries and enhance interaction between adjacent regions, regional soft refinement is applied within the multi-modal attention layers at the subsequent steps to obtain a regional latent, where  $K$  and  $V$  are from regional text tokens while  $Q$  is from original image latent, followed by a weighted recombination of base image latent and regional latent. Furthermore, leveraging robust control and fusion capabilities, our framework supports users to refine specific unsatisfactory regions from the last generation while keeping all other regions intact. Both quantitative and qualitative results demonstrate our superior performance over attribute binding and object relationship than previous state-of-the-art methods. Our contributions are summarized as follows:
+
+- We propose RAGD, a tuning-free Regional-Aware text-to-image Generation framework on the DiT-based model, with two novel components, Regional Hard Binding and Regional Soft Refinement, for precise and harmonious regional control.  
+- RAGD novelly makes image repairing feasible, allowing users to modify specific unsatisfactory regions in the previous generation while keeping all other regions intact without need for additional inpainting models.  
+- Extensive qualitative and quantitative experiments demonstrate that RAGD shows superior performance on T2ICompBench and GenEval benchmark, in comparison with previous state-of-the-arts methods.
+
+# 2. Related Work
+
+Tuning-based Regional Control. Conventional text-to-image generation only uses text as conditional input and injects control signals through cross-attention. In order to handle spatial conditions, some works introduce additional training modules, such as ControlNet [49], to handle new control conditions, including depth maps, sketches, human poses, etc. For regional control, additional module is also introduced for training-based methods [3, 6, 11, 21, 41, 42, 46, 57, 58] to process spatial positions, such as bounding boxes (coordinates) or segmentation masks. GLIGEN [21] adopts Fourier embedding to encode box coordinates and adds trainable gated self-attention layer at each transformer block to accept new grounding input. InstanceDiffusion [41] further allows diverse ways to specify region positions such as simple single points, scribbles, bounding boxes or segmentation masks. Ms-diffusion [42] integrates grounding tokens with its grounding resampler to correlate spe
+
+![](images/8ba41549f82c30c7c12578301f4752b8f63491d4f95869a22f2261b2b48f376b.jpg)  
+Figure 2. The overall framework of RAGD, which divides regional-aware generation into two stages: (1) Regional Hard Binding ensures the proper response of regional prompts by processing each region individually with its fundamental description, and bound at the first  $r$  steps to ensure accurate attribute representation and entity localization. (2) Regional Soft Refinement improves the harmony of adjacent region via enabling the interaction of regional local conditions with global image latent within the multi-modal attention layers at the later  $T - r$  steps. The lower left corner shows the definition of spatial region in regional hard binding and regional soft refinement.
+
+cific entities and spatial constraints. Other works, such as Attend-and-Excite [3], apply regional constraints via gradient optimization within the denoising process to ensure all regional tokens are attended.
+
+Tuning-free Regional Control. Although tuning-based methods show strong performance, collecting training data is time-consuming and labor-intensive, and they are limited to specific models due to the introduction of additional modules on the top of base models. To address these challenges, model agnostic approaches [1, 10, 17, 19, 24, 44, 45, 60] are proposed. DenseDiffusion [19] and Omost [24] directly adjust attention scores within cross-attention layers to ensure that the activations within masked regions are promoted. Mixture of Diffusers [17] and MultiDiffusion [1] denoise different locations separately and then combine the denoised latents using regional masks. Recently, RPG [45] introduces complementary regional diffusion through a resize-and-concatenate approach for region-specific compositional generation, where regional denoised latents are resized and merged as a single concatenated latent at each step. However, among these existing solutions, certain approaches handle individual regions independently through a "divide-and-merge" strategy that lacks cross-region inter
+
+action mechanisms, resulting in boundary artifacts or target loss during merging. Other methods rely solely on attention masks to adjust inter-regional weight distributions but inadequately decouple the fundamental generation process from detail integration phases, which may lead to multi-region control failures. Thus, we propose RAGD, which decouples the compositional generation process into the construction of individual regions and detail refinement. This approach effectively controls the generation effects across multiple regions and significantly enhances the quality of details and the naturalness of boundary handling.
+
+# 3. Method
+
+# 3.1. Preliminaries
+
+Diffusion Transformer (DiT). DiT [25] is a novel architecture integrating transformer as the backbone network within Latent Diffusion Model (LDM), and has become a dominated choice in recent text-to-image generation models like Stable Diffusion 3/3.5 [9] and Flux [2]. By leveraging transformer, DiT efficiently captures complex dependencies in data, resulting in high-quality image generation. Consistent with the design philosophy of LDM, DiT also operates
+
+directly in the latent space, allowing the model to generate high-fidelity images that adhere to specified conditions while reducing computational overhead.
+
+Multi-modal Attention Mechanism. The multi-modal attention mechanism is a crucial component in DiT, enabling effective interactions between the diffusion network and additional control signals such as text or image. To handle inputs from different modalities effectively, MM-DiT assigns different weights to the prompt and image embeddings. During attention computation, the sequences of the prompt and image are merged to be processed independently in their respective spaces, while considering the influence of each other. The attention weights are calculated as follows:
+
+$$
+\operatorname {A t t e n t i o n} (Q, K, V) = \operatorname {s o f t m a x} \left(\frac {Q K ^ {T}}{\sqrt {d}}\right) \cdot V, \tag {1}
+$$
+
+where  $Q$ ,  $K$ , and  $V$  represent the Query, Key, and Value in the attention layer, respectively, and they are projected through a linear layer from the merged sequence of the prompt and the image.
+
+# 3.2. Overview of RAGD
+
+We briefly elucidate the core framework of RAGD, as depicted in Figure 2, which systematically dissociates the compositional generation workflow into two suboperational phases—foundational region construction and detail refinement. The implementation of RAGD consists of the following steps:
+
+(1) Regional Hard Binding (Sec. 3.3): This step involves decomposing the raw and complex input prompt containing multiple objects into a subset of fundamental descriptions for each individual region or object, along with their corresponding spatial positions. Then, each region is processed individually with its fundamental description and bound only at the early stage of denoising to ensure accurate attribute representation and entity localization.  
+(2) Regional Soft Refinement (Sec. 3.4): At this step, highly descriptive sub-prompts are generated for each region along with a global prompt to further enriching the definition of each object and promote the fusion between adjacent regions. Instead of manipulating the image latent, the refinement step achieves the interaction of regional local conditions and global image latent within the multi-modal attention layers.
+
+It is worth noting that based on our setting, RAGD can novelly support image inpainting (Sec. 3.5) in a free lunch manner by only re-initialize the initial noise in target areas, thereby enabling accurate modification of previously generated images while maintaining the overall generation quality without the need for an additional inpainting model.
+
+# 3.3. Regional Hard Binding
+
+To ensure the proper response of regional prompts and mitigate object omission when the number of region or ob
+
+ject increases, we apply regional hard binding in the early steps of denoising process as illustrated in Figure 2, which involves separately denoising the regions with their short fundamental descriptions and then binding local regional latents into global latent.
+
+Specifically, we first decompose the long input prompt  $P$  containing multiple objects into a set of fundamental descriptions  $\hat{p}^i$  with their position sets  $m^i = \{m_{offset}^i, m_{scale}^i\}$  and  $n^i = \{n_{offset}^i, n_{scale}^i\}$ . Subsequently, we perform text encoding on  $P$  and  $\hat{p}^i$  to obtain  $y$  and  $\hat{y}^i$ . The individual latent  $\hat{x}^i$  utilizes  $\hat{y}_i$  as a text condition, while origin latent  $x$  takes the long input prompt  $P$  as condition. The formulaic process is as follows:
+
+$$
+x _ {t - r} = x _ {t - r + 1} - \epsilon_ {\theta} (x _ {t - r + 1}, y) \tag {2}
+$$
+
+$$
+\hat {x} _ {t - r} ^ {i} = \hat {x} _ {t - r + 1} ^ {i} - \epsilon_ {\theta} \left(\hat {x} _ {t - r + 1} ^ {i}, \hat {y} ^ {i}\right), \tag {3}
+$$
+
+where  $i\in [1,k],k$  is the number of regions.  $\epsilon_{\theta}$  is the noise predicted. For each denoising step, we bind  $\hat{x}_{t - r}^2$  to the latent space in the rectangular area given by  $m_i,n_i$  as follows:
+
+$$
+x _ {t - r} = \operatorname {R e p l a c e} \left(x _ {t - r}, \hat {x} _ {t - r} ^ {i}, m ^ {i}, n ^ {i}\right), \tag {4}
+$$
+
+where  $\operatorname{Replace}(\cdot)$  represents the process of pasting the individual latents back to the corresponding area in origin latent. The binding is only executed in the early steps within denoising process. We find that a few steps of binding is sufficient for regional completeness, whereas full-steps
+
+Algorithm 1: RAGD Algorithm Process  
+output:  $x_0$  
+input: Model  $p_{\theta}$  ,Base Prompt  $P$  ,Text Encoder TE, Hard Binding Step  $r$  ,Fusion Strength  $\delta$  ,Hard Binding Position  $\{m^i,n^i\}$  ,Soft Refinement Region  $\{h^i,w^i\}$    
+initialization: Time Step T,Origin Latent  $x$  Individual Latent  $\hat{x}^i$  .   
+//  $\hat{p}^i$  is simple subprompt for Hard Binding,  $\tilde{p}^i$  is descriptive subprompt for Soft Refinement".  $\hat{p}^i,\tilde{p}^i\gets P$  .   
+ $y\gets TE(P),\hat{y}^{i}\gets TE(\hat{p}^{i}),\tilde{y}^{i}\gets TE(\tilde{p}^{i})$  .   
+for  $t\gets T$  to  $(T - r)$  do // Hard Binding;  $x_{t - r}\leftarrow p_{\theta}(x_{t - r + 1},y);$ $\hat{x}_{t - r}^{i}\gets p_{\theta}(\hat{x}_{t - r + 1}^{i},\hat{y}^{i});$ $x_{t - r}\gets \mathrm{Replace}(x_{t - r},\hat{x}_{t - r}^{i},\{m^{i},n^{i}\})$  .   
+for  $t\gets (T - (r + 1))$  to 0 do // Soft Refinement;  $x_{t - (r + 1)}^{i}\gets \mathrm{jointAttn}(x_{t - (r + 1)},\tilde{y}^{i});$ $\tilde{x}_{t - (r + 1)}^{i}\gets \mathrm{Crop}(x_{t - (r + 1)}^{i},\{h^{i},w^{i}\})$  .  $x_{t - (r + 1)}^{r}\gets \mathrm{Replace}(x_{t - (r + 1)},\tilde{x}_{t - (r + 1)}^{i},$ $\{h^i,w^i\})$  .  $x_{t - (r + 1)}\gets x_{t - (r + 1)}*(1 - \delta)_+x_{t - (r + 1)}^r*\delta ;$
+
+<table><tr><td rowspan="2">Model</td><td colspan="5">Geneval</td><td colspan="6">T2ICompBench</td></tr><tr><td>Counting ↑</td><td>Position ↑</td><td>Color_attr ↑</td><td>Two_object ↑</td><td>VQAScore ↑</td><td>Color ↑</td><td>Shape ↑</td><td>Texture ↑</td><td>Spatial ↑</td><td>Complex ↑</td><td>VQAScore ↑</td></tr><tr><td>MultiDiffusion [1] [ICML2023]</td><td>0.40</td><td>0.06</td><td>0.15</td><td>0.42</td><td>0.6370</td><td>0.4811</td><td>0.4341</td><td>0.5105</td><td>0.2320</td><td>0.3278</td><td>0.6882</td></tr><tr><td>Ranni [11] [CVPR2024]</td><td>0.21</td><td>0.11</td><td>0.08</td><td>0.30</td><td>0.5612</td><td>0.3154</td><td>0.3099</td><td>0.3538</td><td>0.1456</td><td>0.1157</td><td>0.5959</td></tr><tr><td>MIGC [58] [CVPR2024]</td><td>0.51</td><td>0.76</td><td>0.36</td><td>0.84</td><td>0.7639</td><td>0.6552</td><td>0.4896</td><td>0.5661</td><td>0.3805</td><td>0.3164</td><td>0.7705</td></tr><tr><td>InstanceDiffusion [41] [CVPR2024]</td><td>0.61</td><td>0.55</td><td>0.28</td><td>0.67</td><td>0.7795</td><td>0.6437</td><td>0.5361</td><td>0.6372</td><td>0.3871</td><td>0.3066</td><td>0.7508</td></tr><tr><td>RPG [45] [ICML2024]</td><td>0.43</td><td>0.63</td><td>0.64</td><td>0.82</td><td>0.6502</td><td>0.7680</td><td>0.5078</td><td>0.6195</td><td>0.4017</td><td>0.3702</td><td>0.6502</td></tr><tr><td>3DIS [59] [ICLR025]</td><td>0.66</td><td>0.72</td><td>0.50</td><td>0.83</td><td>0.7840</td><td>0.5748</td><td>0.3223</td><td>0.5086</td><td>0.3030</td><td>0.3035</td><td>0.7978</td></tr><tr><td>Ours</td><td>0.80</td><td>0.82</td><td>0.79</td><td>0.95</td><td>0.8072</td><td>0.8039</td><td>0.6016</td><td>0.7085</td><td>0.5193</td><td>0.4377</td><td>0.8907</td></tr></table>
+
+Table 1. Comparison of alignment evaluation on Geneval [12] and T2ICompBench [16]. The best results are highlighted in bold, second-best in underline.
+
+binding results in either clear visual boundaries adjacent regions or poor interactivity.
+
+# 3.4. Regional Soft Refinement
+
+Images generated by direct regional hard binding allow for precise control over positioning, effectively preventing object omission. However, the rendering of attributes tends to be relatively coarse, and there is a tendency for noticeable boundaries between adjacent regions. Therefore, we apply regional soft refinement in the later steps of the denoising process to improve the harmony of adjacent regions.
+
+Specifically, similar to the previous binding step, we break down the original long prompt  $P$ , but instead of breaking it down into short fundamental descriptions, we break it down into highly descriptive sub-prompts  $\tilde{p}^i$ , with a set of global regions  $o^i = \{h_{split}^i, w_{split}^i\}$ , and obtain the corresponding representation  $\tilde{y}^i$  through the text encoder. Then, the text condition  $\tilde{y}^i$  is projected into  $K^i$  and  $V^i$  while  $Q^i$  is derived from current image latent  $x_{t - (r + 1)}$  within multi-modal attention layers:
+
+$$
+\begin{array}{l} Q ^ {i} = \ell_ {Q} (x _ {t - (r + 1)}), K ^ {i} = \ell_ {K} (\tilde {y} ^ {i}), V ^ {i} = \ell_ {V} (\tilde {y} ^ {i}) \\ x _ {t - (r + 1)} ^ {i} = \operatorname {S o f t m a x} \left(\frac {Q ^ {i} K ^ {i ^ {T}}}{\sqrt {d}}\right) V ^ {i}, \tag {5} \\ \end{array}
+$$
+
+where  $\ell_{Q},\ell_{k},\ell_{V}$  are linear projections,  $\mathbf{x}_{t - (r + 1)}^i$  is globally-informed latent. We crop  $\mathbf{x}_{t - (r + 1)}^i$  to the region corresponding to different objects to obtain  $\tilde{\mathbf{x}}_{t - (r + 1)}^i$  with rich attributes generated in the global region:
+
+$$
+\tilde {x} _ {t - (r + 1)} ^ {i} = \operatorname {C r o p} \left(x _ {t - (r + 1)} ^ {i}, o ^ {i}\right). \tag {6}
+$$
+
+Then, we also execute Replace  $(\cdot)$  to splice these regions:
+
+$$
+x _ {t - (r + 1)} ^ {r} = \operatorname {R e p l a c e} \left(x _ {t - (r + 1)}, \tilde {x} _ {t - (r + 1)} ^ {i}, o ^ {i}\right). \tag {7}
+$$
+
+To further improve the alignment between each region with the original prompt and enhance adjacent interactions, we perform a linear weighted recombination of  $x_{t - (r + 1)}^r$  and  $x_{t - (r + 1)}$  as follows:
+
+$$
+x _ {t - (r + 1)} = x _ {t - (r + 1)} * (1 - \delta) _ {+} x _ {t - (r + 1)} ^ {r} * \delta , \tag {8}
+$$
+
+where  $\delta$  controls the fusion strength of image latent  $x_{t - (r + 1)}$  and region-aware global latent  $x_{t - (r + 1)}^r$ . The detailed process of our method can be found in algorithm 1.
+
+![](images/3214fe794d692ed078c1ed4712a5eb39c6c612f683385476f1c19332c1cb5516.jpg)  
+Figure 3. Illustration of Re-painting. Different from regular image-to-image inpainting, repainting inherits from last generation with only the target area re-initialized (upper). Given the parameters in previous generation, users are allowed to specify a target area with a new prompt and repaint the image, without relying on additional inpainting models (bottom).
+
+# 3.5. Image Repainting
+
+Based on our task setting, where a long complex prompt containing multiple objects is decoupled into several regional sub-prompts for individual processing, a natural question is raised: Can this approach be used to repaint specific areas? By leveraging the robust control and fusion capabilities of regional hard binding and regional soft refinement, we can reinitialize noise in a specific region requiring modification, enabling repainting of a region without affecting the overall layout or attributes of other areas. Different from typical post-processing inpainting task that usually requires additional inpainting models, repainting regenerates with the same parameters from the last generation, with only the prompts in the target area modified.
+
+As shown in Figure 3, users can modify the description of a specific region within  $P$ ,  $\hat{p}^i$ ,  $\tilde{p}^i$  to obtain new edited prompts  $P_e$ ,  $\hat{p}_e^i$ ,  $\tilde{p}_e^i$ . Subsequently, we encode them as text features  $y_e$ ,  $\hat{y}_e^i$ ,  $\tilde{y}_e^i$ . Given a total denoising step  $T$ , the initial noisy latent  $x_T$  is inherited from the previous generation  $x_T$ , only the target area indicated by mask is re-initialized:
+
+$$
+x _ {T} ^ {\prime} = \operatorname {i n i t} \left(x _ {T}, \text {m a s k}\right). \tag {9}
+$$
+
+To ensure the other regions intact, we simultaneously perform denoising on  $x_{T}$  and  $x_{T}^{\prime}$ . At each timestep  $t$ , we replace the corresponding portions of  $x_{t}$  with the masked
+
+![](images/7bf497b78ac22dbeefd4f90b16eb36d9025ba686ee605d6d1656a09fdba8e3b6.jpg)  
+Figure 4. Qualitative comparisons on compositional text-to-image generation. From top to bottom, we show 5 examples of different prompts and regions. Compared with previous methods, we demonstrate excellent regional control capabilities.
+
+areas of the edited region from  $x_{t}^{\prime}$  for repainting:
+
+$$
+x _ {t} = \operatorname {R e p a i n t} \left(x _ {t}, x _ {t} ^ {\prime}, \text {m a s k}\right). \tag {10}
+$$
+
+Through the regional complementarity facilitated by regional soft refinement, the repainted area can be seamlessly integrated with the surrounding regions. This methodology not only renders image repairing feasible but also ensures the coherence and consistency of the overall scene.
+
+# 4. Experiments
+
+# 4.1. Experiment Setting
+
+Implementation Details. We implement our approach on Flux.1-dev [2]. The inference process is set to 20 steps, with guidance scale of 3.5. For large-scale quantitative evaluations, we employ Chain-of-Thought (CoT) template from [45] and leverage MLLM to automatically decouple multi-object scenes, see Appendix for usage. All experiments are conducted on a single A6000 GPU.
+
+Compared Methods. To comprehensively evaluate the generation quality, we compare our RAGD with several region control state-of-the-art approaches, including tuning-free methods: MultiDiffusion [1], RPG [45]; and tuning-based methods: InstanceDiffusion [41], Ranni [11], MIGC [58], 3DIS [59].
+
+# 4.2. Main Results
+
+Quantitative Comparison. Table 1 presents our alignment evaluation on the GenEval [12] and T2ICompBench [16], while introducing VQAScore [22] across both benchmarks to ensure rigorous assessment of complex regional prompts. Our approach outperforms competitors in key aspects such as attribute binding, object relationships, and complex composition. Notably, despite employing a tuning-free approach, RAGD achieves an average improvement of  $76.6\%$  over both RPG and MultiDiffusion in handling prompts with spatial relationships, underscoring its
+
+![](images/c15a061c4f23dadb38781acb3b151b8850b55e8b7693c5537627a49d9d7ec617.jpg)  
+A Siamese cat lying on the grass.
+
+![](images/b913d221cbcabe429942d356a1e1da27f3073d25bcb0fe4b50079fc2a8268d08.jpg)
+
+![](images/2850219a8ee2d8dffca8692a0864fc09975b722bd8789c623ba9c297660736cd.jpg)
+
+![](images/b5c762a087aae79015a1a36a620440d5b6919eb5f265a87f66e2afedb9e77a53.jpg)  
+A Corgi lying on the grass.
+
+![](images/92ba394079fca6b69d4d3b1fc27126b2d320e4bb15f9ab2725ae43294effc64d.jpg)
+
+![](images/a396dbeee00af96788f94c5b947cc82b660e5d173ed897f17502d4a9358f15ea.jpg)  
+A man on the left, a woman on the right.
+
+![](images/a621e25ae763d8a956c41693b11106aa4d0104b7c3c0475aaeb769a039571d60.jpg)
+
+![](images/f7c188ded28d9e68ed61fc6d184f8aaaa02f7f897fc8b1721a3e8ace8b2408bc.jpg)
+
+![](images/977736f72e9aaa9dfbe04328cee6eac11b068342916aadf4a6b1ceef735eee7e.jpg)  
+A man on the left, an anime woman on the right.
+
+![](images/e8ac5303285b2c818ab22186b8b9d9aaaf564eff8f4953fd0a9fdb4f28e7f464.jpg)
+
+![](images/9e9c1c8857e8f1bae27e806029d4e24b079444bb7d86908c08f407286ee6e1de.jpg)  
+A boy holding a basketball in one hand.
+
+![](images/6031068ee33e9725afd4cefbe2d2dac481c5d016acdee166694b6d83ea78b79d.jpg)
+
+![](images/16828072f7943a2bbe5e9a518036b387c647ae597d20aaf18f8464cff30de4a1.jpg)
+
+![](images/e373f957bc4f5675446763c91f3cda88b393bc4bddf49c45a9ceb302a52ad0f9.jpg)  
+A boy holding a soccer in one hand
+
+![](images/0f1d2fcb3a1e4985132df891d0adb0770f288391f0e6ef725900d69233778621.jpg)
+
+![](images/8b9fc0e56692e333264c962823acbf7cde7436de570e10f56fa389e9a78d14d0.jpg)  
+Three plush toys on the table.
+
+![](images/98ea105dedc31bc5ded9f7ac3eca98f0ad1684ade98fa4281f7884f0c9823a78.jpg)
+
+![](images/a219d2471f8b9e417706cae10c1c10691a11de97674d9aa664789927d013130a.jpg)  
+Figure 5. Qualitative comparisons on image inpainting between our RAGD and the state-of-the-art inpainting model BrushNet. Our results are more region-aware with harmonious effect with the surrounding, revealing diverse potential for applications.
+
+![](images/1bbcfcb2ba66444c89f5109975ba1304051b0c717081207ff32d046bcbb46aa3.jpg)
+
+![](images/449b0d2d3f04b36ea227a973bb66a6714fee96daa71c77787b919b3b9a26b1ee.jpg)  
+Two plush toys and one balloon on the table.
+
+<table><tr><td>Methods</td><td>Aesthetic ↑</td><td>Alignment ↑</td></tr><tr><td>RPG [45] [ICML 2024]</td><td>16.1%</td><td>14.8%</td></tr><tr><td>Stable 3.5 [9] [ICML 2024]</td><td>13.2%</td><td>13.4%</td></tr><tr><td>Flux.1-dev [2] [2024]</td><td>18.8%</td><td>17.8%</td></tr><tr><td>Ours</td><td>51.9%</td><td>54.0%</td></tr></table>
+
+effectiveness in spatially accurate generation. Compared to tuning-based methods such as InstanceDiffusion, Ranni, MIGC, and 3DIS, RPG exhibits equally robust competitiveness in performance. In the VQAScore evaluations of the Geneval and T2ICompBench benchmarks, RPG achieved an average improvement of  $14.0\%$  and  $23.8\%$ , respectively. Quantitative results demonstrate our superior performance in handling complex multi-region prompts.
+
+Qualitative Comparison. Figure 4 illustrates visual comparisons, highlighting our superiority in complex multi-region generation. Our method enables accurate multi-region control via hard binding and soft refinement mechanisms, faithfully conveying details on position, quantity, and attributes based on the input text. Figure 5 shows the comparison with the state-of-the-art inpainting model BrushNet [18], showcasing our strength in inpainting both single and contacted regions without conflict. Even when the inpainted object differs greatly in style or shape, our method successfully generates the intended target while maintaining the layout and regional attributes, enhancing the flexibility and control of the generation process.
+
+User Study. We randomly sampled 109 prompts from the T2ICompBench test set to evaluate the aesthetic quality and text-image consistency (including attributes and spatial positions) of the generated images. During the evaluation, we invited 24 professional users to compare the generation results of RPG [45] and Stable 3.5 [9], Flux.1-dev [2], RAGD, selecting the most suitable generation results for each prompt. Through this blind test, we obtained 2,616
+
+Table 2. User study on aesthetics and text-image alignment. Our approach shows a significant improvement.  
+
+<table><tr><td colspan="2">Stage</td><td colspan="6">T2ICompBench</td></tr><tr><td>Harding Binding</td><td>Soft Refinement</td><td>Color</td><td>Shape</td><td>Texture</td><td>Spatial</td><td>Complex</td><td>VQAScore</td></tr><tr><td></td><td>✓</td><td>0.7828</td><td>0.5683</td><td>0.6617</td><td>0.2821</td><td>0.3559</td><td>0.7656</td></tr><tr><td></td><td></td><td>0.7238</td><td>0.5012</td><td>0.5832</td><td>0.4939</td><td>0.3897</td><td>0.8413</td></tr><tr><td></td><td>✓</td><td>0.8039</td><td>0.6016</td><td>0.7085</td><td>0.5193</td><td>0.4377</td><td>0.8907</td></tr></table>
+
+Table 3. Ablation performance of RAGD. Regional soft refinement helps refine attributes and merge boundaries, and regional hard binding is beneficial for accurate spatial positioning of complex layouts.
+
+![](images/765682427a45113f9b5206dd21370ab75e838b2ee68678d816b12d98ca7338d9.jpg)
+
+![](images/dc0e9d0468d8637cf06bb0b7da05a5f9d5c12a2b1903775ab3e02b44e23afef8.jpg)
+
+![](images/6530b81990edab2d56e15d60c1ddffe8dfe8fc58175ad1905d0f91b2ac27628c.jpg)
+
+![](images/ec1e7a1b55f31f6612012d5e07762c3c9b127346e83982d121aca4d250ee3b10.jpg)
+
+![](images/9ac765e4936a30d5669b90f46a0e390ca3fafa8d6013f3a6c1a86049d22c2cd0.jpg)  
+w/o Hard Binding w/o Soft Refinement  
+Figure 6. Qualitative analysis of Hard Binding and Soft Refinement. The former ensures the proper responses of each region, while the latter enhances the coherence among regions.
+
+![](images/c5638cf208926de064d75038ffc98a6ccc114996012cd57d71f036a4769d98e0.jpg)  
+w/Hard Binding w/o Soft Refinement
+
+![](images/989f80751a0668e4bd8067ed6e4f389fa8b54b47e8a6cdad532d209dc6af069c.jpg)  
+W/o Hard Binding W/ Soft Refinement
+
+![](images/91615e005f16e8a6004a22ea36b6a6e9a66a9f167228ccbe2c1bb8179a0435e7.jpg)  
+w/ Hard Binding w/ Soft Refinement
+
+user votes. The results are shown in Table 2. RAGD is far ahead in terms of both aesthetics and alignment.
+
+# 4.3. Ablation Study
+
+Effectiveness of Hard Binding & Soft Refinement. The proposed RAGD comprises two key components: hard binding and soft refinement. We conducted ablation experiments on these two parts, with visual results shown in Figure 6. Table 3 shows the ablation performance of the two stages. Results reveal that hard binding achieves precise object positioning but yields coarse attribute rendering and limited integration among objects. With soft refine-
+
+<table><tr><td rowspan="2"></td><td colspan="6">T2ICompBench</td></tr><tr><td>Color ↑</td><td>Shape ↑</td><td>Texture ↑</td><td>Spatial ↑</td><td>Complex ↑</td><td>VQAScore ↑</td></tr><tr><td>SD3.5</td><td>0.7870</td><td>0.6101</td><td>0.7068</td><td>0.2660</td><td>0.3310</td><td>0.8393</td></tr><tr><td>RPG+SD3.5</td><td>0.7343</td><td>0.5436</td><td>0.6591</td><td>0.4008</td><td>0.3436</td><td>0.8340</td></tr><tr><td>Ours+SD3.5</td><td>0.8222</td><td>0.6304</td><td>0.7375</td><td>0.4360</td><td>0.3623</td><td>0.8543</td></tr><tr><td>Flux</td><td>0.7680</td><td>0.5078</td><td>0.6195</td><td>0.2606</td><td>0.3650</td><td>0.7438</td></tr><tr><td>RPG+Flux</td><td>0.7033</td><td>0.5224</td><td>0.6231</td><td>0.4393</td><td>0.3579</td><td>0.8213</td></tr><tr><td>Ours+Flux</td><td>0.8039</td><td>0.6016</td><td>0.7085</td><td>0.5193</td><td>0.4377</td><td>0.8907</td></tr></table>
+
+Table 4. RAGD can seamlessly integrate various text-to-image models and exhibits superior enhancement capabilities compared to other solutions.
+
+![](images/b50d131390f7b5b3a81e66d10b3b36a31b364ea8e658a20551dc2db9cf3437b4.jpg)  
+Figure 7. Our method shows strong visual competitiveness in different frameworks.
+
+ment, object attributes are richly detailed and relationships are harmonious, though precise positioning may be compromised, and object omission may sometimes occur.
+
+Generalizability of the method. As shown in Table 4 and Figure 7, RAGD can be migrated to different T2I models and demonstrates stronger enhancement effects compared to other approaches. Additionally, as illustrated in Figure 8, RAGD possesses strong generalization abilities and is compatible with plug-and-play modules such as LoRA [15, 33, 34] and IPAdapter [13, 47]. The integration of these expansion modules enriches the diversity of generated results, improving content detail representation while further enhancing the adaptability and scalability of RAGD.
+
+Analysis of Inference Time. In RAGD, the decoupled multi-region generation operation processes each region independently, leading to increased inference time as the number of regions grows. However, because RAGD does not modify the underlying architecture of the original model, existing acceleration frameworks, such as HyperFlux [29], remain compatible with RAGD. As shown in Figure 9, combining RAGD with Hyper-Flux results in inference being 2.5-fold faster while preserving the stability of accuracy and detail control in regional generation. This demonstrates that, although inference speed presents a challenge, with appropriate acceleration strategies, RAGD can efficiently generate multi-region images with high quality and maintain control over interactions between regions.
+
+![](images/5fb99aa133cd4ab2197338a26f216969ac786f0c5efd4ffc792e12cd7e0acf41.jpg)  
+Figure 8. Ours can work with different plugins and provide region control capabilities to increase usability.
+
+![](images/099498b1a7e3d7d0962579390e64259196b99f37672ac02c73f57a10871789fb.jpg)
+
+![](images/447f4604e4b177eb58f9c7fc25f3f7d9de70d60ee84f3195b61344dbc0012704.jpg)  
+From left to right: a red cake, an orange cake, a yellow cake, and a green cake.
+
+![](images/708a7cdcc79eda022542932cbd2de73c36cb5b0a717bcd980198b9f90c0b15dd.jpg)  
+Figure 9. RAGD, accelerated by Hyper-Flux, is  $2.5 \times$  faster than the original version, maintaining visual quality.
+
+# 5. Conclusion
+
+In this paper, we introduce RAGD, a novel tuning-free region-aware diffusion model for text-to-image generation, designed to address the challenges posed by regional prompts. RAGD operates through two key stages. First, regional hard binding independently constructs content within each designated region. Subsequently, regional soft refinement enhances interactions between adjacent regions while improving attribute generation accuracy. Furthermore, RAGD bypasses the need for external inpainting models, enabling direct image painting to modify unsatisfactory regions from last generations. Extensive experimental results demonstrate the superiority of RAGD in compositional generation compared to prior methods.
+
+Limitation and Future Work. RAGD offers precise regional control and flexible image repairing but has limitations. Its multi-region decoupling increases inference time as region count grows. Future work will focus on improving RAGD's inference efficiency and integrating with other diffusion models for enhanced scalability and performance.
+
+# Acknowledgment
+
+This work was supported by Natural Science Foundation of China: No. 62406135, Natural Science Foundation of Jiangsu Province: BK20241198, the Gusu Innovation and Entrepreneur leading Talents: No. ZXL2024362, and Nanjing University-China Mobile Communications Group Co. Ltd. Joint Institute.
+
+# References
+
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+[3] Hila Chefer, Yuval Alaluf, Yael Vinker, Lior Wolf, and Daniel Cohen-Or. Attend-and-excite: Attention-based semantic guidance for text-to-image diffusion models. ACM Transactions on Graphics (TOG), 42(4):1-10, 2023. 2, 3  
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+[5] Zhennan Chen, Rongrong Gao, Tian-Zhu Xiang, and Fan Lin. Diffusion model for camouflaged object detection. In ECAI 2023, pages 445-452. IOS Press, 2023. 2  
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+[7] Zhengxiao Du, Yujie Qian, Xiao Liu, Ming Ding, Jiezhong Qiu, Zhilin Yang, and Jie Tang. Glm: General language model pretraining with autoregressive blank infilling. arXiv preprint arXiv:2103.10360, 2021. 2  
+[8] Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Amy Yang, Angela Fan, et al. The llama 3 herd of models. arXiv preprint arXiv:2407.21783, 2024. 2  
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ICCV/2025/RAGDiffusion_ Faithful Cloth Generation via External Knowledge Assimilation/full.md

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+# RAGDiffusion: Faithful Cloth Generation via External Knowledge Assimilation
+
+Yuhan Li $^{1*†}$ , Xianfeng Tan $^{2*}$ , Wenxiang Shang $^{2}$ , Yubo Wu $^{2}$ , Jian Wang $^{2}$ , Xuanhong Chen $^{1}$ , Yi Zhang $^{1}$ , Hangcheng Zhu $^{2‡}$ , Bingbing Ni $^{1‡}$
+
+$^{1}$ Shanghai Jiao Tong University  $^{2}$ Alibaba Group
+
+https://colorful-liyu.github.io/RAGDiffusion-page/
+
+# Abstract
+
+Standard clothing asset generation involves restoring forward-facing flat-lay garment images displayed on a clear background by extracting clothing information from diverse real-world contexts, which presents significant challenges due to highly standardized structure sampling distributions and clothing semantic absence in complex scenarios. Existing models have limited spatial perception, often exhibiting structural hallucinations and texture distortion in this high-specification generative task. To address this issue, we propose a novel Retrieval-Augmented Generation (RAG) framework, termed RAGDiffusion, to enhance structure determinacy and mitigate hallucinations by assimilating knowledge from language models and external databases. RAGDiffusion consists of two processes: (1) Retrieval-based structure aggregation, which employs contrastive learning and a Structure Locally Linear Embedding (SLLE) to derive global structure and spatial landmarks, providing both soft and hard guidance to counteract structural ambiguities; and (2) Omni-level faithful garment generation, which introduces a coarse-to-fine texture alignment that ensures fidelity in pattern and detail components within the diffusing. Extensive experiments on challenging real-world datasets demonstrate that RAGDiffusion synthesizes structurally and texture-faithful clothing assets with significant performance improvements, representing a pioneering effort in high-specification faithful generation with RAG to confront intrinsic hallucinations and enhance fidelity.
+
+# 1. Introduction
+
+While the high quality of images generated by diffusion models [20, 45] has significantly lowered the barriers for individuals to engage in content creation, the generation of 2D standard clothing assets from in-the-wild data has been relatively underexplored [43]. Standard clothing asset gen
+
+![](images/ef8c238a23b454c65877eea4c3736a2f2596d093e7f759e17f907ecec90ca13b.jpg)
+
+![](images/7cd74fb3ddda5fea273e9c065efc91acadbe6baa12b0a967f02228a44be18b4d.jpg)  
+Figure 1. RAGDiffusion synthesizes structurally and pattern-wise faithful standard garments by assimilating retrieved knowledge.
+
+eration refers to generating forward-facing flat-lay garment images [49] on a clear background by recovering clothing information from arbitrary real-world scenes (e.g., garments hung on hangers, worn by models, or casually laid on chairs in Fig. 1). Standard garments serve as a crucial intermediary variable, connecting various downstream applications such as e-commerce catalogs maintenance, garment design, product marketing and virtual fitting [19, 64, 65].
+
+The garment generation task presents dual technical challenges distinct from conventional virtual try-on paradigms. First, standard clothing generation necessitates standard structure and frontal positioning while inherently limiting stylistic flexibility, constrained by the narrow manifold of high-specification garment distributions [62]. Second, the complexity of in-the-wild condi
+
+tions involving occlusions, multi-layer outfits, truncations, or extreme lateral viewpoints notably exacerbates structural uncertainty and pattern ambiguity. Collectively, experimental evaluations reveal that existing methods [21, 51] fail to achieve practical usability thresholds with structural and texture distortion, particularly manifesting a pathological structure hallucinations in inaccurate structure, fitness and length estimation under challenging scenes (see Fig. 3 and Fig. 5), which we attribute to the limited spatial reasoning capacity inherent in Stable Diffusion (SD) architectures.
+
+Despite its critical commercial relevance, the garment restoration problem remains insufficiently addressed in literature [43, 49, 51, 57]. Early GAN-based frameworks [57] suffer from pattern distortions constrained by their generative priors. Recent approaches [43, 49, 51] employing pretrained SD exhibit several limitations: (i) inadequate handling of structural hallucinations in hard cases (occluded, multi-layer, etc.), (ii) commercially unfaithful logo/texture reproduction which is extremely sensitive to e-commerce sellers. In summary, no existing solution achieves the dual objectives of high-structural integrity and photorealistic texture synthesis under real-world complexity.
+
+We propose RAGDiffusion, as a Retrieval-Augmented Generation (RAG) [38] paradigm including two processes: information aggregation based on retrieval, and conditional generation with omni-level fidelity, to address the issue of structural and texture distortion respectively. (1) Retrieval-based Structure Aggregation: Our key insight lies in enhancing structural determinacy through the assimilating of external structural landmarks and world knowledge, thereby rectifying visual models' misconceptions regarding garment structure, fitness and proportions. During RAG process, contrastive learning [10, 18] is firstly introduced to train a dual tower network to extract multi-modal structure embeddings from images of two branches as well as attributes derived from a frozen large language model (LLM) [1, 2]. Considering potential encoding bias in real-world data, we propose a structure retrieval named Structure Locally Linear Embedding (SLLE) to project the predicted structure embedding towards a standard manifold [41, 56] as well as offer a silhouette landmark. The remapped latent structure embedding and the landmarks provide soft and hard structure guidance respectively through Embedding Prompt Adapter and Landmark Guider to eliminate structural hallucinations. (2) Omni-level Faithful Garment Generation: RAGDiffusion establishes coarse-to-fine texture alignment for pattern faithfulness and detail faithfulness for generated garment. Specifically, we ensure the generated pattern matches the conditioning through ReferenceNet [21], a conditioning UNet isomorphic to the denoising UNet. However, problematic detail and logo artifacts persist partially due to resolution limitations of VAE decoders, rendering the generated images commercially un
+
+usable for e-commerce sellers, which is an under-addressed issue across prior research [43, 49, 51]. To mitigate reconstruction distortions inherent in original VAE [25], we propose Parameter Gradual Encoding Adaptation (PGEA) to adapt the SDXL [35] backbone to a more powerful VAE.
+
+To the best of our knowledge, RAGDiffusion stands as a pioneering multi-modal RAG method to solve intrinsic hallucination and unfaithfulness during image synthesis. Furthermore, we discover two additional benefits brought by RAG: zero-shot generalizability for unseen scenarios via retrieval database expansion, and human-interpretable control mechanisms through landmark manipulation. The core contributions of this work are threefold:
+
+- We propose RAGDiffusion, a RAG framework for clothing generation with representation learning and SLLE to offer structure determinacy and eliminate hallucination.  
+- We employ a coarse-to-fine texture alignment in RAGDiffusion, addressing pattern and detail aspects, ensuring faithfulness of clothing on this high-specification task.  
+- Comprehensive experiments on challenging in-the-wild sets demonstrate RAGDiffusion is capable of synthesizing both structure and texture faithful clothing assets, outperforming current methods by a substantial margin. Furthermore, the ablation study has validated the effectiveness of different parts of RAGDiffusion.
+
+# 2. Related works
+
+Retrieval-augmented generative models. Retrieval-augmented strategies leverage external databases to enhance the capabilities of generative models across a variety of tasks. For instance, the RETRO [5] modifies an LLM to effectively utilize external databases. In the realm of image synthesis, retrieval has been employed in both GANs [7, 47] and diffusion models [4, 44], accommodating 3D generation [42], video generation [60] and artistic styles [40]. The essence of these works lies in retrieving similar images to serve as mimetic references for generating specified content, particularly in cases where models are insufficiently trained. Our RAGDiffusion not only builds upon this generalizability through convenient retrieval expansion, but also aggregates structural information, thereby mitigating intrinsic hallucinations on the high-standard tasks.
+
+Controllable text-to-image diffusion models. To attain conditional control in text-to-image diffusion models, ControlNet [59], T2I-Adapter [31] and IP-Adapter [55] incorporate additional trainable modules to fuse conditions on feature maps. Additionally, recent investigations have utilized a variety of prompt engineering techniques [26, 54, 63] and implemented cross-attention constraints [9, 23, 52, 66] to facilitate more controllable generative processes. Furthermore, some studies further investigate multi-condition or multi-modal generation [22, 27, 36, 67]. However, these methods rely on the associative capabilities of stable diffu
+
+![](images/e456df3062dd684e285ca414813efd44f033df272969bf3172346520c92a22f7.jpg)
+
+![](images/37be8abec8fa2faeb7f91a08c290fec093f1f7788d19d3a90d349eeebe566a0d.jpg)
+
+![](images/7a683cb64f9c4a1773a3998332df7369bf32b4ef07f48b90c91b3b9cbf464f7e.jpg)  
+Figure 2. Overall framework of RAGDiffusion. StructureNet provides latent structural embeddings, while SLLE facilitates the embedding fusion along with landmark retrieval. The generative model synthesizes multiple conditions to achieve omni-level high-fidelity generation.
+
+![](images/e11ce2dac8d5219d7052d79bf86fbef208f11424109c0fe278c99c9e3096414c.jpg)
+
+sion, which cannot guarantee fidelity, particularly with the highly standardized sampling of standard garments.
+
+Garment restoration. Standard clothing generation involves restoring flat-lay garment images on from real-world contexts. TileGAN [57] pioneered a two-stage GAN [16] framework, suffering from backbone capability limitations. Recent works including TryOffDiff [49], TryOffAnyone [51], and IGR [43] have adopted pretrained SD as base backbones, yielding obvious improvements through enhanced generative priors. Specifically, TryOffDiff utilizes SigLIP [58] to extract garment features; TryOffAnyone employs direct image concatenation for conditional generation; IGR implements ReferenceNet-inspired [21] architectures for pattern consistency. However, these methods exhibit three critical shortcomings: (1) They ignore structural hallucinations and distortions arising from real-world complexities (multi-layer, extreme viewpoints, etc.). (2) Their detail fidelity fails to meet commercial standards. (3) Adaptation to new garment categories/scenarios requires costly paired data and retraining. Our RAGDiffusion systematically resolves these limitations through RAG paradigm and a coarse-to-fine alignment pipeline.
+
+# 3. Method
+
+An overview of the RAGDiffusion is presented in Fig. 2. The backbone of RAGDiffusion employs the SDXL [39], with the preliminary detailed in Appendix. Given an inthe-wild clothing image  $x_{itw} \in \mathbb{R}^{H \times W \times 3}$ , RAGDiffusion
+
+is aimed to generate an authentic standard flat lay in-shop garment image  $x_{std}$ . A dual tower StructureNet extracts latent structure embeddings by contrastive learning as detailed in Sec. 3.1, and SLLE retrieves and fuses structure embeddings and landmarks as in Sec. 3.2. Coarse-to-fine alignment generation involves ReferenceNet, and PGEA for pattern, and decoding faithfulness described in Sec. 3.3.
+
+# 3.1. Dual-tower embeddings extraction
+
+To eliminate structural hallucinations, a straightforward approach is to extract structural features from images and feed them into generative networks, as seen in StyleGAN [24] and LADI-VTON [30], which use additional latent coding to module conditions. Accordingly, we extract latent structure embeddings through contrastive learning [37], using garments that share similar canny but are texture-dissimilar as training pairs. This process exploits the structural similarities between specialized pairs, which are not emphasized during the conventional training of diffusion.
+
+Contrastive learning. Given a batch of  $N$  (in-the-wild clothing  $x_{itw}$ , standard clothing  $x_{std}$ ) pairs, StructureNet  $g_{\theta}$  is trained to predict which of the  $N \times N$  possible ( $x_{itw}$ ,  $x_{std}$ ) pairings across a batch actually occurred according to structure similarity. To do this, StructureNet learns a multimodal embedding space by jointly training a dual tower encoder tailored for  $x_{itw}$  and  $x_{std}$  to maximize the cosine similarity of the embeddings of the  $N$  real pairs (marked with superscript +) in the batch while minimizing the similarity of the  $N^2 - N$  incorrect pairs (marked with superscript
+
+-). To be specific, the LLM is used to extract 10 types of discrete attributes of clothing (e.g., Category, FitType, CollarTechnique, IfTopTuckIn), which incorporates general in-context image knowledge from the language model [1, 2], eliminating semantic deficiencies and ambiguities present in vision. Then we assign a learnable embedding  $f_{attr}$  to each discrete attribute. The image structure features  $f_{img}$  are extracted by the twin ViT [14] encoder and concatenated with the attributes embeddings  $f_{attr}$  to form the final latent structure embeddings  $e$  after non-linear Resampler [55] head. We optimize the InforNCE loss [10] over these latent structure embeddings  $\{e_{itw}, e_{std}\}$  from  $\{x_{itw}, x_{std}\}$  as:
+
+$$
+\mathcal {L} = \frac {- 1}{N} \sum_ {i = 1} ^ {N} \log \frac {\exp \left(e _ {i t w , i} \odot e _ {s t d} ^ {+} / \tau\right)}{\exp \left(e _ {i t w , i} \odot e _ {s t d} ^ {+} / \tau\right) + \sum_ {e _ {s t d} ^ {-}} \exp \left(e _ {i t w , i} \odot e _ {s t d} ^ {-} / \tau\right)}, \tag {1}
+$$
+
+where  $\odot$  is cosine similarity between two vectors,  $N$  is the batch size, and  $\tau$  is a temperature scalar.
+
+# 3.2. Retrieval-augmented SLLE
+
+By integrating structural knowledge from StructureNet into the SD, we have improved the style and structure of generated flat-lay clothing as shown in Sec. 4.3. However, due to the limited spatial perception inherent in the SD [6, 28], it often struggles to accurately represent the length and contours of clothing, particularly in hard cases (occlusions, multi-layer, lateral viewpoints, etc.), as in Fig. 5. Furthermore, since StructureNet is trained on a limited set of contrastive pairs, it may perform poorly with out-of-distribution samples, making it unreliable for real-world applications.
+
+We have observed that creating a comprehensive database of standard flat-lay clothing for retrieval is easier than gathering comprehensive in-the-wild samples (numerous scenarios). In this context, we set standard clothing  $e_{std}$  as basic vectors and propose Structure Locally Linear Embedding (SLLE), which is a manifold projection [41] to correct each predicted structure embedding  $e_{itw}$  into the target space of standard embedding  $e_{std}$  to mitigate potential error. Meanwhile, the retrieval database provides structure landmarks to strengthen explicit spatial constraints.
+
+Memory database. To execute SLLE, we establish a retrieval memory database. We first encode the collected standard flat-lay clothing image dataset into a series of latent structure embeddings  $e_{std}$  with StructureNet  $g_{\theta}$ . The silhouette landmarks  $L_{sil}$  are also extracted to designate areas for generated content. Thus an external memory database  $\mathcal{D}$  that consists of embedding-landmark pairs  $(e_{std}, L_{sil})$  is obtained. These structure embeddings are utilized in matching algorithms [17], enabling a given in-the-wild garment to find the most compatible standard features  $e_{std}$  and landmarks during inference. Notice that landmarks can be any structural figure. Here, we use the outline of clothing, primarily to tackle the challenges of limited spatial perception in SD (e.g. length and contour) [6, 28].
+
+Structure LLE algorithm. In this process, retrieval-augmented SLLE drags in-the-wild embedding closer to the standard flat-lay garment embeddings to void outliers during inference, as well as offer silhouette landmarks. Motivated by the successful practice of classic locally linear embedding in [3], we assume that the garment embedding or landmark and its nearby points are locally linear on the manifold, eliminating the need to project them into a higher-dimensional space as vanilla LLE [41] does. Specifically, given an extracted garment embedding  $e_{itw}$ , the goal of SLLE is to reconstruct embedding  $e_{itw}'$  with standard embeddings  $e_{std}$  as basis vectors. We start by searching the  $K$  nearest standard embeddings  $\{e_{std}^1, \dots, e_{std}^K\}$  from the standard garment memory database  $\mathcal{D}$  using cosine similarity. Thus  $K$  corresponding flat-lay cloth silhouette landmarks  $\{L_{sil}^1, \dots, L_{sil}^K\}$  are obtained as well. Next, a linear combination of these neighbors is sought to reconstruct  $e_{itw}'$  by minimizing the error  $\| e_{itw}' - e_{itw} \|_2$ , which could be formulated as the least-squared optimization problem:
+
+$$
+\min  \left\| e _ {i t w} - \sum_ {i = 1} ^ {K} w _ {i} \cdot e _ {s t d} ^ {i} \right\| _ {2}, \quad s. t. \sum_ {i = 1} ^ {K} w _ {i} = 1, \tag {2}
+$$
+
+where  $w_{i}$  is the barycentric weight of the  $i$ -th nearest embedding  $e^{i}_{std}$ . The optimal weights  $\{w_{1},\ldots ,w_{K}\}$  can be determined by solving Eq. (2). Subsequently, we can reconstruct the shape embedding as  $e^{\prime}_{itw} = \sum_{i = 1}^{K}w_{i}^{*}\cdot e^{i}_{std}$ . Ideally, the reconstructed embedding  $e^{\prime}_{itw}$  serves as an indomain data point that retains structural accuracy and appropriate fitness, albeit with some information loss. In practice, we use a linear combination of original structure embedding  $e_{itw}$  and reconstructed one  $e^{\prime}_{itw}$  as the final structure representation during inference:
+
+$$
+\hat {e} _ {i t w} = \alpha \cdot \sum_ {i = 1} ^ {K} w _ {i} ^ {*} \cdot e _ {s t d} ^ {i} + (1 - \alpha) \cdot e _ {i t w}, \tag {3}
+$$
+
+where  $\alpha \in [0,1]$  controls the trade-off and is set to be 0.5. The final landmark  $L_{\text{sil}}$  is also fused with optimal weights. Structure conditioning. Inspired by IP-Adapter [55], we adopt a similar Embedding Prompt Adapter (EP-Adapter) to condition the high-level structure semantics. While maintaining the text branch unchanged, fused structure embeddings  $\hat{e}_{itw}$  after SLLE are fed into additional projection layers to generate key and value matrices for the structure representations. Two parallel cross-attention layers process the text modality and the structure embedding modality, with results being summed to replace the original single text one: Attention  $(Q,K_{\text{text}},V_{\text{text}})+$  Attention  $(Q,K_{\text{emb}},V_{\text{emb}})$ . The EP-Adapter enhances the global/inner structural faithfulness by incorporating prior knowledge from LLM and structural training pairs as a soft constraint. Meanwhile, the contour landmark  $L_{\text{sil}}$  involves external spatial structural information. A Landmark Guider [21] with 4 convolution layers ( $4\times 4$  kernels,  $2\times 2$  strides, 16, 32, 64, 128 channels) is incorporated to align the silhouette mask with  $z_{t}$  as an explicit and hard constrain.
+
+# 3.3. Omni-Level faithful garment generation
+
+Pattern faithfulness. Inspired by success in human editing [8, 21], we introduce an additional UNet encoder (i.e. ReferenceNet [21]) to precisely preserve the fine-grained details of clothing assets, which is isomorphic to the main generative UNet (i.e. MainNet) and shares same initial parameter weights. The latent of in-the-wild garment image is passed through ReferenceNet to obtain the intermediate key and value features  $\{z_R^k,z_R^v\} \in \mathbb{R}^{N\times l\times d}$  in self-attention, which are concatenated with the features  $\{z_M^k,z_M^v\} \in \mathbb{R}^{N\times l\times d}$  from the MainNet along the  $l$  dimension to obtain the final  $\{z_C^k,z_C^v\} \in \mathbb{R}^{N\times 2l\times d}$ . Then we compute the self-attention on the concatenated features as:
+
+$$
+\text {A t t e n t i o n} \left\{z _ {M} ^ {q}, z _ {C} ^ {k}, z _ {C} ^ {v} \right\} = \operatorname {s o f t m a x} \left(\frac {z _ {M} ^ {q} z _ {C} ^ {k T}}{\sqrt {d}}\right) z _ {C} ^ {v}, \tag {4}
+$$
+
+where  $z_{M}^{q}$  represents Query features in self-attention from MainNet. ReferenceNet plays an important role in texture preserving of garments when it has complicated patterns.
+
+Detail faithfulness. The cloth restoration technique primarily serves e-commerce sellers for product catalog maintenance and marketing purposes. The requirement for brand logo fidelity is so stringent that existing methods' results [43, 49, 51] are practically unusable even with ReferenceNet, partially because of the fine-grained logo decoding degradation caused by the high compression ratio of SDXL's VAE, as shown in Fig. 5. Although the VAE in FLUX [15] greatly alleviates the loss by inflating latent channels, challenges intrinsic to the DiT framework [34], such as slow convergence, and high data requirements, hinder its widespread adoption in the community.
+
+To address this, we propose a versatile three-stage parameter gradual encoding adaption (PGEA) to align the SDXL UNet with the FLUX VAE. Specifically, we expand the channels in conv in and conv out layers (from 4 to 16) in UNet to match FLUX VAE, enabling direct modification on the SD config file to load adapted weights. Stage I: we focus on distilling the knowledge from the original conv in layer to the adapted conv in layer. The input image is encoded through different VAEs and passed into the 4 and 16-channel conv in layers respectively, applying a reconstruction loss between their output to update the 16-channel conv in layer for fast adaption. Stage II: we train the UNet on a standard text-to-image task for 20,000 steps, where only the 16-channel conv in and conv out layers are updated. Stage III: we train and update the entire UNet on the standard text-to-image task for 200,000 steps. The complete training of PGEA lasts for 4 days on 8 H20 GPUs. It is noteworthy that the adapted general UNet with extremely low decoding loss can be applied to various downstream tasks. Crucially, despite marginal gains in quantitative metrics, RAGDiffusion's breakthrough in brand logo fidelity makes it commercially viable, the first in industrial garment restoration.
+
+![](images/12560db60f9c062404e653fd8509b868666a4b3f13b69350ecc2a2a53604bd49.jpg)  
+Figure 3. RAGDiffusion delivers both loyal structures and superior details on challenging layered and side-view situations.
+
+<table><tr><td>Method</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>FID ↓</td><td>KID ↓</td><td>DISTS ↓</td></tr><tr><td>PBE</td><td>0.5278</td><td>0.4821</td><td>26.55</td><td>10.08</td><td>0.352</td></tr><tr><td>ControlNet</td><td>0.5225</td><td>0.4792</td><td>23.02</td><td>9.231</td><td>0.345</td></tr><tr><td>IP-Adapter</td><td>0.6067</td><td>0.4728</td><td>14.50</td><td>3.747</td><td>0.264</td></tr><tr><td>TryOffDiff</td><td>0.6124</td><td>0.5007</td><td>34.34</td><td>14.19</td><td>0.335</td></tr><tr><td>TryOffAnyone</td><td>0.6575</td><td>0.4335</td><td>18.86</td><td>7.919</td><td>0.245</td></tr><tr><td>ReferenceNet</td><td>0.6546</td><td>0.3979</td><td>10.70</td><td>1.399</td><td>0.224</td></tr><tr><td>RAGDiffusion</td><td>0.6963</td><td>0.3684</td><td>9.990</td><td>1.092</td><td>0.192</td></tr></table>
+
+Table 1. Quantitative comparisons on the STGarment dataset.
+
+# 4. Experiments
+
+# 4.1. Experimental setup
+
+Datasets. We collected 65,131 pairs of (in-the-wild upper clothing, standard flat lay upper clothing) for training and 1969 pairs for testing, named STGarment. Among the in-the-wild clothing, there are three main displays: clothing worn on a person, clothing laid indoors, and clothing hung on hangers. We use Qwen2-VL-7B [2] to provide prompt annotations for each pair along with 10 discrete attributes (3.5 seconds per image). Additionally, we matched each pair of images with the most structurally similar flatlay clothing for StructureNet training based on canny image similarity. We employed a clustering approach to filter and construct a memory database for retrieval, which contains 4,000 embedding-landmark pairs from the training set. Please refer to the Appendix for more details.
+
+Implementation details. We initialize the RAGDiffusion with a pre-trained SDXL model and train it on STGarment using an AdamW optimizer with the learning rate of  $5e - 5$  at a resolution of  $768 \times 768$ . The models are trained for 5
+
+<table><tr><td>Method</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>FID ↓</td><td>KID ↓</td><td>DISTS ↓</td></tr><tr><td>Vanilla Model</td><td>0.6576</td><td>0.3961</td><td>10.65</td><td>1.405</td><td>0.222</td></tr><tr><td>+ emb</td><td>0.6614</td><td>0.3917</td><td>10.55</td><td>1.354</td><td>0.217</td></tr><tr><td>+ emb + sil</td><td>0.6926</td><td>0.3690</td><td>10.22</td><td>0.940</td><td>0.210</td></tr><tr><td>Generating mask</td><td>0.6426</td><td>0.4186</td><td>14.55</td><td>3.570</td><td>0.239</td></tr><tr><td>+ emb + sil + PGEA (Full)</td><td>0.6963</td><td>0.3684</td><td>9.990</td><td>1.092</td><td>0.192</td></tr></table>
+
+Table 2. Quantitative ablation study of each component.  
+
+<table><tr><td>Dataset</td><td colspan="2">Viton-HD</td><td colspan="2">DC-upper</td><td colspan="2">DC-lower</td><td colspan="2">DC-dress</td></tr><tr><td>Method</td><td>FID</td><td>KID</td><td>FID</td><td>KID</td><td>FID</td><td>KID</td><td>FID</td><td>KID</td></tr><tr><td>PBE</td><td>80.8</td><td>52.9</td><td>45.0</td><td>21.1</td><td>158.8</td><td>128.3</td><td>105.1</td><td>74.6</td></tr><tr><td>ControlNet</td><td>69.9</td><td>43.2</td><td>48.9</td><td>23.6</td><td>174.7</td><td>161.7</td><td>118.3</td><td>95.4</td></tr><tr><td>IP-Adapter</td><td>46.8</td><td>17.8</td><td>28.8</td><td>11.1</td><td>111.3</td><td>62.7</td><td>47.8</td><td>19.0</td></tr><tr><td>TryOffDiff*</td><td>14.0</td><td>3.31</td><td>38.9</td><td>16.7</td><td>158.7</td><td>130.0</td><td>74.3</td><td>48.6</td></tr><tr><td>TryOffAnyone*</td><td>11.4</td><td>1.97</td><td>24.4</td><td>9.30</td><td>114.2</td><td>79.6</td><td>38.4</td><td>20.4</td></tr><tr><td>ReferenceNet</td><td>15.2</td><td>3.23</td><td>17.8</td><td>6.24</td><td>124.5</td><td>90.2</td><td>51.2</td><td>22.4</td></tr><tr><td>Ours</td><td>12.3</td><td>1.45</td><td>15.9</td><td>4.51</td><td>40.5</td><td>19.4</td><td>23.1</td><td>6.22</td></tr></table>
+
+Table 3. Cross dataset evaluation on Viton-HD, DressCode. Model with * means inner-dataset test which is trained on Viton-HD.  
+
+<table><tr><td>Scale</td><td>Top-1 Acc. ↑</td><td>Top-5 Acc. ↑</td><td>IOU ↑</td></tr><tr><td>1000</td><td>76.6%</td><td>93.4%</td><td>0.872</td></tr><tr><td>2000</td><td>78.2%</td><td>93.2%</td><td>0.885</td></tr><tr><td>4000</td><td>80.6%</td><td>93.7%</td><td>0.902</td></tr><tr><td>8000</td><td>79.7%</td><td>93.4%</td><td>0.905</td></tr></table>
+
+Table 4. Retrieval accuracy at different scales of external database.
+
+days on 8 H20 GPUs with DeepSpeed [29] ZeRO-2 to reduce memory usage, at a batch size of 15.  $K = 4$  in SLLE in Eq. (2). The StructureNet (i.e. embedding encoder) utilizes CLIP-ViT-L/14 image encoder as the backbone and is fine-tuned on nearly 2 million various garment images following DinoV2 [32]. StructureNet is further trained on STGarment with contrastive learning for 4 days on 4 H20 GPUs at a batch size of 128. At inference time, we run RAGDiffusion on a single NVIDIA RTX 3090 GPU for 30 sampling steps with the DDIM sampler [45]. Please refer to the Appendix for more details.
+
+Evaluation protocols. About generation quality, we utilize LPIPS [61], SSIM [50] to assess the reconstruction accuracy, DISTS [13] to evaluate image similarity on both perceptual and structural level. Additionally, we employ FID [33] and KID [46] metrics to evaluate the realism and authenticity of the generated distributions. In terms of retrieval ability, we evaluate the top-1 accuracy and top-5 accuracy of retrieval results from the memory database  $\mathcal{D}$  across 1969 test samples, alongside the average Intersection over Union (IoU) of the corresponding silhouette masks with GT ones. Given the absence of GT masks of test samples in the memory database  $\mathcal{D}$ , we define the retrieved masks to be accurate if their IoU exceeds 0.85.
+
+Baselines. We compare RAGDiffusion with recent works TryOffDiff [49] and TryOffAnyone [51] with official checkpoints. We also train 4 classic conditional generation methods on STGarment with SDXL backbone for fair comparison: IP-Adapter [55], ReferenceNet [21], ControlNet [59] and Paint-by-Example [53] (PBE) as baselines.
+
+![](images/37aced32194da58fd148a1da1ee60f5c99ebd29a255a064e0824f60a51217fd6.jpg)  
+Figure 4. Boxplot illustration of user study. RAGDiffusion demonstrates better performance and stability across scenes.
+
+# 4.2. Generation comparisons with baselines
+
+Qualitative results. Fig. 3 presents a qualitative comparison between RAGDiffusion and baselines on the STGarment dataset. TryOffDiff has yielded entirely unsuccessful outputs. Meanwhile, naive ReferenceNet and TryOffAnyone manage to maintain correct textures in challenging scenarios, but encounter structural confusion and distortion. This phenomenon may stem from TryOffDiff and ReferenceNet's over-reliance on local visual texture features, lacking the benefits of a global perspective in challenging cases. RAGDiffusion employs a retrieval-aggregate approach to capture structural information and integrates conditional controls from EP-Adapter, Landmark Guider and PGEA, yielding promising performance in both structurally faithful and detail-oriented garment conversion. Notably, while trained on the same dataset with naive ReferenceNet, RAGDiffusion assimilates high-quality contour landmarks and structure embeddings as external prior to producing visually compelling results that enhance depth and realism.
+
+Quantitative results. As indicated in Tab. 1, we quantitatively evaluate the generation quality of various methods on the STGarment dataset, demonstrating that RAGDiffusion significantly outperforms all baseline approaches. This confirms RAGDiffusion's ability to deliver superior and accurate garment generation across diverse scenarios. Retrieval, as a crucial component of RAGDiffusion for assimilating external knowledge, plays a significant role. Using the evaluation metrics described in Sec. 4.1, we report the retrieval accuracy at different sizes of the external memory database  $\mathcal{D}$  in Tab. 4. Specifically, we employ clustering and downsampling algorithms to iteratively eliminate outliers and highly similar samples from the original memory database, constructing retrieval libraries of four different scales: 1000, 2000, 4000, and 8000 samples. When the memory database  $\mathcal{D}$  is too large, outliers may adversely affect quality if embeddings are inaccurate, while redundant samples reduce retrieval efficiency. Conversely, if the memory database  $\mathcal{D}$  is too small, the retrieval library may lack sufficient representativeness and completeness, adversely affecting the generation performance for specific categories. Notably, a memory database comprising 4000 samples achieved the best trade-off in performance. Please refer to the Appendix for more technical details.
+
+![](images/eac183df222a00d214f0aedcbfa3072104ec47b3eac6e77eb50f5b06b1660ea1.jpg)  
+Figure 5. Ablation study. Without landmarks, RAGDiffusion suffers inaccurate shape. Embed- Figure 6. RAG significantly improves dings from StructureNet improve inner structure, while PGEA enhances detail preservation. generalization on untrained categories.
+
+User study. When metrics like FID assess the realism and authenticity of standard garment generation, they tend to be less sensitive to high-frequency information such as contours, collar variations, buttons, and color shifts [11]. We conducted user studies involving 100 participants to evaluate different methods based on user preferences across 200 randomly selected image pairs from the test set. Participants were asked to assign a preference score (ranging from  $1 \sim 10$ ) in terms of structural fidelity and detail fidelity for each sample generated by anonymized methods. As illustrated in Fig. 4, we report the distribution of the scores, encompassing medians, means, quartiles, and outliers. Our findings reveal that RAGDiffusion is significantly preferred over all baseline methods in terms of structural fidelity (mean = 8.34) and detail fidelity (mean = 8.52). Additionally, the narrow range of outliers in our method indicates a more stable generation across various scenes.
+
+# 4.3. Ablation study
+
+To validate our core contributions, we define a Vanilla Model that removes structure embedding  $\hat{e}_{itw}$ , silhouette landmarks  $\hat{L}_{sil}$  and PGEA. Specifically, its  $\hat{e}_{itw}$  and  $\hat{L}_{sil}$  are set to zero vectors while using original SDXL VAE.
+
+Soft guidance of structure embeddings. Since structure embeddings serve as prerequisites for retrieval in SLLE and inputs to EP-Adapter, we first add structure embeddings  $\hat{e}_{itw}$  into EP-Adapter of vanilla model (denoted as “+ emb”). As in Tab. 2 and Fig. 5, vanilla model lacking structure embedding frequently exhibits artifacts in clothing internal structures, such as inaccurate collars, missing pockets, and occlusion confusion. This demonstrates that structure embedding provides global guidance and plays a
+
+fundamental role in optimizing apparel internal structures.
+
+Hard guidance of silhouette landmarks. The core of RAG is to retrieve silhouette landmarks that enhance explicit spatial constraints. Thus we add landmarks on "+" emb" version as the ablation named "+" emb + sil" in Tab. 2. The model without retrieval exhibits significant contour errors, particularly around the back collar, sleeve length, and garment length. This is attributed to the fact that retrievalaugmented SLLE incorporates priors from LLM, which transcend visual limitations and aid in accurate spatial structures through the use of landmarks. Furthermore, we investigate the role of SLLE in embedding remapping in Sec. 4.5. Alternative to RAG: generating masks via UNet. As RAG requires a memory database and contrastive learning for embeddings, we try a simpler alternative by employing an SDXL UNet to directly predict landmarks. Specifically, we modify the input of the alternative UNet to a three-channel in-the-wild image  $x_{itw}$ , with outputs being one-channel predicted landmarks  $L_{sil}$  that are directly fed into RAGDiffusion's denoising UNet. However, this alternative produces landmarks with noticeable errors and degraded generation quality, due to limitations in visual understanding and the absence of proper pre-trained weights.
+
+PGEA. PGEA is employed to mitigate information loss during the VAE encoding and decoding process. We add PGEA on “+ emb + sil” version as Full Model. The full model utilizing PGEA achieves clearer and more accurate edges in high-frequency patterns simulation; additionally, it shows significant improvements in the recovery of logos and text. PGEA greatly alleviates the long-standing issue of distortion in detail and makes RAGDiffusion commercially
+
+viable, the first in industrial garment restoration.
+
+# 4.4. Additional rationale for introducing RAG
+
+In addition to structural faithfulness, RAGDiffusion demonstrates excellent generalizability and robustness across untrained categories and scenes simply by updating retrieval database, without the need for collecting expensive paired data and retraining. Besides, please refer to Appendix for another rationale of human-interpretable control.
+
+Cross category evaluation. RAGDiffusion is trained on upper-body clothing data and has not encountered lower-body garments during training. To validate the generalizability, we collect 856 flat-lay lower-body/dress images (no in-the-wild image is needed) and incorporate them with silhouette masks into the external memory database through StructureNet. Subsequently, we test it on 50 lower-body in-the-wild clothing samples, using a ReferenceNet as baseline. The results in Fig. 6 demonstrate that retrieval significantly improves generalization capabilities, serving as a cost-effective zero-shot generalizing solution. The quantitative results on lower-body/dress categories in Tab. 3 also validate the generalizability boost.
+
+Cross dataset evaluation. Despite zero exposure to the Viton-HD [12] and DressCode [19] datasets during training, RAGDiffusion shows strong out-of-distribution (OOD) compatibility over baselines without tuning illustrated in Tab. 3. This boost in generalization increases the operational maturity of RAGDiffusion, enabling it to effectively handle various OOD images submitted by users.
+
+# 4.5. Component analysis
+
+Latent structure embedding distributions. We further visualize the learned latent embedding distribution in Fig. 7(b) to gain an in-depth comprehension of how the embeddings work in retrieval and the EP-Adapter. For this purpose, we sample  $N = 200$  pairs of (in-the-wild cloth embedding  $e_{itw}$ , standard cloth embedding  $e_{std}$ ) pairs from our dual-tower StructureNet. We then employ t-SNE [48] to project each feature representation into a point within Fig. 7. Notably, 1) the dual-branch embeddings  $(e_{itw}, e_{std})$  corresponding to the same category exhibit clustering behavior, indicating that the learned priors in StructureNet effectively perform structural alignment cross domains, thus facilitating retrieval based on structural similarity; and 2) representations from different categories are clearly dispersed, demonstrating that the embeddings encompass discriminative structural information, which aids in generation through the EP-Adapter. Lastly, we also visualize the distribution of cosine similarity between a given sample and images from the external memory database  $\mathcal{D}$  in Fig. 8. The cosine similarities present a normal distribution, affirming that the constructed embedding library is representative and comprehensive. Furthermore, the examples visualized for different similarity retrieval results effectively illustrate the efficacy of the landmark retrieval mechanism.
+
+![](images/fef8d3817323215d5a0c8554f34cc750a0a21e17239fc879a25a5140a9b75e56.jpg)  
+Figure 7. Illustrations of component analysis.
+
+![](images/19427e421d3148182fc7e3caa2137140071d2caf2a5ef8a7b9cad15619129762.jpg)
+
+![](images/4ef970b0196ed10d121b94891ec7937ec0d6fe7d4bc7f26b4ca05012b8fcaa5d.jpg)  
+Cosine Similarity Distribution Given a Specific Embedding  
+Figure 8. Distribution of cosine similarity between a given sample and images from the external memory database.
+
+Number of retrieved embeddings. As the number  $K$  of retrieved nearest neighbors in Eq. (2) during SLLE plays a fundamental role in the properties of the final structure embeddings and landmarks, we demonstrate the fusion sensitivity to  $K$  in Fig. 7(a). A smaller  $K$  value facilitates the sharp edge of landmarks, whereas a larger  $K$  value enhances the accurate representation of the reconstructed embedding  $e_{itw}^{\prime}$  in Eq. (3). It can be observed that the optimal performance occurs at  $K = 4$ , which also serves as the default parameter setting for other experimental parts.
+
+# 5. Conclusion
+
+In conclusion, RAGDiffusion presents a significant advancement in the generation of standardized clothing assets by effectively addressing the prevalent challenges of structural hallucinations and texture fidelity. By integrating retrieval-based structure aggregation to get soft and hard guidance, as well as omni-level faithful generation pipeline, RAGDiffusion is capable of synthesizing both structure and texture faithful clothing assets. Comprehensive experiments and in-depth analysis demonstrate notable performance improvements over existing models. We hope that RAGDiffusion helps open avenues for RAG in diverse high-specification faithful generation tasks, bringing us closer to the goal of professional content creation for all.
+
+# Acknowledgements
+
+This work is supported by the Science and Technology Commission of Shanghai Municipality under research grant No. 25ZR1401187.
+
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+# RAGNet: Large-scale Reasoning-based Affordance Segmentation Benchmark towards General Grasping
+
+Dongming Wu $^{1}$ , Yanping Fu $^{2\star}$ , Saise Huang $^{3}$ , Yingfei Liu $^{3\dagger}$ , Fan Jia $^{3}$ , Nian Liu $^{4}$ , Feng Dai $^{2}$ , Tiancai Wang $^{3}$ , Rao Muhammad Anwer $^{4}$ , Fahad Shahbaz Khan $^{4}$ , Jianbing Shen $^{5\dagger}$
+
+<sup>1</sup> The Chinese University of Hong Kong, <sup>2</sup> Institute of Computing Technology, Chinese Academy of Sciences,  
+$^{3}$  Dexamal,  $^{4}$  Mohamed bin Zayed University of Artificial Intelligence,  $^{5}$  SKL-IOTSC, CIS, University of Macau
+
+![](images/6b0c5f89646363d20d1753591a41aad1eb855304a50c25efbb653174ad05e2e2.jpg)  
+I need grip a hammer.
+
+![](images/b2ec3c0dceb133904f161c7ce750c11e0c1d0e16ff3551dc29f57830a5226629.jpg)  
+You can grip its handle.
+
+![](images/5ddadc49694c3750b75ae301ed9b79d4a9d37d2bc2041f3652818b4a38e2b69c.jpg)  
+I need a tool to drive a nail into the wall.
+
+![](images/8daae7934551c1ed7245e27e87023579854bc701e26b4fdb6c21041ad3ea4076.jpg)
+
+![](images/d526c39563e2da3c42f6574699105c344183917ffa91df0fd8d7d0e0f00f2479.jpg)
+
+![](images/12dc266e19577ab89deba519df80538578e2e104e3c6359c0e8b0c8556015db7.jpg)  
+Large-scale Reasoning-based Affordance Segmentation Dataset
+
+![](images/1bc7a04b5766b384f56f3285ebe788d98438082c0936b8d6df3956d55841def1.jpg)  
+Figure 1. Large-scale benchmark for reasoning-based affordance segmentation, which sources from various embodied domains: wild, robot, ego-centric indoor, and simulation. By leveraging the extensive high-quality dataset for training, our model AffordanceNet exhibits remarkable open-world generalization capabilities, steering further towards robust general-purpose object grasping.
+
+![](images/d694aa7e3f1927995851e8534dd01f288d24c3360c812830cc762c8657b7cda5.jpg)
+
+![](images/bab39f53428ec5049978cf9f554684593e0ea330f49a51a1d31db8ccf737c965.jpg)
+
+![](images/29a3a0d06ce194265f52fad8dec22af616ea8cd27db2fd449dcd86b15e359ef1.jpg)
+
+![](images/e3008e3ffa05fa51f19c4eb898ec5608b8c544d9c7f227ac0e8a62a28e61179a.jpg)
+
+![](images/b6d893f7bc409b6863747e754ff93b9e2a8ac7af2916b5f77d6a22804edb472f.jpg)  
+Sure, you can utilize the hammer by gripping its handle.
+
+![](images/18873eb3f414d91c2d492489590c9b1245674aa0e4200a9bd3f10ee65c51c8dd.jpg)
+
+![](images/dc971dce7231e65b807d36fad4a23d5de5916967b6a29e112922ab38a2a0d995.jpg)  
+General Grasping
+
+![](images/d5cb209fc3e24c8d056a8ec1007f2072a5e409e061b1701bffc9e1d17f87592c.jpg)
+
+![](images/93e681ca398f4792d68c4b7f93e1f069e59e6aff3a50a1964de1a8a610e0c4f9.jpg)
+
+# Abstract
+
+General robotic grasping systems require accurate object affordance perception in diverse open-world scenarios following human instructions. However, current studies suffer from the problem of lacking reasoning-based large-scale affordance prediction data, leading to considerable concern about open-world effectiveness. To address this limitation, we build a large-scale grasping-oriented affordance segmentation benchmark with human-like instructions, named RAGNet. It contains 273k images, 180 categories, and 26k reasoning instructions. The images cover diverse embodied data domains, such as wild, robot, ego-centric, and even
+
+simulation data. They are carefully annotated with an affordance map, while the difficulty of language instructions is largely increased by removing their category name and only providing functional descriptions. Furthermore, we propose a comprehensive affordance-based grasping framework, named AffordanceNet, which consists of a VLM pretrained on our massive affordance data and a grasping network that conditions an affordance map to grasp the target. Extensive experiments on affordance segmentation benchmarks and real-robot manipulation tasks show that our model has a powerful open-world generalization ability. Our data and code is available at this link.
+
+# 1. Introduction
+
+Affordance prediction is a foundational research topic that significantly contributes to diverse practical applications, including robotic manipulation [15, 17, 18, 38, 52] and human-object interaction [3, 20, 22, 51, 57, 58]. It requires
+
+<table><tr><td>Dataset</td><td>Images</td><td>Categories</td><td>Wild</td><td>Robot</td><td>Ego-centric</td><td>Simulation</td><td>Reasoning</td><td>Output</td></tr><tr><td>UMD [37] ICRA2015</td><td>10k</td><td>17</td><td>✓</td><td></td><td></td><td></td><td>✓</td><td>Seg</td></tr><tr><td>AGD20k [35] CVPR2020</td><td>20k</td><td>50</td><td>✓</td><td></td><td></td><td></td><td></td><td>Seg</td></tr><tr><td>HANDAL [14] IROS2023</td><td>200k</td><td>17</td><td>✓</td><td></td><td></td><td></td><td></td><td>Seg/Box</td></tr><tr><td>AED [28]Arxiv2024</td><td>-</td><td>21</td><td></td><td>✓</td><td></td><td>✓</td><td></td><td>Seg</td></tr><tr><td>3DOI [42]ICCV2023</td><td>10k</td><td>-</td><td>✓</td><td></td><td>✓</td><td></td><td></td><td>Seg</td></tr><tr><td>AffordanceLLM [44]CVPR2024</td><td>20k</td><td>-</td><td>✓</td><td></td><td></td><td></td><td></td><td>Seg</td></tr><tr><td>ManipVQA [16] IROS2024</td><td>84k</td><td>-</td><td>✓</td><td></td><td>✓</td><td></td><td>✓</td><td>Seg</td></tr><tr><td>RAGNet (Ours)</td><td>273k</td><td>180</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>Seg</td></tr></table>
+
+Table 1. Comparisons between previous affordance data and our collection. “(11k)” represents the number of video clips. “-” means unavailable data. “Reasoning” refers to reasoning instructions.
+
+comprehensively understanding the geometry and function of an object (e.g., a wok affords to hold, a microwave door affords to pull) for further detecting graspable regions. Nonetheless, this task faces two additional primary difficulties in the realm of open-world generalization concerning vision and language instructions: 1) The capability to generalize in a broad range of unseen object categories and image domains. 2) The alignment of commands that mimic human-like high-level instructions.
+
+Initial studies often specialize in particular domains, as depicted in Table 1. For instance, UMD [37] offers 10,000 RGB-D image pairs from three cluttered scenes with pixel-level affordance annotations. This dataset is categorized as robot data, characterized by a distinct operational table and a relatively stable background. Despite the abundance of public robot datasets [4, 41, 56], they often lack meticulous fine-grained labeling. Ego-centric data, which is captured from a first-person or egocentric viewpoint, is the most prevalent type of data [7, 13]. Nevertheless, this data is often collected in indoor kitchens and workshops, resulting in a lack of diversity in the data category distribution. Wild data, another prevalent type, is gathered in various situations, which usually cover diverse categories [35, 46, 53]. However, certain categories within this data, like bicycles, motorcycles, sofas and etc., are not suitable for robotic manipulation. In addition, these data often fail to generalize to unseen domains and novel objects for affordance prediction.
+
+To enhance open-world generalization, Vision Language Model (VLM) with massive image-text training [29, 32] has become an important increment in various visual prediction tasks [25, 47]. Inspired by this, VLM also has an increasing interest in affordance prediction along with complex reasoning, and several recent works are attempting to predict affordance regions [16, 27, 30, 44, 60, 62]. For example, ManipVQA [16] proposes tool detection, affordance recognition, and a broader understanding of physical concepts in a unified framework. However, these works employ a fixed format of language prompt and a limited data scale, which brings some concerns about open-world generalization and complex reasoning. Overall, current efforts are either constrained by insufficiently diverse datasets or by the absence of effective reasoning mechanisms, which hampers the ability to perform open-world grasping.
+
+To address these challenges, we first build large-scale affordance segmentation data from various image sources, including wild, robot, ego-centric, and even simulated data, named RAGNet. It has 273k images and 180 categories. We design a set of affordance annotation tools for labeling the regions of objects that are amenable to grasping. Furthermore, we leverage Large Language Models (LLMs) to generate a vast array of reasoning-based instructions, totaling 26k distinct expressions. Here, we create two types of reasoning-based instructions beyond the template-based. One includes the name of the object and the other omits it. Take a knife as an example: "Please provide a knife" versus "I want something to slice the bread". This approach closely mirrors real-life human interactions. In summary, we have constructed a massive-scale database with domains, object categories, and complex reasoning instructions.
+
+Furthermore, we introduce an affordance-based grasping framework, titled AffordanceNet. It presents a deployable and general grasping pipeline, which stands out from prior MLLM-based affordance prediction methods [16, 44] that have not yet demonstrated real-robot deployment. Our model includes two crucial components, AffordanceVLM and Pose Generator. The AffordanceVLM transforms RGB images and human instruction into an accurate affordance map, while the pose generator uses the 2D affordance with a depth image to produce 3D grasper pose. In this work, we conduct extensive experiments to assess its open-world generalization and reasoning capabilities. First, we create two distinct validation datasets to assess open-world generalization: one for zero-shot category recognition and another for out-of-domain affordance prediction. Second, to test reasoning ability, we implement an affordance segmentation validation based on instructions that do not contain any target category names. Thirdly, we carry out a range of close-loop real-robot grasping tasks in an entirely out-of-domain setting. Last but not least, we test several representative simulation tasks from RLBench. All experiments show that our proposed method has great generalization and reasoning ability. In summary, our contributions are three-fold:
+
+- We present a large-scale reasoning-based affordance segmentation benchmark, RAGNet, for general grasping. It is collected from diverse sources and carefully annotated with affordance mask and reasoning instructions.
+
+![](images/884500542a2c2b24384aa45bfcd87ee058ea4d500d78c2a8c385b2addc35b98e.jpg)  
+Figure 2. Overview of our data annotation pipeline and manipulation model. We collect data from several public datasets, including HANDAL, GraspNet, Open-X, etc. A variety of models and manual annotation are utilized to annotate affordance masks. Subsequently, we refine textual instructions using templates and GPT4 to emulate human-like commands. For grasp operations, the VLM model is employed to identify affordance regions, which are then converted into the required grasp poses by integrating depth information.
+
+- We introduce an affordance-based grasping baseline, AffordanceNet, which bridges the gap between VLM-based affordance prediction and real-robot general grasping.  
+- We conduct extensive experiments, including zero-shot and out-of-domain affordance segmentation, real-robot grasping evaluation, which show great performance.
+
+# 2. Related Work
+
+The investigation of affordances has a rich history in the computer vision and robotics communities [1, 11, 12, 24]. For embodied agents to successfully interact with the functional components within a scene, they need the capability to comprehend visual affordances. To advance research in this area, previous studies have dedicated significant resources to two main areas: benchmarks and algorithms.
+
+Benchmark. With the advances in deep learning, there has been a growing demand for the creation of large-scale affordance databases. UMD [37] stands out as a prior effort, which defines objects with effective affordances as those that an agent can grasp to produce an effect on another object. In addition, it offers a dataset of 10k RGB-D images, each accompanied by a pixel-level affordance segmentation mask. OPRA [10] proposes a different affordance learning pattern, which employs demonstration videos to guide the prediction of interaction region on a target image. It includes 20,612 video clips, each corresponding to an image and an annotation of interaction heatmap and action label. Despite the pioneering efforts in affordance learning,
+
+the existing datasets [6, 10, 34, 37, 39, 50] still face constraints regarding affordance category diversity, image quality, and scene complexity. Afterward, Luo et al. establish a large-scale affordance grounding dataset, AGD20k [35], which contains 20k exocentric images from 36 affordance categories. Guo et al. build the HANDANL dataset [14] for real-world robot manipulation, which provides precise handle annotation for 17 hardware and kitchen tool categories. Recently, there are a variety of datasets on affordance prediction that have been introduced with different output formats, such as key points [21, 30, 42, 48], bounding box [54, 55], pixel-wise mask [27, 28, 31]. However, most current research tends to focus on specific domains, such as robotics or first-person perspectives, which limits their applicability to other areas. In contrast, our research aims to investigate the potential for open-world generalization in affordance prediction by leveraging extensive data.
+
+Algorithm. In the deep learning era, the common methods use supervised learning for affordance prediction [6, 8, 14, 34, 39]. However, these approaches struggle to generalize to domains outside of their training environments. To tackle this issue, certain studies utilize transfer learning [26, 35, 36, 61] or self-supervised learning techniques [5] to enable affordance prediction from data originating in different domains. With the significant progress of VLM, attempting these foundation models in affordance prediction has attracted much interest in the research community [16, 27, 30, 44, 60, 62]. However, these methods
+
+<table><tr><td>Data source</td><td>Domain</td><td>Annotation</td><td>Rea. Inst.</td><td>Categories</td></tr><tr><td>HANDAL [14]</td><td>Wild</td><td>➀</td><td>8.5k</td><td>17</td></tr><tr><td>Open-X [41]</td><td>Robot</td><td>➂➁➉</td><td>-</td><td>124</td></tr><tr><td>GraspNet [9]</td><td>Robot</td><td>➂➂</td><td>-</td><td>32</td></tr><tr><td>EgoObjects [65]</td><td>Ego</td><td>➂➂➉</td><td>17.4k</td><td>74</td></tr><tr><td>RLBench [19]</td><td>Simulation</td><td>➂</td><td>-</td><td>10</td></tr></table>
+
+Table 2. Details of training data annotation in RAGNet. The affordance mask annotation are in §3.2 and the generation details of reasoning instructions (Rea. Inst.) can be found in §3.3.
+
+usually learn from limited affordance demonstration data, which opens up opportunities for further research into how large-scale data can impact generalization in open-world scenarios and enhance knowledge reasoning.
+
+# 3. Dataset
+
+In this section, we will present how to build the large-scale reasoning-based affordance segmentation benchmark RAG-Net. First, we gather extensive data from various sources, as detailed in §3.1. Then, we introduce five tools to annotate this data with grasping-oriented affordance masks according to the original dataset characteristics in §3.2. Meanwhile, we offer detailed instructions for reasoning-based affordance segmentation in §3.3. Lastly, we establish multiple validation benchmarks for testing grasping-oriented affordance segmentation in §3.4. The data annotation pipeline is illustrated in Fig. 2.
+
+# 3.1. Data Source
+
+Given that robotics can function across various embodiment realms, including real-world settings and robotic hardware, we collect a broad spectrum of data. The dataset comprises sources such as wild data (i.e., HANDAL [14]), real robots (i.e., Open-X [41], GraspNet [9]), and ego-centric data (i.e., EgoObjects [65]). For a fair comparison environment, we consider a collection of simulation data (i.e., RL-bench [19]). We gather 273k images as shown in Table 2.
+
+# 3.2. Affordance Map Annotation
+
+To facilitate affordance segmentation with reduced manual input, we develop a suite of annotation tools. The annotation workflow is designed to be adaptable, taking into account the functional and physical characteristics of various object categories. For instance, when dealing with an object like a soda can, the robotic system typically grasps the entire object, necessitating full object annotation. On the other hand, an object such as a wok requires precise annotation of its handle for effective grasping. This tool suite comprises five annotation tools, each with its own level of priority.
+
+1 Original mask: Certain datasets specify affordance segmentation with precision (such as HANDAL dataset [14]), while others, like those featuring objects without handles (e.g., computer mouse, soda can, and pen), do not require
+
+![](images/bb7ecdf203ccbd760897c06d2013599f781e8e9a063d557a07256ffcdb8358f3.jpg)  
+User:  
+Figure 3. Easy (left) v.s. Hard (right) Reasoning Instruction. The hard version has no category name itself.
+
+![](images/e9efab979998ab32c45affeb82fe395002439a7dc99329cff69d88a2ef587aab.jpg)  
+Can you find a mug for tea?  
+User:  
+I need something to drink coffee.
+
+# Assistant:
+
+The mug has a handle which you can hold to pour the coffee. [AFF]
+
+# Assistant:
+
+The mug is suitable for this, its handle can be held to drink coffee safely. [AFF]
+
+detailed affordance masks for grasping. In these cases, we utilize the original masks as our affordance annotations without further refinement.
+
+$\Theta$  SAM2: For objects that lack handles, SAM2 [49] can still be utilized to generate a mask, when only the ground-truth bounding box is available (like EgoObjects [65]).  
+$\bullet$  Florence2 + SAM2: Due to the presence of language instructions (like Open-X [41]), Florence2 [59] which generates polygon boxes coupled with SAM2 can be used to produce an affordance map for objects that are handle-free.  
+$\mathbf{4}$  VLPart + SAM2: VLPart [53] enables part-level recognition (i.e., knife handle and mug handle), hence we leverage it and SAM2 for segmenting object handles if the corresponding category has been trained within VLPart.  
+$\Theta$  Human  $(+SAM2)$ : If the above four tools fail to complete the affordance segmentation accurately, we will consider manual affordance annotation. The use of SAM2 is optional, particularly when dealing with video sequences.
+
+According to the original annotation information offered by data sources, we employ different compositions for affordance mask annotation. The composition details are listed in Table 2. We incorporate more detailed annotations, encompassing variations in tool arrangement across subsets and categories, within the supplementary. Besides, we provide several representative examples in Fig. 1 and more annotation examples can also be found in the supplementary.
+
+# 3.3. Reasoning Instruction Annotation
+
+As previously mentioned, the current VLM possesses compelling reasoning capabilities. To harness these capabilities for affordance reasoning, we construct a set of instructions. In this section, we introduce three types of instructions, including one template-based and two reasoning-based.
+
+The first kind of instruction is template-based. For instance, a template is "Please segment the affordance map of <category_name> in this image". This template can
+
+<table><tr><td>Validation Set</td><td>Images</td><td>Zero-shot</td><td>Reason.</td><td>Anno.</td></tr><tr><td>HANDAL [14]</td><td>65k</td><td>-</td><td>N/A</td><td>1</td></tr><tr><td>\( \text{HANDAL}^{\dagger} \) [14]</td><td>1k</td><td>-</td><td>N/A</td><td>1</td></tr><tr><td>GraspNet seen [9]</td><td>1k</td><td>-</td><td>N/A</td><td>15</td></tr><tr><td>GraspNet novel [9]</td><td>1k</td><td>✓</td><td>N/A</td><td>15</td></tr><tr><td>3DOI [42]</td><td>1k</td><td>✓</td><td>N/A</td><td>5</td></tr><tr><td>\( \text{HANDAL}^{\dagger} \) [14]</td><td>1k</td><td>-</td><td>easy</td><td>1</td></tr><tr><td>\( \text{HANDAL}^{\dagger} \) [14]</td><td>1k</td><td>-</td><td>hard</td><td>1</td></tr><tr><td>3DOI [42]</td><td>1k</td><td>��</td><td>easy</td><td>5</td></tr></table>
+
+Table 3. Details of validation set.  $\dagger$  means a HANDAL subset. Gray means zero-shot setting. As highly replicated images, we randomly select 1k images from the source dataset for validation.
+
+be utilized in our entire dataset for affordance prediction. The second category consists of easy reasoning-based instructions that are based on straightforward reasoning. A key aspect of these instructions is the explicit mention of the object being referred to. In contrast to template-based approaches and previous studies [16, 25, 44], the third category comprises hard reasoning-based instructions, which do not include the category name. For precise identification of the target object, the hard mode instructions utilize a functional description. Fig. 3 presents a typical example. Towards grasping a mug, the easy instruction might be "Can you find a mug for tea", while the hard instruction is "I need something to drink coffee".
+
+To produce these reasoning-based instructions with minimal human labor and computational resources, we make full use of the capabilities of GPT-4 [2]. The specific prompt utilized is detailed in the supplementary material. According to our data, we craft 8.5k hard instructions for the HAN-DAL dataset, 12.7k easy ones and 4.7k hard ones for the EgoObjects, totaling 26k reasoning-based instructions.
+
+# 3.4. Evaluation Dataset
+
+To assess the open-world generalization of our affordance prediction model, we contribute two distinct zero-shot affordance evaluation scenarios. The first scenario evaluates the affordance model by extending its predictions to object categories not encountered during training. The second scenario evaluates the model generalization ability across different data domains. For this purpose, we select the 3DOI dataset [42], which includes data from Articulation [43], EpicKitchen [7], and Taskonomy [63], ensuring that there is no overlap with the training data in the validation set.
+
+We present four different validation sets in Table 3. Due to high-similarity images, we construct a subset from the HANDAL, which is marked with ‘†’. For the same reason, other validation sets also utilize 1k images from the source dataset. HANDAL and GraspNet seen represent the object categories and image domains that the model has been trained on. GraspNet novel represents the unseen object category, while 3DOI refers to the unseen image domain.
+
+In addition, we provide three reasoning-based affordance segmentation validation sets, as illustrated in Table 3. The reasoning instruction version used in each subset is marked as "easy" or "hard". We utilize the generalized Intersection over Union (gIoU) and complete Intersection over Union (cIoU) as our primary metrics.
+
+# 4. AffordanceNet
+
+To achieve the goal of open-world grasping, we propose a comprehensive framework, named AffordanceNet. This model consists of two key components: AffordanceVLM for predicting affordance segmentation mask and pose generation for transforming the mask into grasper position in 3D space. The overall framework is illustrated in Fig. 2.
+
+# 4.1. AffordanceVLM
+
+Our AffordanceVLM is based on the vision-language segmentation model LISA [25] and incorporates two essential task-specific modifications to enhance affordance prediction: (1) developing a specialized system prompt, and (2) introducing a unique <AFF> token.
+
+Specifically, we first process the input image using an image encoder (i.e., ViT-CLIP [45]), which is then projected into the LLM's embedding space via a linear layer projector. Meanwhile, the language prompt is tokenized by a text tokenizer, where each affordance instruction is enhanced by "You are an embodied robot." The resulting image and text features are concatenated and fed into the LLM (i.e., Vicuna-7B [64]). For general segmentation, the LLM generates a response that includes a special token  $<\mathrm{SEG}>$ . However, since  $<\mathrm{SEG}>$  is a token within the LLM's vocabulary, its representation is confined to a fixed feature space. This limitation restricts its representation capacity, thereby affecting the quality of the decoded mask. To address this issue, we introduce another special token  $<\mathrm{AFF}>$  to enrich the original mask embedding. The underlying motivation is to explicitly direct the final mask embedding to focus more on affordance-specific language expressions. Finally, SAM [23] is used as a mask decoder to convert this mask embedding into a pixel-wise mask.
+
+Implementation Details. Beyond our reasoning-based affordance segmentation data, we also incorporate a variety of generic segmentation datasets into our training, which use  $<\mathrm{SEG}>$  token. During inference, we first extract the  $<\mathrm{AFF}>$  token, followed by the  $<\mathrm{SEG}>$  token. More implementation details about data sampling and training settings can be found in the supplementary.
+
+# 4.2. Pose Generator
+
+Once obtained AffordanceVLM that delivers precise affordance segmentation prediction, we start to apply the model to robotic grasping tasks, aiming to bridge the gap for the
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">HANDAL</td><td colspan="2">HANDAL†</td><td colspan="2">GraspNet seen</td><td colspan="2">GraspNet novel</td><td colspan="2">3DOI</td></tr><tr><td>gIoU</td><td>cIoU</td><td>gIoU</td><td>cIoU</td><td>gIoU</td><td>cIoU</td><td>gIoU</td><td>cIoU</td><td>gIoU</td><td>cIoU</td></tr><tr><td colspan="11">Foundation Model without LLMs</td></tr><tr><td>VLPart [53] + SAM2 [49]</td><td>40.9</td><td>28.9</td><td>40.7</td><td>27.6</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Grounding DINO [33] + SAM2 [49]</td><td>34.7</td><td>26.8</td><td>34.9</td><td>26.9</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Florence 2 [59] + SAM2 [49]</td><td>39.7</td><td>22.4</td><td>39.4</td><td>22.5</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td colspan="11">Generalist MLLMs</td></tr><tr><td>LISA [25]</td><td>16.2</td><td>12.0</td><td>15.4</td><td>11.8</td><td>17.7</td><td>17.7</td><td>25.2</td><td>24.1</td><td>21.5</td><td>13.7</td></tr><tr><td>GLaMM [47]</td><td>24.9</td><td>17.2</td><td>25.1</td><td>17.0</td><td>21.6</td><td>10.5</td><td>19.2</td><td>8.6</td><td>19.7</td><td>14.1</td></tr><tr><td>AffordanceNet (Ours)</td><td>60.3</td><td>60.8</td><td>60.5</td><td>60.3</td><td>63.3</td><td>64.0</td><td>45.6</td><td>33.2</td><td>37.4</td><td>37.4</td></tr></table>
+
+Table 4. Quantitative results on affordance segmentation. We use the fixed format of "<category_name> handle" in foundation models without LLMs, while utilize "affordance map of <category_name>" in generalist MLLMs. Gray means zero-shot benchmark.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">HANDAL†</td><td colspan="2">Grasp. novel</td><td colspan="2">3DOI</td></tr><tr><td>gIoU</td><td>cIoU</td><td>gIoU</td><td>cIoU</td><td>gIoU</td><td>cIoU</td></tr><tr><td>LISA</td><td>16.2</td><td>12.0</td><td>25.2</td><td>24.1</td><td>21.5</td><td>13.7</td></tr><tr><td>+ HANDAL</td><td>56.3</td><td>54.9</td><td>16.6</td><td>14.4</td><td>18.0</td><td>12.2</td></tr><tr><td>+ Open-X</td><td>59.3</td><td>56.7</td><td>19.2</td><td>18.4</td><td>24.5</td><td>16.0</td></tr><tr><td>+ EgoObjects</td><td>61.8</td><td>61.6</td><td>8.0</td><td>6.9</td><td>35.5</td><td>34.6</td></tr><tr><td>+ GraspNet</td><td>61.7</td><td>61.7</td><td>51.5</td><td>38.5</td><td>40.9</td><td>41.8</td></tr><tr><td>+ Reasoning</td><td>56.5</td><td>55.4</td><td>43.0</td><td>33.8</td><td>36.8</td><td>40.2</td></tr><tr><td>+ RLBench</td><td>56.7</td><td>55.0</td><td>42.8</td><td>33.2</td><td>36.5</td><td>39.9</td></tr><tr><td>Ours</td><td>60.5</td><td>60.3</td><td>45.6</td><td>33.2</td><td>37.4</td><td>37.4</td></tr></table>
+
+final steps in object grasping and manipulation. The impressive affordance segmentation results can be found in §5.1 and §5.2. In the following part, we will discuss more details about our grasp pose generator and the process of converting 2D affordance masks into the 3D pose estimates required for robotic arms.
+
+As illustrated in Fig. 2, we project the depth maps into 3D space for precise grasp pose generation. Let  $P$  denotes the set of points on the 2D image. Firstly, we filter the affordance region by applying the affordance mask  $M$  to  $P$  through a binary multiplication  $\otimes$ , resulting in  $\hat{P} = P \otimes M$ . Subsequently, for each 2D position  $(u, v)$  within the point set  $\hat{P}$ , we have
+
+$$
+\left[ \begin{array}{c} x \\ y \\ z \\ 1 \end{array} \right] = T \cdot K ^ {- 1} \left[ \begin{array}{c} u \times d \\ v \times d \\ d \\ 1 \end{array} \right], \tag {1}
+$$
+
+where  $\mathrm{d}$  is the along the axis orthogonal to the image plane,  $(x,y,z)$  are the corresponding world coordinates.  $\mathbf{K} \in \mathbb{R}^{4 \times 4}$  and  $\mathbf{T} \in \mathbb{R}^{4 \times 4}$  represent the camera intrinsic and extrinsic parameters, respectively. After getting the 3D position of object affordance, we can use various grasping
+
+Table 5. Ablation study of data on affordance segmentation. Each data is added one by one. Compared to “+ RLBench”, our final model is enhanced by task-specific modifications, including specialized system prompt and unique <AFF> token (see §4.1).  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">HANDAL (easy)</td><td colspan="2">HANDAL (hard)</td><td colspan="2">3DOI</td></tr><tr><td>gIoU</td><td>cIoU</td><td>gIoU</td><td>cIoU</td><td>gIoU</td><td>cIoU</td></tr><tr><td>G-DINO</td><td>3.6</td><td>3.0</td><td>3.4</td><td>3.1</td><td>4.1</td><td>3.9</td></tr><tr><td>LISA</td><td>15.5</td><td>11.9</td><td>12.3</td><td>8.1</td><td>12.3</td><td>8.1</td></tr><tr><td>GLaMM</td><td>4.7</td><td>3.5</td><td>5.0</td><td>3.5</td><td>4.4</td><td>2.9</td></tr><tr><td>Ours</td><td>58.3</td><td>58.1</td><td>58.2</td><td>57.8</td><td>38.1</td><td>39.4</td></tr></table>
+
+Table 6. Quantitative results on reasoning-based affordance segmentation. 'G-DINO' is the short name of Grounding-DINO. They all use reasoning-based instructions as language prompts.
+
+models to generate grasper position. Finally, the grasper arrive the requested position and grasp the target object.
+
+# 5. Experiments on Visual Affordance
+
+To minimize unnecessary source expenditure, we initially validate the quality of affordance segmentation (§4.1) prior to object grasping (§4.2).
+
+# 5.1. Evaluation on Affordance Segmentation
+
+Implementation Details. To evaluate the task of affordance segmentation, we implement various advanced open-sourced approaches with potential affordance segmentation ability. In specific, we choose the foundation models without LLMs (e.g., VLPart [53], Grounding DINO [33], Florence2 [59]), and the generalist MLLMs (e.g., LISA [25], GLaMM [47]). Since these foundation models only output bounding boxes or polygon boxes, we additionally employ SAM2 [49] for mask refinement. We load their official checkpoints for direct evaluation. Given the ambiguous nature of the "affordance map of <category_name>" concept, which poses a challenge to the foundation models without LLMs, we shift to a fixed format of instruction "<category_name> handle" and evaluate them on only HANDAL dataset as each object have a handle. In contrast, we employ "affordance map of <category_name>" when testing the generalist MLLMs.
+
+Experiment Results. The main results on affordance segmentation are shown in Table 4. We can see our model out
+
+![](images/587e4763623ef2b02a89d3e6001564fa59f936d44eccd5cb9d28e7cd81f77bc4.jpg)  
+Figure 4. Affordance segmentation from our AffordanceNet. Even though they source from various data sources, such as wild, robot, ego-centric and simulation, our model can accurately capture their affordance region. More visualizations are included in supplementary.
+
+![](images/87b6b9b9f17045c9d30b18b36e4685d89703749096cc8a6667015df5a756d826.jpg)
+
+![](images/45ef5d95b007b3053c24065e2abf8033af57b86dedb5a7691c6be2003f37900c.jpg)
+
+![](images/fe57a8960839b371f74513015d46484c0d0139d071dfa6dbffbe8d681878b6e0.jpg)
+
+![](images/ec89effd97225cb208e8712ed93021b6c357504b8f118575047469ebc6edce35.jpg)
+
+![](images/3e49221583db16398d08b2673a3baaf4d3a7e4334b2ec4df0b83de01258b8231.jpg)  
+Can you find a knife for me?
+
+![](images/1289c018f328f094b9a03f6664b98b555dea50c46415f32bafdf9525b959fded.jpg)  
+I need a fork for the dinner table.
+
+![](images/e0cb55a5fba4115f86e6e51757d806ba1da07e0df506e25f6ff2645944b00573.jpg)  
+Could you grab a mug for me, please?
+
+![](images/bfcce477dcb37f91383007df133fb714dd79967c06731e458e5518a6b27378cb.jpg)  
+I need a tool to drive nails into wood.
+
+![](images/36f1a50b66aad7cd4df30db9dbc5d6d8f5fd5b29a865082015804fa9db773816.jpg)  
+Fetch something to drink hot tea.  
+Figure 5. Reasoning-based affordance segmentation from our AffordanceNet. The left examples represent easy reasoning-based instructions with referent name, while the right are hard instructions that include object function or intention rather than the name itself.
+
+performs all other competitors across all datasets. Besides, the scores on the entire HANDAL dataset and its small subset are similar, guaranteeing the diversity and representative of the small subset. Several visualizations across various domains are shown in Fig. 4. Here, the wok handle is accurately segmented even if its scene has never been encountered, indicating remarkable open-world generalization.
+
+Ablation Study. It is of interest to examine the impact of individual datasets on affordance segmentation tasks. In Table 5, we incrementally incorporate each dataset into the training process. We can see that the absence of HANDAL data significantly impairs the model performance on the HANDAL test set. Furthermore, the incorporation of reasoning data leads to a slight decline in performance metrics. However, the introduction of task-specific modifications, such as a specialized system prompt and a unique <AFF> token, enhances model performance. Overall, our model shows powerful open-world affordance segmentation.
+
+# 5.2. Evaluation on Reasoning Affordance
+
+We also test the foundation models and generalist MLLMs on reasoning-based affordance segmentation datasets. All the experiment settings are aligned with the above section.
+
+Experiment Results. Despite this challenging task, the results in Table 6 show our model outperforms other methods by a large margin. We provide several reasoning-based qualitative results in Fig. 5. The last two examples show that our model can predict precise hammer and mug handles even if there is no target mentioned in the instructions. These results confirm the reasoning ability of our model.
+
+Remark. The above two vision experiments demonstrate that only our model excels in both affordance perception and reasoning in zero-shot domain. This provides a solid foundation for the subsequent object grasping tasks.
+
+# 6. Experiments on Object Grasping
+
+# 6.1. Evaluation on Real Robot
+
+Implementation Details. To evaluate the effectiveness of our model for open-world generalization in real-world environments, we introduce a series of manipulation experiments. Specifically, we deploy UR5 robot arm with a third-person RGB-D camera (Intel RealSense). We design 10 distinct grasping tasks, including grasping the can, pen, screwdriver, hammer, wok, mouse, circle, toy, spatula, scissors. Half of them require accurately localizing the affordance region, like the screwdriver handle. Each task is performed 10 times, and we report the average success rate. Note that, we never provide any demonstration images or videos from this scene for our model training. The well-trained AffordanceVLM is directly used for the zero-shot evaluation. As for the pose generation, we follow GraspNet [9] condition 3D affordance point cloud to generate a 3D grasp proposal for grasper operation. We compare our model with a popular grasping model, GraspNet [9]. Since GraspNet lacks the capability for language-conditioned grasping, we ensure that only the target object remains on the table.
+
+Experiment Results. Table 7 displays the performance comparison between ours and GraspNet. Clearly, our model AffordanceNet has superior success rates, even in challenging and complicated environments. Fig. 6 highlights four sequences, which show accurate affordance perception and effective object grasping (i.e., screwdriver, wok, circle, and mouse). More grasping examples are in our supplementary.
+
+Ablation Study. Table 8 shows ablations of AffordanceNet on affordance prediction models (replaced by VLPart and LISA) and instruction types (replaced by easy and hard reasoning-based instructions) using five tasks. As demonstrated, AffordanceNet delivers superior affordance predic
+
+![](images/135478edf54dd6e491949a30d7e98b00e850b3ca56b4f9d38723436a52459221.jpg)
+
+![](images/a740784824b521d83aa29d9968177ef00046fbe387436f199c22b335eaea916b.jpg)
+
+![](images/9fc76fe99c6b4d9d3ca5bef391eaee72f5266a07e7e191d575e4c82d2fc11701.jpg)
+
+![](images/9d53a6fa96e8989bd86a302d1be972c586b03fdf001216685243e6794434c4c8.jpg)  
+Figure 6. Object grasping results from our AffordanceNet on robot arm UR5. The instructions are "I need a screwdriver for repairing", "Can you hand me the wok, please?", "Give me the circle", "Please hand me a computer mouse", respectively.
+
+<table><tr><td>Method</td><td>Can</td><td>Pen</td><td>Screwdriver</td><td>Hammer</td><td>Wok</td><td>Mouse</td><td>Circle</td><td>Toy</td><td>Spatula</td><td>Scissors</td><td>Average</td></tr><tr><td>GraspNet [9]</td><td>40%</td><td>10%</td><td>10%</td><td>20%</td><td>60%</td><td>50%</td><td>10%</td><td>60%</td><td>30%</td><td>30%</td><td>32%</td></tr><tr><td>AffordanceNet (Ours)</td><td>80%</td><td>60%</td><td>60%</td><td>80%</td><td>70%</td><td>80%</td><td>40%</td><td>90%</td><td>70%</td><td>70%</td><td>70%</td></tr></table>
+
+Table 7. Average success rates on robotic grasping. GraspNet cannot support language (see §6.1). Each task is conducted by 10 times.  
+
+<table><tr><td>Method</td><td>Can</td><td>Pen</td><td>Screw.</td><td>Ham.</td><td>Wok</td><td>Average</td></tr><tr><td>VLPart [53]</td><td>70%</td><td>30%</td><td>40%</td><td>30%</td><td>0</td><td>34%</td></tr><tr><td>LISA [25]</td><td>80%</td><td>40%</td><td>0</td><td>10%</td><td>0</td><td>26%</td></tr><tr><td>Easy Reasoning</td><td>70%</td><td>50%</td><td>50%</td><td>80%</td><td>60%</td><td>62%</td></tr><tr><td>Hard Reasoning</td><td>60%</td><td>40%</td><td>40%</td><td>60%</td><td>40%</td><td>48%</td></tr><tr><td>AffordanceNet</td><td>80%</td><td>60%</td><td>60%</td><td>80%</td><td>70%</td><td>70%</td></tr></table>
+
+tion while maintaining its reasoning capabilities.
+
+# 6.2. Evaluation on Simulation
+
+Implementation Details. We conduct simulations based on RLBench sub-task [19] to validate our approach, including open drawer, close jar, and slide block to target. In practice, we divide each task into several keyframes, as follows: open drawer (3 keyframes), close jar (4 keyframes), slide block to target (5 keyframes). More details are in the supplementary.
+
+Experiment Results. We conduct 25 episodes for each task and calculate its average success rate as the primary evaluation metric. The quantitative results are in Table 9. Compared to another LLM-based method LLARVA [40] that is fine-tuned for a specific environment, our model focuses on
+
+Table 8. Ablation studies on real-robot grasping in terms of different affordance prediction models (i.e., VLPart and LISA) and different instructions (i.e., easy reasoning and hard reasoning).  
+
+<table><tr><td>Task</td><td>LLARVA [40]</td><td>AffordanceNet (Ours)</td></tr><tr><td>Open drawer</td><td>60%</td><td>56%</td></tr><tr><td>Slide block to target</td><td>100%</td><td>64%</td></tr><tr><td>Close jar</td><td>28%</td><td>44%</td></tr><tr><td>Average</td><td>62%</td><td>54.7%</td></tr></table>
+
+Table 9. Success rates of our model on RLBench simulation. Each task is conducted by 25 episodes.
+
+stronger generalization. Therefore, achieving comparable performance on RLBench is quite satisfying.
+
+# 7. Conclusion
+
+In this work, we presented a new large-scale and diverse reasoning-based affordance segmentation dataset, named RAGNet, which aims to advance the capabilities of general robotic grasping systems in varied open-world scenarios. Further, we proposed the model AffordanceNet, a comprehensive framework including the AffordanceVLM and the grasping module, which uses our extensive affordance data to achieve open-world affordance capture and 3D grasper pose prediction, respectively. Through extensive experiments, we observed the superior performance and generalization ability of our AffordanceNet in zero-shot affordance segmentation, reasoning-based affordance segmentation, real-robot grasping evaluation, and simulation tasks.
+
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+# RALoc: Enhancing Outdoor LiDAR Localization via Rotation Awareness
+
+Yuyang Yang $^{1,2*}$  Wen Li $^{1,2*}$  Sheng Ao $^{1,2}$  Qingshan Xu $^{3}$  Shangshu Yu $^{4}$  Yu Guo $^{1,2}$  Yin Zhou $^{5}$  Siqi Shen $^{1,2}$  Cheng Wang $^{1,2\dagger}$
+
+$^{1}$ Fujian Key Laboratory of Sensing and Computing for Smart Cities, Xiamen University  $^{2}$ Key Laboratory of Multimedia Trusted Perception and Efficient Computing, Ministry of Education of China, Xiamen University  $^{3}$ Nanyang Technological University  $^{4}$ Northeastern University  $^{5}$ GAC R&D Center
+
+# Abstract
+
+LiDAR localization is a fundamental task in autonomous driving and robotics. Scene Coordinate Regression (SCR) exhibits leading pose accuracy, achieving impressive results in learning-based localization. We observe that the real-world LiDAR scans captured from different viewpoints usually result in the catastrophic collapse of SCR. However, existing LiDAR localization methods have largely overlooked the issue of rotation sensitivity in SCR. In this paper, we present RALoc, an outdoor LiDAR localization method with rotation awareness to achieve accurate localization. The key to our approach is to design a Point Cloud Canonicalization module, which leverages a powerful equivariant key feature aggregation to transform the input LiDAR scan towards a consistent orientation, effectively eliminating the adverse effects of rotation. This proposed module has promising scalability and can be seamlessly integrated with the existing LiDAR localization network. Moreover, we propose the Bidirectional LiDAR Localization (BiLiLo) dataset as a benchmark to evaluate the performance of various methods in large outdoor scenes with significant rotation changes. Extensive experiments show that RALoc significantly improves localization performance in scenarios with large rotation changes, and also achieves competitive performance in the Oxford Radar RobotCar dataset. Our project is available at https://etheryangyy.github.io/raloc.github.io.
+
+# 1. Introduction
+
+LiDAR localization is a crucial task that plays an important role in various applications, such as autonomous driving [34], robotics and augmented reality. The objective of LiDAR localization is to use the point cloud of the scene
+
+![](images/3319f04b384d7dd32d101337daa7db9c939cd858ceb0cd9fba2b7640b0a550fe.jpg)  
+Figure 1. Teaser. This paper primarily investigates the problem of rotation-robust LiDAR localization. We present ground truth and predicted trajectories on the collected rotation changes dataset. Left: the forward trajectory (aligned with the training set driving direction). Right: the reverse trajectory (completely opposite to the training set driving direction). Compared to the current state-of-the-art method, LiSA [55], RALoc retains high accuracy in the forward trajectory and avoids catastrophic failures due to rotation in the reverse trajectory.
+
+![](images/2f6fd4641ce5f8fafff463d230425daed2ddd2a92985553af85de49d45a43dcd.jpg)
+
+captured by the LiDAR as input and output its 6 degrees-of-freedom (DoF) pose. However, due to uneven data quality (e.g., noise distribution, non-uniform density, and varying viewing angles), it remains challenging to estimate accurate 6-DoF pose in large-scale real-world applications.
+
+Most existing methods [12, 27, 45, 54] typically follow the retrieval-registration paradigm for self-localization, which involves retrieving candidate scenes from a database, verifying their correctness, and subsequently estimating the 6-DoF relative pose via point cloud registration [35, 40]. However, when dealing with a large amount of LiDAR point cloud data, this approach not only imposes significant demands on storage and communication resources, but also struggles to achieve efficient localization from scratch [57].
+
+Learning-based regression has been shown to be a promising research direction to address the aforementioned issues by memorizing specific scenes within a neural network [57]. Existing methods can be categorized into Abso
+
+![](images/6f507c7ac25e02923bc740f531af42e08e6456d4cd709587ff3403925dac4ac8.jpg)  
+Figure 2. Motivation. (a) The rotation problems caused by changing lanes, turning, and reversing. (b) The impact of Yaw angle variation on LiSA's [55] recall rate within 5 meters and 3 degrees.
+
+lute Pose Regression (APR) and Scene Coordinate Regression (SCR). APR [25, 31, 50] directly estimates the global pose of the sensor in an end-to-end manner. Despite its effectiveness, sub-optimal results are achieved due to the highly abstract global feature used to represent the scene. Unlike the APR method, the SCR [7-9, 30] technique regresses the correspondences between the point cloud in the LiDAR coordinate and the world coordinate frame, followed by RANSAC [19] algorithm to estimate a precise 6-DoF pose. By explicitly capturing scene geometry, SCR achieves significant performance improvements.
+
+Nonetheless, as shown in the right side of Fig. 1, we observe that the learning-based regression method suffers from catastrophic collapse due to large viewpoint discrepancies when the scanned point cloud is rotated relative to the training data. In practical applications, factors such as oncoming traffic, lane changes, and turns often result in unpredictable changes in vehicle direction. To illustrate the effect of rotation changes, we take a recently proposed superior method, LiSA [55], to uncover this problem. As shown in Fig. 2, we conducted a pilot study with various rotation changes and recorded the localization recall. Specifically, we randomly rotate the query point cloud by the Yaw axis to simulate the challenge of a real driving scenario. Clearly, recall decreases significantly as the rotation increases. When rotations exceed 30 degrees, the recall drops below  $1\%$ , indicating that localization algorithms fail in such cases. These experiments demonstrate that rotation changes negatively impact the performance of existing localization models.
+
+We believe that the main reason is that the neural network used lacks robustness to rotations [47]. Although data augmentation can improve the rotational robustness of networks to some extent, it compromises the overall performance of the network and necessitates larger capacities along with more complex architectures [1, 6, 52]. In contrast, equivariant models [38, 39] provide a strong inductive bias for the network, which is expected to fundamen
+
+tally address the issue of regression methods being sensitive to rotations. Furthermore, we found that test scenarios in commonly used benchmarks [4, 11] are relatively simple and rarely account for situations where the vehicle direction changes. To close this gap, we contribute a large-scale outdoor localization dataset with substantial rotation variations, which can offer a more accurate basis for assessing model robustness under real-world conditions.
+
+In this paper, we propose a novel localization framework, RALoc, to address the issue of current LiDAR localization models being vulnerable to rotations. Explicitly, we introduce an equivariant network to canonicalize the input point clouds. Additionally, to address the presence of noise interference in outdoor LiDAR localization tasks, we design an equivariant key feature aggregation module that effectively extracts scene features to better capture rotation changes. Moreover, to evaluate the rotational robustness of SCR in real-world driving scenarios, we establish equipment setups and collect a large-scale outdoor LiDAR localization dataset characterized by significant rotational variations.
+
+Our contributions can be summarized as follows:
+
+- We reveal that learning-based regression methods are sensitive to rotation changes, which greatly weakens their localization performance in real-world applications. To this end, we propose RALoc, the first attempt to introduce an equivariant network to SCR.  
+- We introduce a novel equivariant key feature aggregation module designed to mitigate interference from noisy point clouds, enhancing our approach with robust rotation-equivariant awareness.  
+- We collect a large-scale outdoor LiDAR localization dataset with significant rotation variations, providing an effective benchmark to facilitate related research.  
+- Extensive experiments on the proposed rotation challenge and Oxford Radar RobotCar [4] datasets demonstrate the effectiveness of our method. In particular, we show that RALoc achieves robust performance even with significant rotational variations (see Fig. 1).
+
+# 2. Related work
+
+# 2.1. Conventional Localization
+
+Conventional localization methods aim to match the query point cloud with a pre-built 3D map, which can be classified into retrieval-based methods [29, 48, 53] and matching-based methods [23, 42, 46]. Retrieval-based methods cast localization as a problem of place recognition, which requires a pre-built database with feature descriptors and relies on querying the most similar point cloud in the database [37, 59]. Matching-based methods are typically based on either searching for similar frames in a pre-built global descriptor database or 3D point clouds and match features between the query frame and the map [2, 33]. Both
+
+![](images/4ce92e7bb0150ab5f6e50492d14257314908e4ef7c7ff7f5d190ec9c3055cacb.jpg)  
+Figure 3. The pipeline of RALoc. RALoc consists of two main components: (1) the Point Cloud Canonicalization (PCC) network and (2) the Scene Coordinate Regression (SCR) network. Specifically, the PCC network captured from various rotations in the scene to a canonical view. The canonicalized point clouds are then fed into the SCR network, which outputs the 6-DoF pose.
+
+methods depend on pre-stored maps, resulting in challenges related to storage and communication.
+
+# 2.2. Regression-based Localization
+
+Recent advances in deep learning have spurred interest in regression-based localization methods that directly predict 6-DoF poses end-to-end. PoseNet [25] is a widely used APR method that regresses camera poses via a feature encoder and regressor. Given LiDAR's robustness to lighting and weather, APR has also been extended to LiDAR [58]. PointLoc [50] introduced LiDAR-based APR, and HypLiLoc [49] leveraged multi-level features to capture richer scene characteristics. DiffLoc [31] improved accuracy by transforming the pose regression process into multiple iterative steps through the diffusion model [22].
+
+However, as mentioned in [30, 44], APR methods focus on high-dimensional pose-feature mappings, like retrieval-based techniques, but overlook scene geometry, limiting their accuracy. To address this issue, SCR predicts the coordinates of each point in the world coordinate, effectively encoding scene geometry. Ultimately, RANSAC is used to estimate the pose. SGLoc [30] is the first to incorporate SCR into LiDAR localization, followed by LiSA [55], which mitigates the impact of disruptive points in the scene by introducing semantic information, further enhancing accuracy. Although APR and SCR have achieved commendable accuracy in LiDAR localization, these methods struggle with rotation-related issues in realistic scenarios.
+
+# 2.3. SO(3)-Equivariant Network
+
+With growing performance issues due to rotation, equivariant networks have seen notable advances in recent years [14, 20, 32, 43, 51, 56]. Although data augmentation can mitigate rotation issues during training, this often affects the overall performance of the model when dealing with large datasets [6, 38, 52]. Therefore, maintaining rotational equivariance is essential when processing point cloud data. Various studies [13, 36, 61] have effectively addressed this problem through different approaches. Among them, the Vector Neurons [16] (VNN) is a lightweight equivariant framework that integrates well with existing point cloud processing networks, and many subsequent works [3, 24, 60] have expanded upon it. Consequently, we have constructed an equivariant network for processing outdoor LiDAR point clouds using VNN as the foundation. Moreover, we design an equivariant key feature aggregation module to further boost rotation robustness.
+
+# 3. Method
+
+Recent SCR methods [30, 55] have achieved impressive results in outdoor LiDAR localization. However, in scenarios with vehicular trajectory variations, as shown in Fig. 2 (a), they fail due to rotational deviations between scanned point clouds and the training data. In this paper, we propose RALoc, which utilizes the equivariant network to solve the problem of rotation sensitivity by point cloud canonicaliza
+
+tion (Sec. 3.1). In addition, to evaluate the rotation robustness of localization methods in the real driving scenario, we propose a large-scale outdoor dataset with significant rotation variations (Sec. 3.2).
+
+# 3.1.RALoc
+
+We now introduce RALoc, as shown in Fig. 3, which can be divided into (1) Point Cloud Canonicalization (PCC): aligning LiDAR point cloud data with different orientations, efficiently sensing rotations through an equivariant network, and reorienting the LiDAR point clouds accordingly. (2) Scene Coordinate Regression (SCR): estimate the global pose by matching the scanned point cloud to the regressed point cloud in the world coordinate [30].
+
+In this work, we design a VNN-based [16] equivariant network to implement PCC. This network extracts LiDAR point cloud features using VN-MLP, aggregates scene features through Equivariant Key Feature Aggregation (EKFA), and then regresses the rotation matrix with respect to scene rotation changes.
+
+Point cloud canonicalization. Here we formulate the framework of PCC. For point clouds captured from diverse orientations, we aim to align them into a consistent reference frame, termed as the canonicalization coordinate.
+
+To establish this coordinate, we leverage the trajectory data from the training set. For a fixed position in the scene, the canonicalization coordinate is defined as the orientation of the LiDAR at that position in the training set.
+
+Specifically, given a point cloud scanned from arbitrary vehicle direction  $Rx$ , where  $R \in SO(3)$ ,  $x \in \mathbb{R}^{N \times 3}$  represent the point cloud in the LiDAR coordinate, PCC can be represented as follows:
+
+$$
+\operatorname {P C C} (R x) = \phi (R x) ^ {- 1} R x, \tag {1}
+$$
+
+where  $\phi$  denotes a VNN-based equivariant network. This network ensures that the PCC produces consistent outputs by leveraging the properties of equivariant networks:
+
+$$
+\phi (R x) = R \phi (x). \tag {2}
+$$
+
+As shown in Fig. 3, we utilize the equivariant network to perceive the rotational state of the vehicle at the feature level, and regress the matrix. Then, we use the Schmidt orthogonalization, which is also equivariant (as proved in the supplementary), to ensure its a rotation matrix. Finally, we apply the inverse transformation of this rotation to the input point cloud, resulting in a canonical point cloud. This canonical point cloud can then be fed into the subsequent LiDAR localization network, enhancing the robustness of the localization network against rotation. More details on the architecture can be found in the supplementary.
+
+Equivariant key feature aggregation. As described above, the task of equivariant network  $\phi$  is to ensure that
+
+![](images/7f29838c700477bd139fedbae64d486a249bd8f862907776015cf23e846f3f0e.jpg)  
+Figure 4. Equivariant Key Feature Aggregation (EKFA) module.
+
+point clouds scanned from different orientations of the same scene exhibit the same rotational relationship in their extracted equivariant features. However, due to the challenges of outdoor scenes, such as dynamic objects, not all points benefit the extraction of robust features [55]. Therefore, to effectively select the useful features, we introduce an equivariant key feature aggregation module.
+
+As shown in Fig. 4, the EKFA module takes the equivariant features  $F_{in} \in \mathbb{R}^{C \times 3 \times N}$  as input. We first use VN-MLP to generate features, denoted as  $Q$ ,  $K$ , and  $V$ , each with the same dimension of  $F_{in}$ . Then, to ensure strict equivariance, we compute the Frobenius inner product [3] of  $Q$  and  $K$ , divide it by  $\sqrt{3C}$ , and apply softmax to obtain the attention matrix  $A$ . This process can be expressed as follows:
+
+$$
+A = \operatorname {S o f t m a x} \left(\frac {\langle Q , K \rangle_ {F}}{\sqrt {3 C}}\right), \tag {3}
+$$
+
+where  $\langle \cdot \rangle_F$  is the Frobenius inner product, which is rotation invariant. The square root of the vector neurons features dimension count  $\sqrt{3C}$  serves as a scaling factor, and the shape of  $A$  is  $N\times N$ .
+
+To obtain the aggregation weights  $W$ , we sum the attention matrix  $A$  along its last dimension (i.e., across columns), sort  $W \in \mathbb{R}^N$  in descending order, and select the top  $k$  indices to construct a key feature mask  $A'$  from  $A$ :
+
+$$
+\operatorname {i d x} = \operatorname {t o p k} (W), \tag {4}
+$$
+
+$$
+A ^ {\prime} = A [ \mathrm {i d x},: ]. \tag {5}
+$$
+
+Finally, we perform a matrix multiplication with  $V$  to obtain aggregated features enriched with key information after filtering out scene noise. The output can be expressed by matrix multiplication:
+
+$$
+F _ {o u t} = V \times A ^ {\prime} ^ {T}. \tag {6}
+$$
+
+Scene coordinate regression. After obtaining the canonicalized point cloud, the next step is to input it into SCR,
+
+![](images/1aa25d53aa1df37783c06598c12616df9692f6cbaaaa64910fb4ccaa261759b4.jpg)  
+Figure 5. We scan point clouds and record ground truth using a vehicle equipped with an Ouster OS1-64 spanning LiDAR and a M39 GPS/IMU device. Coordinate frames illustrate the direction of each sensor on the vehicle with the convention: X-axis (red), Y-axis (green), and Z-axis (blue).
+
+SGLoc [30] in this work, to get the global pose. Specifically, SCR regresses the corresponding point cloud in the world coordinate, and matches them inside a RANSAC loop for robust pose estimation.
+
+Loss function. The output of RALoc consists of canonicalized point clouds and poses. Therefore, the total loss function  $\mathcal{L}$  should contain both canonicalization  $\mathcal{L}_{pcc}$  and regression  $\mathcal{L}_{reg}$  components. Following the definition of previous work [24, 38]. We choose the original LiDAR coordinate system in the training data as the canonical orientation, and utilize  $\mathcal{L}_{pcc}$  to keep point cloud canonicalization output point cloud orientation as constant as possible. Specifically, we use Mean Squared Error loss to optimize the point cloud canonicalization:
+
+$$
+\mathcal {L} _ {p c c} = \frac {1}{n} \sum_ {i = 1} ^ {n} (R _ {c} - I) ^ {2}, R _ {c} \in S O _ {3}, \tag {7}
+$$
+
+where the rotation matrix  $R_{c}$  is obtained by applying Schmidt orthogonalization to the equivariant features and  $I$  denotes the identity matrix.
+
+For the pose estimation, we employ  $L_{1}$  loss to guide SCR prediction correspondences to achieve localization.
+
+The overall loss function of the entire network is:
+
+$$
+\mathcal {L} = \lambda_ {1} \mathcal {L} _ {r e g} + \lambda_ {2} \mathcal {L} _ {p c c}, \tag {8}
+$$
+
+where  $\lambda_{1}$  and  $\lambda_{2}$  are hyper-parameters to balance the losses.
+
+# 3.2. Dataset
+
+At first glance, SCR yields satisfactory results. However, accuracy degrades markedly with changes in vehicle orientation (see Fig. 2 (a)). In real-world settings, avoiding such
+
+<table><tr><td>Dataset</td><td>LiDAR</td><td>GT</td><td>Reverse</td><td>Unobstructed view</td><td>Long Interval</td></tr><tr><td>KITTI [21]</td><td>1×64</td><td>GPS/IMU</td><td>X</td><td>✓</td><td>X</td></tr><tr><td>Oxford [4]</td><td>2×32</td><td>GPS/IMU</td><td>X</td><td>X</td><td>X</td></tr><tr><td>NCLT [11]</td><td>1×32</td><td>SLAM</td><td>X</td><td>✓</td><td>✓</td></tr><tr><td>Boreas [10]</td><td>1×128</td><td>GPS/IMU</td><td>X</td><td>✓</td><td>✓</td></tr><tr><td>MulRan [26]</td><td>1×64</td><td>SLAM</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>BiLiLo (Ours)</td><td>1×64</td><td>GPS/IMU</td><td>✓</td><td>✓</td><td>✓</td></tr></table>
+
+Table 1. Related Datasets. GT: Ground truth poses. Reverse: Presence of trajectories in the opposite direction. Unobstructed View: Minimal obstructions in the LiDAR's field of view. Long Interval: Extended time intervals between data collections.
+
+directional shifts during lane changes and turns proves difficult (Fig. 2 (b)). Due to the lack of localization datasets with significant directional variation, previous work [18] simulates these situations by rotating point clouds. While these simulations can somewhat validate the model's robustness to rotation, there are still discrepancies with the real scanned data, such as missing data caused by changes in scanning direction, etc. This motivates us to create a dataset with significant rotation changes in real-world scenarios to better evaluate existing methods.
+
+Sensors setup. Our dataset mainly consists of two sensors, as shown in Fig. 5, including (1) Ouster OS1-64, a 64-beam spinning LiDAR to collect point cloud data, and (2) M39, a GPS/IMU device, to obtain the ego-motion pose. We set the FOV, resolution, and FPS as  $[-22.5^{\circ}, 22.5^{\circ}]$ ,  $64*1024$  and 10, respectively. The FPS of M39 is set to 200, to provide dense and smoothing trajectories. We design a rigid support system for securing sensors to ensure reliably.
+
+Sensors calibration. Following KITTI [21]. We use ICP [5] to accurately register point clouds of a parking sequence, which provides a wide variety of orientations and translations essential for effectively conditioning the minimization problem. Next, we randomly sample 1,000 pairs of poses from this sequence and obtain the desired result using [17] to achieve LiDAR-to-GPS/IMU calibration.
+
+Target environments. Our dataset is collected in a campus environment featuring multiple distinguishable structures and a broad field of view. To assess the robustness of localization methods against translation and rotation, we deliberately incorporated multiple reverse revisits and revisits with lane-level translations.
+
+Furthermore, to enhance data diversity, the collection period spanned both high-traffic intervals between classes and low-traffic periods during class sessions on campus. Note that we include two reverse trajectories, which pose challenges for localization due to missing data resulting from changes in scanning direction.
+
+The dataset comprises 8 sequences for training and testing, each approximately 10 kilometers long, including 6 forward trajectories and 2 reverse trajectories. More details can be found in the supplementary.
+
+Comparison with other datasets. Tab. 1 summarizes the
+
+<table><tr><td rowspan="2">Methods</td><td colspan="3">SO(3) Rotation Augmentation</td><td colspan="4">Without Augmentation</td></tr><tr><td>DiffLoc</td><td>SGLoc</td><td>LiSA</td><td>DiffLoc</td><td>SGLoc</td><td>LiSA</td><td>RALoc</td></tr><tr><td>15-13-06-37</td><td>4.87m, 1.62°</td><td>3.79m, 5.58°</td><td>3.78m, 5.83°</td><td>4.09m, 1.58°</td><td>45.82m, 27.77°</td><td>52.81m, 21.47°</td><td>3.17m, 4.08°</td></tr><tr><td>17-13-26-39</td><td>7.35m, 2.01°</td><td>4.44m, 5.00°</td><td>4.48m, 4.92°</td><td>4.17m, 1.30°</td><td>42.59m, 25.14°</td><td>56.02m, 22.89°</td><td>3.87m, 3.96°</td></tr><tr><td>17-14-03-00</td><td>6.52m, 2.14°</td><td>3.66m, 4.98°</td><td>3.93m, 5.22°</td><td>4.61m, 1.26°</td><td>41.05m, 25.32°</td><td>50.65m, 22.54°</td><td>3.32m, 3.83°</td></tr><tr><td>18-14-14-42</td><td>3.83m, 1.43°</td><td>2.76m, 4.38°</td><td>2.90m, 4.25°</td><td>3.22m, 1.23°</td><td>38.51m, 24.75°</td><td>51.25m, 21.94°</td><td>2.58m, 3.70°</td></tr><tr><td>Average</td><td>5.64m, 1.80°</td><td>3.66m, 4.99°</td><td>3.77m, 5.06°</td><td>4.02m, 1.34°</td><td>41.99m, 25.75°</td><td>52.68m, 22.21°</td><td>3.24m, 3.89°</td></tr></table>
+
+Table 2. Quantitative results on the Oxford dataset with small rotation. Mean position error (m) and mean orientation error  $(^{\circ})$  are reported, with best results in bold and second best results underlined. Here, small rotation refers to a random rotation of  $[-10^{\circ}, 10^{\circ}]$  degrees applied to Roll, Pitch, and Yaw axes. SO(3) rotation augmentation involves random rotations of training data within  $[-180^{\circ}, 180^{\circ}]$ .  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="3">SO(3) Rotation Augmentation</td><td colspan="4">Without Augmentation</td></tr><tr><td>DiffLoc</td><td>SGLoc</td><td>LiSA</td><td>DiffLoc</td><td>SGLoc</td><td>LiSA</td><td>RALoc</td></tr><tr><td>15-13-06-37</td><td>4.90m, 1.61°</td><td>4.18m, 5.66°</td><td>3.66m, 5.43°</td><td>122.70m, 43.57°</td><td>341.79m, 94.04°</td><td>332.43m, 79.40°</td><td>3.19m, 4.07°</td></tr><tr><td>17-13-26-39</td><td>8.03m, 2.09°</td><td>4.55m, 5.05°</td><td>4.64m, 5.04°</td><td>153.37m, 43.03°</td><td>341.70m, 89.57°</td><td>324.07m, 76.47°</td><td>3.87m, 3.96°</td></tr><tr><td>17-14-03-00</td><td>7.05m, 2.26°</td><td>3.70m, 5.11°</td><td>4.00m, 5.37°</td><td>138.43m, 43.16°</td><td>334.34m, 88.43°</td><td>323.45m, 76.94°</td><td>3.33m, 3.88°</td></tr><tr><td>18-14-14-42</td><td>4.11m, 1.52°</td><td>2.82m, 4.45°</td><td>2.94m, 4.38°</td><td>129.65m, 41.08°</td><td>343.08m, 91.18°</td><td>336.76m, 78.59°</td><td>2.58m, 3.73°</td></tr><tr><td>Average</td><td>6.02m, 1.87°</td><td>3.81m, 5.07°</td><td>3.81m, 5.06°</td><td>136.04m, 42.71°</td><td>340.23m, 90.81°</td><td>329.18m, 77.85°</td><td>3.24m, 3.91°</td></tr></table>
+
+Table 3. Quantitative results on the Oxford dataset with large rotation. Mean position error (m) and mean orientation error  $(^{\circ})$  are reported, with best results in bold and second best results underlined. Here, large rotation refers to a random rotation of  $[-180^{\circ}, 180^{\circ}]$  degrees applied to the Yaw axis. SO(3) rotation augmentation involves random rotations of training data within  $[-180^{\circ}, 180^{\circ}]$ .
+
+comparison of our dataset with the existing widely used datasets. Our objective is to verify the method's robustness to rotation by collecting datasets with rotation changes. Compared to Oxford Radar Robotcar [4] and NCLT [11], which are widely used for localization evaluation, we provide multiple reverse trajectories. MulRan [26] offers reverse direction data but suffers from Radar occlusion that restricts visibility and challenges localization consistency. In contrast, our dataset emphasizes the following features: (1) sensors are vertically mounted to reduce inter-sensor occlusions, ensuring near-complete 360-degree scene coverage. (2) data collection spans three months, offering diverse conditions for a robust evaluation of localization methods. See the supplementary for detailed comparisons.
+
+# 4. Experiment
+
+# 4.1. Setup
+
+Datasets and metrics. We evaluate RALoc for LiDAR localization on two large-scale outdoor datasets: Oxford Radar RobotCar [4] and BiLiLo datasets. During the evaluation, we select the mean position and orientation error as the evaluation metrics.
+
+Oxford Radar RobotCar. The Oxford Radar RobotCar (Oxford) dataset is a critical benchmark for urban scene localization. It covers a  $2\mathrm{km}^2$  area, with each trajectory spanning nearly  $10\mathrm{km}$ . The dataset collects data from multiple sensors, such as LiDAR, cameras, radar, and GPS/INS. Our method only utilizes the information from LiDAR. The Oxford dataset captures a wide range of traffic conditions,
+
+making it an ideal resource for evaluating LiDAR-based localization models. Following previous works [30, 31, 55], we use data from 11-14-02-26, 14-12-05-52, 14-14-48-55, and 18-15-20-12 for training, and data from 15-13-06-37, 17-13-26-39, 17-14-03-00, and 18-14-14-42 for testing.
+
+BiLiLo. Our collected BiLiLo dataset is an outdoor campus scene localization benchmark, where each trajectory is nearly  $10\mathrm{km}$  in length. It contains 8 trajectories obtained through LiDAR, with 2 trajectories specifically designed to have driving directions entirely opposite to the others. This makes the BiLiLo dataset a complementary resource to other localization datasets, enabling a more comprehensive evaluation of model performance across various aspects. We use the data from 11-28-11-20, 11-28-14-54, 11-28-15-26, and 12-06-13-57 for training, and data from 12-06-10-30, 12-06-10-59, 03-04-16-04, and 03-04-16-29 for testing, where the last two trajectories in each set are reverse data. Note the naming convention for the trajectories is based on the data collection start time, formatted as month-date-hour-minute.
+
+Implementation. RALoc is implemented by Pytorch [41] and Spconv [15]. We conduct our experiments on a server equipped with an Intel Xeon(R) Gold 6342 CPU, and 4 NVIDIA RTX 4090 GPUs. For the point cloud canonicalization process, we randomly down sample 4,096 point clouds from the scene as input, and the subsequent LiDAR localization network is based on SGLoc. During training, we use the Adam [28] optimizer with a learning rate of 0.002 and a batch size of 120. On Oxford Radar RobotCar dataset, we set EkFA with  $k = 2048$ , and set the loss
+
+<table><tr><td rowspan="2">Methods</td><td colspan="3">SO(3) Rotation Augmentation</td><td colspan="4">Without Augmentation</td></tr><tr><td>DiffLoc</td><td>SGLoc</td><td>LiSA</td><td>DiffLoc</td><td>SGLoc</td><td>LiSA</td><td>RALoc</td></tr><tr><td>15-13-06-37</td><td>4.88m, 1.62°</td><td>4.42m, 6.17°</td><td>3.77m, 5.81°</td><td>3.57m, 0.88°</td><td>3.01m, 1.91°</td><td>2.36m, 1.29°</td><td>3.19m, 4.10°</td></tr><tr><td>17-13-26-39</td><td>7.89m, 2.01°</td><td>4.62m, 5.60°</td><td>4.58m, 5.47°</td><td>3.65m, 0.68°</td><td>4.07m, 2.07°</td><td>3.47m, 1.43°</td><td>3.87m, 3.96°</td></tr><tr><td>17-14-03-00</td><td>7.16m, 2.26°</td><td>3.84m, 5.63°</td><td>4.08m, 5.67°</td><td>4.03m, 0.70°</td><td>3.37m, 1.89°</td><td>3.19m, 1.34°</td><td>3.32m, 3.87°</td></tr><tr><td>18-14-14-42</td><td>4.22m, 1.40°</td><td>2.89m, 4.83°</td><td>3.05m, 4.67°</td><td>2.86m, 0.60°</td><td>2.12m, 1.66°</td><td>1.95m, 1.23°</td><td>2.59m, 3.71°</td></tr><tr><td>Average</td><td>6.04m, 1.82°</td><td>3.94m, 5.56°</td><td>3.87m, 5.41°</td><td>3.53m, 0.72°</td><td>3.14m, 1.88°</td><td>2.74m, 1.32°</td><td>3.24m, 3.91°</td></tr></table>
+
+Table 4. Quantitative results on the Oxford dataset without rotation. Mean position error (m) and mean orientation error  $(^{\circ})$  for various methods are reported, with best results in bold and second best results underlined. SO(3) rotation augmentation involves random rotations of training data along Roll, Pitch, and Yaw axes within  $[-180^{\circ}, 180^{\circ}]$ .  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="3">SO(3) Rotation Augmentation</td><td colspan="4">Without Augmentation</td></tr><tr><td>DiffLoc</td><td>SGLoc</td><td>LiSA</td><td>DiffLoc</td><td>SGLoc</td><td>LiSA</td><td>RALoc</td></tr><tr><td>12-06-10-30</td><td>6.93m, 10.26°</td><td>3.35m, 2.93°</td><td>2.87m, 1.96°</td><td>2.78m, 0.77°</td><td>2.14m, 1.81°</td><td>1.92m, 1.02°</td><td>1.91m, 2.90°</td></tr><tr><td>12-06-10-59</td><td>6.69m, 9.66°</td><td>3.29m, 2.88°</td><td>2.73m, 1.80°</td><td>2.62m, 0.73°</td><td>2.13m, 1.69°</td><td>1.85m, 0.96°</td><td>1.89m, 2.75°</td></tr><tr><td>03-04-16-04</td><td>27.99m, 23.75°</td><td>10.12m, 10.47°</td><td>24.93m, 62.85°</td><td>383.85m, 72.70°</td><td>379.96m, 90.73°</td><td>322.93m, 94.56°</td><td>5.24m, 9.59°</td></tr><tr><td>03-04-16-29</td><td>45.61m, 29.46°</td><td>11.08m, 13.60°</td><td>27.66m, 66.42°</td><td>395.29m, 78.82°</td><td>378.96m, 92.43°</td><td>322.32m, 95.81°</td><td>6.97m, 11.02°</td></tr><tr><td>Average</td><td>21.81m, 18.28°</td><td>6.96m, 7.47°</td><td>14.55m, 33.26°</td><td>196.14m, 38.26°</td><td>190.80m, 46.67°</td><td>162.26m, 48.09°</td><td>4.00m, 6.57°</td></tr></table>
+
+Table 5. Quantitative results on the BiLiLo dataset. Mean position error (m) and mean orientation error  $(^{\circ})$  for various methods are reported, with best results in bold and second best results underlined. SO(3) rotation augmentation involves random rotations of training data along Yaw, Pitch, and Roll axes within  $[-180^{\circ}, 180^{\circ}]$ . The red-marked trajectories are aligned with the overall driving direction during training, while the blue ones are in the reverse direction.
+
+weights to  $\lambda_1 = 1$ ,  $\lambda_2 = 1200$ . On BiLiLo dataset, we set  $k = 512$ ,  $\lambda_1 = 1$  and  $\lambda_2 = 1600$ .
+
+Baselines. To more effectively evaluate our model's performance, we select several representative and competitive baselines. For the APR method, we include the current state-of-the-art DiffLoc [31] for comprehensive comparison. For the SCR method, we choose SGLoc [30] and LiSA [55], where LiSA incorporates semantics into SGLoc through distillation while preserving a consistent framework. Note LiSA is the current state-of-the-art regression-based LiDAR localization method.
+
+# 4.2. Results
+
+Results on Oxford with Rotation. In this experiment, we introduce random rotations within 10 degrees in Roll, Pitch, and Yaw axes to the point cloud. Tab. 2 presents quantitative results on the Oxford dataset with small rotations (within  $[-10^{\circ}, 10^{\circ}]$ ), comparing baseline performance without augmentation to results with random rotation augmentation applied during training. RALoc achieves an average error of  $3.24\mathrm{m} / 3.89^{\circ}$ . It is clear that the results of the previous method experienced a significant decline without the introduction of rotation augmentation. Even after introducing data augmentation, our method still outperforms our baseline, SGLoc, with  $3.24\mathrm{m} / 3.89^{\circ}$  vs  $3.66\mathrm{m} / 4.99^{\circ}$ .
+
+Additionally, to account for the potential need for frequent direction changes during vehicle operation, we apply random rotations around the Yaw axis (within  $[-180^{\circ}, 180^{\circ}]$ ) to the point clouds and adjust the ground-truth values accordingly. As shown in Tab. 3, RALoc achieves
+
+![](images/a6a9c7f4af6dce0720b64af42516fe29612d302be666172dc76a6aea78344e67.jpg)  
+(a) SGLoc (10.12m, 10.47°)
+
+![](images/e8cda00149f50fa264e59fed472ad4429dfe6727c0f5f433e76d3d593a962bc8.jpg)  
+(b) DiffLoc  $(27.99\mathrm{m},23.75^{\circ})$
+
+![](images/3210250f161680364e9e4b18d549bb9e4bd9115f6666373f88c12556a81a89a7.jpg)  
+(c) LiSA (24.93m,62.85°)
+
+![](images/4da7166aa6355faa191f2754723f91762c0a91df9a5b49c4e48b05249d4d1d4c.jpg)  
+(d) RALoc  $(5.24\mathrm{m},9.59^{\circ})$  
+Figure 6. Visualization of different methods on BiLiLo. We select a reverse trajectory for testing. The black and red points represent the ground-truth and estimation poses, respectively, and the star indicates the first frame. The caption of each subfigure shows the mean position error (m) and orientation error  $(^{\circ})$ .
+
+$3.24 \mathrm{~m} / 3.91^{\circ}$ , reaching state-of-the-art performance in position, with no observable accuracy loss compared to previous evaluations. This result effectively demonstrates our model's resilience to significant rotational changes.
+
+Results on Oxford. We also evaluate RALoc on the Oxford dataset without rotation interference. Tab. 4 reports
+
+the results of RALoc and all other baselines with and without random rotation augmentation during training. RALoc achieves  $3.24\mathrm{m} / 3.91^{\circ}$  average error. Although the proposed method shows a decrease in orientation accuracy compared to our baseline, SGLoc, it becomes more robust across various rotation scenarios. SGLoc has significantly lower accuracy than us after adding rotation augmentation. Meanwhile, our method is not significantly affected in terms of position accuracy and even outperforms our baseline on certain trajectories.
+
+Results on BiLiLo. As mentioned earlier, simulated experiments struggle to comprehensively evaluate model performance, so we collected a real dataset with significant rotational variations for validation. Tab. 5 presents the evaluation results on the BiLiLo dataset. In particular, trajectories 03-04-16-04 and 03-04-16-29 have driving directions entirely opposite to the training data, enabling a rigorous evaluation of each model's rotational robustness. Our method achieves  $4.00\mathrm{m} / 6.57^{\circ}$  average error. Compared to previous methods, RALoc achieves a substantial improvement in position accuracy on the forward trajectories, reaching state-of-the-art performance. On the reverse trajectories, our model produces superior results, significantly outperforming other baselines.
+
+Fig. 6 illustrates the qualitative results of compartments with rotation augmentation on trajectory 03-04-16-04 with mean position error (m) and orientation error  $(^{\circ})$ . It is clear that RALoc offers a clean trajectory, indicating its capacity to produce more robust results.
+
+Speed and parameter. Real-time performance is a critical metric for localization tasks. Given that commonly used LiDAR sensors operate at a frequency of  $20\mathrm{Hz}$ , our inference time must remain below 50ms. We quantitatively evaluate the inference speed and parameter count of our proposed model, RALoc. The average inference time on the two datasets is 26ms. Additionally, in terms of total parameter count, we employ a relatively lightweight approach to achieve equivariance in the localization model. This requires only an additional 0.4M parameters compared to SGLoc, representing an increase of only  $0.0043\%$ .
+
+# 4.3. Ablation study
+
+Study on Rotation Augmentation. As shown in Tab. 6 between Row 1 and Row 2, using data augmentation can, to some extent, mitigate catastrophic performance losses caused by rotation. However, as shown in Tab. 5, for the normal trajectories, it also brings a negative impact. By contrast, our method (Row 4, Tab. 6), outperforms it, achieving  $4.00\mathrm{m} / 6.57^{\circ}$  vs.  $6.96\mathrm{m} / 7.47^{\circ}$ , while avoiding significant localization accuracy losses on normal trajectories. These results highlight the superior robustness of our approach.
+
+Study on PCC. We further conduct ablation experiments to demonstrate the importance of PCC. The comparison be
+
+<table><tr><td></td><td>Augmentation</td><td>PCC</td><td>EKFA</td><td>Average</td></tr><tr><td>1</td><td></td><td></td><td></td><td>190.80m, 46.67°</td></tr><tr><td>2</td><td>✓</td><td></td><td></td><td>6.96m, 7.47°</td></tr><tr><td>3</td><td></td><td>✓</td><td></td><td>5.79m, 8.02°</td></tr><tr><td>4</td><td></td><td>✓</td><td>✓</td><td>4.00m, 6.57°</td></tr></table>
+
+Table 6. Ablation study on the BiLiLo dataset. Augmentation: using data augmentation to increase the rotational diversity of training data. PCC: using Point Cloud Canonicalization process to perceptive rotation and align point cloud into canonicalization coordinate. EKFA: using Equivariant Key Feature Aggregation module to guide feature aggregation.
+
+tween Row 1 and Row 3 show PCC can solve the challenges brought by rotation changes. Moreover, from Row 2 and Row 3, when compared to data augmentation, PCC also takes an average improvement of  $16.8\%$  on position accuracy. This shows that PCC can get a better result than rotation augmentation.
+
+Study on EKFA. We evaluate the EKFA module's impact on handling noise in real-world LiDAR point clouds. The EKFA module is designed to mitigate scene noise, aiming to enhance the equivariant network's robustness to rotation and reduce noise-induced localization errors. Compared to Row 3 and Row 4, it yields a process of  $30.9\% /18.1\%$  on position and orientation accuracy, respectively. Compared to the data augmentation, it also get an improvement of  $42.5\% /12.0\%$ . Moreover, as shown in Tab. 5, integrating EKFA into PCC improves position accuracy by an average of  $11.0\%$  on normal trajectories compared to the vanilla method (SGLoc in this paper). These results show that the EKFA module effectively extracts scene-relevant information, reducing noise impact on the equivariant network and enhancing localization robustness.
+
+# 5. Conclusion
+
+In this paper, we reveal that current learning-based regression methods are sensitive to rotations, resulting in significant accuracy loss under rotational conditions. We propose RALoc, a novel rotation-robust scene coordinate regression framework for LiDAR-based localization. To more realistically evaluate the rotational robustness of the localization method, we establish equipment setups and collect a large-scale outdoor localization dataset, BiLiLo, with significant rotational variations. Extensive experiments demonstrate that the proposed RALoc significantly outperforms the state-of-the-art methods in scenarios with large rotations. In the future, we aim to enhance the training efficiency of RALoc and integrate multimodal information to further improve localization accuracy.
+
+Acknowledgements. This work is supported in part by the Fundamental Research Funds for the Central Universities (No. 20720230033) and Xiaomi Young Talents Program.
+
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ICCV/2025/RANKCLIP_ Ranking-Consistent Language-Image Pretraining/full.md

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+# RANKCLIP: Ranking-Consistent Language-Image Pretraining
+
+Yiming Zhang\*1,2, Zhuokai Zhao\*3, Zhaorun Chen\*3, Zhili Feng4, Zenghui Ding\*1, Yining Sun\*1 HFIPS, Chinese Academy of Sciences 2 University of Science and Technology of China 3 University of Chicago 4 Carnegie Mellon University
+
+yimingzhang@mail.ustc.edu.cn, zhuokai@uchicago.edu
+
+# Abstract
+
+Self-supervised contrastive learning models, such as CLIP, have set new benchmarks for vision-language models in many downstream tasks. However, their dependency on rigid one-to-one mappings overlooks the complex and latent semantic attributes relationships between and within texts and images. To this end, we introduce RANKCLIP, a novel pretraining method that extends beyond the rigid one-to-one matching framework of CLIP and its variants. By extending the traditional pair-wise contrastive loss to list-wise ranking consistency loss, and leveraging both in-modal and cross-modal ranking consistency, RANKCLIP improves the alignment process, enabling it to capture the nuanced many-to-many relationships between and within each modality. Through comprehensive experiments, we demonstrate the effectiveness of RANKCLIP in various downstream tasks, achieving significant gains over state-of-the-art methods, underscoring the importance of this enhanced learning process. Code is available at https://github.com/Jam1ezhang/RankCLIP
+
+# 1. Introduction
+
+In the realm of computer vision (CV) [55], natural language processing (NLP) [7], and multimodal deep learning [4, 25, 60], the alignment between visual and textual modalities [5, 49] has emerged as a cornerstone for downstream applications, ranging from image captioning [18] to zero-shot classification [42]. Contrastive Language-Image Pretraining (CLIP) [43] marks a significant advancement in this field, demonstrating incredible performance from training on large amounts of text-image pairs to create self-supervised models that understand [6, 22, 23] and generate [11, 44] descriptions of visual contents. Following the success of this contrastive learning paradigm, many recent works have been developed upon the original CLIP. More specifically, these enhancements focus on optimizing data efficiency through intrinsic supervision [28], as well
+
+![](images/6674a22815789f9455932c8adef998f927653f0d2b8f49d514c4e4c0952310b8.jpg)  
+Figure 1. Comparison of learning outcomes between CLIP and RANKCLIP using three text-image pairs: dog (red), cat (blue), and car (yellow). (a) Contrastive loss treats all unmatched relationships equally, failing to distinguish latent similar attributes between dog and cat versus airplane. RANKCLIP addresses this issue by leveraging the shared attributes in (c) during training, improving the final trained embedding distribution from (b) to (d).
+
+as improving downstream performance via cross-modal late interaction [59], hierarchical feature alignment [15], geometric consistency regularization [19], additional learning [36], adaptive loss [58], hierarchy-aware attentions [17], and softer cross-modal alignment [16].
+
+Despite the improvements, these methods often have reliance on strict pairwise, cross-modal, and one-to-one mappings between images and texts, overlooking the actual many-to-many relationships that exist both cross-modal and
+
+in-modal in real-world data [8]. For example, as shown in Fig. 1, while pretrained models like CLIP can correctly classify dog, cat and airplane, they do not explicitly learn that dog and cat are more close to each other than dog and airplane, in terms of both in-modal (dog text is more similar to cat text than to airplane text) and cross-modal (dog text is more matched to cat image than to airplane image) similarities. Since it is rooted from the current contrastive loss that only the correct pairs are optimized while the rest of the unmatched pairs are treated the same, a large amount of information not used and unknown to the model during and after the training process.
+
+Recognizing the complex many-to-many relationships as well as the rich information contained within both in-modal and cross-modal data, we introduce **Ranking-Consistent Language-Image Pretraining, (RANKCLIP)**, which employs ranking consistency to learn and optimize similarity levels both between (cross-modal) and within (in-modal) the text-image pairs. The concept of ranking consistency stems from the simple observations that similar texts often correlate with similar images, as seen with the dog, cat and airplane example in Fig. 1. It effectively captures secondary similarity relationships among unmatched pairs, enabling the model to learn more efficiently for free compared to relying solely on matched pairs. Ranking consistency is conveniently modeled as an additional loss term to the traditional contrastive loss, requiring no extra external modules. It acts as a plug-and-play improvement for many existing methods, including those focusing on data-efficiency [28], potentially boosting performance in both efficiency and effectiveness.
+
+The main contributions of this paper are: 1) RANKCLIP, a novel contrastive pretraining method that uses ranking consistency to exploit the many-to-many relationships within data, thereby enhancing performance in downstream tasks such as zero-shot classification and retrieval accuracy; and 2) through comprehensive experiments conducted on multiple datasets, we demonstrate the superior effectiveness of RANKCLIP in improving pretraining model performance without requiring any additional data or computational resources.
+
+# 2. Related Work
+
+Vision-language pretraining has witnessed significant advancements over the past years [3, 14, 31]. Models such as CLIP [43], ALIGN [26] and FLAVA [49] have pioneered the contrastive learning paradigm applied with text-image pairs, showcasing remarkable performance and robustness in downstream tasks. Many follow-up works, mostly built upon CLIP, have been proposed since then. Li et al. [28] introduced DeCLIP, improving zero-shot performance through intrinsic supervision. FILIP [59] advances CLIP's alignment between image patches and text with a cross
+
+modal interaction mechanism. Gao et al. [15] developed PyramidCLIP, using hierarchical feature alignment to boost model efficiency and performance. Additionally, SLIP [36] merges self-supervised learning with CLIP pre-training for improved visual representation and accuracy. Goel et al. [19] introduced CyCLIP, augmenting CLIP with geometric consistency regularizers to enhance robustness and performance under varied conditions.
+
+Recently, Yang et al. [58] introduced ALIP, an adaptive pre-training model that enhances language-image alignment using raw text and synthetic captions with dynamic adjustments. HiCLIP [17] refines CLIP by adding hierarchy-aware attentions to uncover semantic hierarchies in images and texts. EqSim [57] incorporates equivariance loss into vision-language models, significantly improving sensitivity to semantic changes in image-text pairs. Additionally, SoftCLIP [16] softens CLIP's one-to-one constraint, enabling more flexible cross-modal alignment through fine-grained adjustments.
+
+Compared with existing approaches, RANKCLIP sets itself apart by fully leveraging the many-to-many relationships within each batch of text-image pairs, promoting learning from both matched and unmatched pairs with varying similarities by integrating in-modal and cross-modal list-wise ranking consistencies into the contrastive training objective. Crucially, RANKCLIP diverges from existing models' pair-wise training objective by adopting a global, list-wise optimization approach. In other words, it considers the rankings of all images and texts collectively within each batch, rather than focusing on pairwise similarities as seen in other methods.
+
+# 3. RANKCLIP
+
+RANKCLIP efficiently leverages the many-to-many relationships in real-world data by focusing on both matched and unmatched pairs. As in Fig. 2, it not only identifies if an image-text pair matches but also assesses their relative semantic similarities to other images and texts of both modalities in the dataset through self-supervised ranking consistency. Uniquely, RANKCLIP employs a list-wise loss for training batches, distinguishing it from other methods that solely rely on pair-wise relationships, as discussed in §2.
+
+# 3.1. Ranking Model Formulation
+
+RANKCLIP leverages the Plackett-Luce (PL) ranking model [20, 32, 41] to estimate the probability distribution over rankings for every image-text pair  $(V_{i},T_{j})$ , so that the consistency in their relative ordering with respect to a reference ranking can be measured. Specifically, for a given data pair, whether it is in-modal (image-image, text-text), or cross-modal (image-text), we calculate its in- or cross-modal cosine similarity  $S_{ij}$  to serve as the score when measuring the alignment of its ranking with respect to another
+
+![](images/01f6702ad53f0fb47b06dd4ba1bb8d103ed8cf83024f198174a0331d3cec5ee3.jpg)  
+Figure 2. Overview of RANKCLIP. Unlike conventional contrastive loss, which includes only the middle term, RANKCLIP introduces both cross-modal and in-modal consistency terms by minimizing a self-supervised, list-wise ranking loss. Paired images and texts are indicated by matching contour line colors.  $V$ ,  $T$ , and  $S$  represent image embeddings, text embeddings, and similarity scores, respectively.
+
+reference ranking  $y_{\mathrm{ref}}$
+
+Following [41], we first sort the reference ranking in a descending order to construct the optimal ranking  $y^{*}$ , and assume that the ego ranking  $y$  is sampled from  $y^{*}$ . The probability that item  $d$  with score  $S_{ij}$  is ranked  $k^{\text{th}}$  in the ego ranking  $y$  from a set of items  $\mathcal{D}$  is the score of  $e^{S_{ij}}$  divided by the sum of scores for the items that have not been placed yet:
+
+$$
+\pi (d \mid y _ {1: k - 1}, y _ {\text {r e f}}, \mathcal {D}) = \frac {e ^ {S _ {i j}}}{\sum_ {d ^ {\prime} \in \mathcal {D} \backslash y _ {1 : k - 1}} e ^ {S _ {i j} ^ {\prime}}}, \tag {1}
+$$
+
+where  $y_{1:k-1} = [y_1, y_2, \dots, y_{k-1}]$  denotes the set of items ranked before  $d$ . Consequently, the probability of the entire ranking  $y$  is the product of all individual placement probabilities:
+
+$$
+\mathcal {P} \left(y, y _ {\text {r e f}}\right) = \prod_ {k = 1} ^ {K} \pi \left(y _ {k} \mid y _ {1: k - 1}, \mathbf {y} _ {\text {r e f}}, \mathcal {D}\right). \tag {2}
+$$
+
+RANKCLIP's objective is to maximize the consistency log-likelihood of the list ranking in one modality towards the reference ranking (from the same/in-modal and different/cross-modal data), which conveniently aligns with minimizing the negative log-likelihood loss:
+
+$$
+\mathcal {L} _ {\mathrm {P L}} = - \log \mathcal {P} (y, y _ {\text {r e f}}) \tag {3}
+$$
+
+# 3.2. Cross-modal Consistency Ranking
+
+As illustrated by the green box in Fig. 2, RANKCLIP utilizes secondary relationships between unmatched visual and
+
+textual representations by constructing a list-wise rank loss. This approach ensures that the semantic similarity rankings between one image and multiple texts align with those between one corresponding text and multiple images. For example, as shown in Fig. 1, from the dog perspective, the semantic distance between dog image and cat text is closer compared to the plane text. This relationship should also apply between the dog text and the cat, plane images. Mathematically, Eq. (3) can be specified as:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\text {c r o s s - m o d a l}} = - \log \mathcal {P} (\mathbf {y} _ {\text {i m a g e - t e x}}, \mathbf {y} _ {\text {t e x t - i m a g e}}) (4) \\ = - \log \mathcal {P} (\hat {\mathbf {v}} \cdot \hat {\mathbf {t}} ^ {\mathbf {T}}, \hat {\mathbf {t}} \cdot \hat {\mathbf {v}} ^ {\mathbf {T}}) (5) \\ \end{array}
+$$
+
+By optimizing Eq. (4), RANKCLIP enhances its ability to bridge the semantic gap between modalities by leveraging nuanced unmatched correlations. This can also be viewed as learning a symmetric cosine-similarity matrix, further reinforcing semantic consistency across modalities.
+
+# 3.3. In-modal Consistency Ranking
+
+The pink box in Fig. 2 highlights the in-modal consistency component of the proposed rank loss. RANKCLIP ensures semantic consistency within each modality – image to image and text to text – enhancing the use of secondary unmatched relationships as an optimization objective. The underlying principle is that similar images should correspond to similar texts. For example, in Fig. 1, from the dog image perspective, the cat image is the most similar, followed by the plane image. This relationship should hold true
+
+<table><tr><td rowspan="3"></td><td rowspan="2" colspan="3">ImageNet1K</td><td colspan="6">MSCOCO</td></tr><tr><td colspan="3">Image-to-Text Retrieval</td><td colspan="3">Text-to-Image Retrieval</td></tr><tr><td>Top-1</td><td>Top-3</td><td>Top-5</td><td>Recall@1</td><td>Recall@5</td><td>Recall@10</td><td>Recall@1</td><td>Recall@5</td><td>Recall@10</td></tr><tr><td>CLIP [43]</td><td>9.06%</td><td>16.94%</td><td>21.63%</td><td>6.68%</td><td>18.36%</td><td>26.94%</td><td>3.70%</td><td>9.74%</td><td>14.04%</td></tr><tr><td>CyCLIP [19]</td><td>9.40%</td><td>17.32%</td><td>21.72%</td><td>6.50%</td><td>19.34%</td><td>29.14%</td><td>3.72%</td><td>11.16%</td><td>16.06%</td></tr><tr><td>ALIP [58]</td><td>9.71%</td><td>18.31%</td><td>23.07%</td><td>6.04%</td><td>18.04%</td><td>26.92%</td><td>3.70%</td><td>10.22%</td><td>14.38%</td></tr><tr><td>RANKCLIP</td><td>10.16%</td><td>19.57%</td><td>24.01%</td><td>7.18%</td><td>19.46%</td><td>28.48%</td><td>3.74%</td><td>10.28%</td><td>14.18%</td></tr></table>
+
+Table 1. Zero-shot top-1, top-3, and top-5 classification accuracy on ImageNet1K, along with retrieval performance on MS-COCO. The proposed RANKCLIP consistently outperforms all baselines across both tasks. All models are trained on CC3M with ViT-B/32 backbone.
+
+for their corresponding texts as well, where we utilize this to construct our  $y$  and  $y_{\mathrm{ref}}$  from Eq. (3). Mathematically, Eq. (3) can be specified as:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\text {i n - m o d a l}} = - \log \mathcal {P} \left(\mathbf {y} _ {\text {t e x t - t e x t}}, \mathbf {y} _ {\text {i m a g e - i m a g e}}\right) (6) \\ = - \log \mathcal {P} (\hat {\mathbf {t}} \cdot \hat {\mathbf {t}} ^ {\mathbf {T}}, \hat {\mathbf {v}} \cdot \hat {\mathbf {v}} ^ {\mathbf {T}}) (7) \\ \end{array}
+$$
+
+where  $\hat{\mathbf{t}}$  and  $\hat{\mathbf{v}}$  are the text and image batch embedding matrix, respectively. Via Eq. (6), the model can efficiently leverage the nuanced in-modal relationships to learn a richer and more structured semantic representation.
+
+# 3.4. RANKCLIP Loss
+
+Combining both cross-modal and in-modal consistency with the traditional contrastive loss (more details in Appendix B), the complete rank loss is thus formulated as:
+
+$$
+\mathcal {L} _ {\text {R A N K C L I P}} = \mathcal {L} _ {\text {C L I P}} + \lambda_ {1} \mathcal {L} _ {\text {i n - m o d a l}} + \lambda_ {2} \mathcal {L} _ {\text {c r o s s - m o d a l}} \tag {8}
+$$
+
+which is also depicted in Fig. 2. By supplementing the pairwise contrastive loss with cross-modal and in-modality ranking consistency loss, RANKCLIP systematically organizes embeddings to fully exploit both global and fine-grained unmatched relationships, which enhances the learning of more informative and accurate representations, better supporting downstream multi-modal tasks.
+
+# 3.5. Training Recipe on Selecting  $\lambda_{1}$  and  $\lambda_{2}$
+
+In the early stage of pre-training, rank consistency is highly unstable due to random initialization. Overemphasizing ranking consistency at this stage can impede the optimization of the embedding space. To address this, we gradually increase the weights  $\lambda_{1}$  and  $\lambda_{2}$  of the ranking loss as training progresses. Specifically, we have:
+
+$$
+\lambda_ {1} = \lambda_ {2} = \operatorname {c l i p} \left(\frac {3 i - 1}{n - 1}, 0, 2\right)
+$$
+
+where  $i$  and  $n$  denote the current training epoch and total number of epoch, respectively. The full RANKCLIP framework is outlined in Algorithm 1.
+
+# 4. Experiments
+
+# 4.1. Experimental Setup
+
+Baselines. The most direct baseline to RANKCLIP is the original CLIP [43]. To further demonstrate the supe
+
+rior performance of RANKCLIP, we include CyCLIP [19], which introduces cyclic consistency constraints to enforce more robust alignment between visual and textual representations, improving generalization and semantic coherence. We also include ALIP [58], which leverages synthetic captions to enhance vision-language representation learning. More specifically, it employs a unique architecture that dynamically adjusts sample and pair weights to mitigate the impact of noisy or irrelevant data, making its approach complementary to ours. The training procedures and parameters for all models are detailed in Appendix A.
+
+Data. All approaches are pretrained on the Conceptual Captions 3M (CC3M) dataset [48], which contains approximately 3.3 million text-image pairs. Although significantly smaller than CLIP's original dataset [24], CC3M remains a standard benchmark for vision-language pretraining, enabling strong zero-shot performance [2, 19, 28, 36, 53]. As discussed in §5.2, we also train CLIP and RANKLIP on a larger 15M-image subset of YFCC100M [54] (YFCC15M) to study the effect of scaling up the dataset size.
+
+# 4.2. Zero-shot Classification
+
+We evaluate the zero-shot classification performance of CLIP [43], CyCLIP [19], ALIP [58], and RANKCLIP on ImageNet1K [12, 46]. As shown in Table 1, RANKCLIP consistently outperforms CLIP, which highlights the effectiveness of ranking consistency in enhancing language-image alignment with the same training data. Compared to CyCLIP [19], which enforces cyclic consistency to improve semantic coherence, RANKCLIP achieves higher accuracy across all metrics, suggesting that ranking consistency provides a more direct and effective regularization for representation learning. Additionally, RANKCLIP surpasses ALIP [58], indicating that ranking consistency is a stronger alternative to synthetic caption-based supervision. Notably, RANKCLIP shows the most significant improvement in top-1 accuracy, reinforcing its practical advantages where the highest-ranked prediction is most critical.
+
+# 4.3. Zero-shot Cross-modal Retrieval
+
+We further evaluate RANKCLIP on zero-shot cross-modal retrieval tasks, including image-to-text and text-to-image retrieval, using the MSCOCO [30] dataset. As shown in Table 1, RANKCLIP outperforms all baselines, though the
+
+<table><tr><td></td><td colspan="3">ImageNetV2-Matched</td><td colspan="3">ImageNetV2-Threshold</td><td colspan="3">ImageNetV2-Top</td><td colspan="3">ImageNet-R</td></tr><tr><td></td><td>Top1</td><td>Top3</td><td>Top5</td><td>Top1</td><td>Top3</td><td>Top5</td><td>Top1</td><td>Top3</td><td>Top5</td><td>Top1</td><td>Top3</td><td>Top5</td></tr><tr><td>CLIP [43]</td><td>7.53%</td><td>14.99%</td><td>19.61%</td><td>8.89%</td><td>17.22%</td><td>21.86%</td><td>10.76%</td><td>19.80%</td><td>24.87%</td><td>9.36%</td><td>10.56%</td><td>19.76%</td></tr><tr><td>CyCLIP [19]</td><td>7.68%</td><td>15.07%</td><td>19.11%</td><td>9.10%</td><td>17.42%</td><td>21.94%</td><td>11.20%</td><td>20.18%</td><td>25.34%</td><td>9.23%</td><td>16.72%</td><td>21.64%</td></tr><tr><td>ALIP [58]</td><td>7.82%</td><td>15.56%</td><td>19.81%</td><td>9.65%</td><td>18.31%</td><td>22.85%</td><td>11.43%</td><td>20.88%</td><td>26.10%</td><td>10.92%</td><td>20.27%</td><td>26.24%</td></tr><tr><td>RANKCLIP</td><td>9.01%</td><td>16.95%</td><td>21.12%</td><td>10.32%</td><td>19.31%</td><td>24.13%</td><td>12.31%</td><td>22.11%</td><td>27.17%</td><td>11.34%</td><td>20.88%</td><td>26.94%</td></tr></table>
+
+Table 2. Zero-shot top-1, 3, and 5 accuracy on ImageNet1K variants with natural distribution shifts. Compared to baselines, RANKCLIP achieves higher accuracies. Notably, these gains are more pronounced than on standard ImageNet1K, highlighting improved robustness.  
+
+<table><tr><td></td><td>CIFAR-10</td><td>CIFAR-100</td><td>DTD</td><td>FGVCAircraft</td><td>Food101</td><td>GTSRB</td><td>OxfordPets</td><td>SST2</td><td>STL10</td><td>SVHN</td><td>Average</td></tr><tr><td>CLIP [43]</td><td>77.6%</td><td>56.2%</td><td>43.2%</td><td>22.6%</td><td>39.7%</td><td>60.0%</td><td>40.4%</td><td>51.0%</td><td>79.0%</td><td>50.5%</td><td>52.0%</td></tr><tr><td>CyCLIP [19]</td><td>76.8%</td><td>54.3%</td><td>45.8%</td><td>19.2%</td><td>37.5%</td><td>58.6%</td><td>44.2%</td><td>51.5%</td><td>82.3%</td><td>41.3%</td><td>51.2%</td></tr><tr><td>ALIP [58]</td><td>71.1%</td><td>49.1%</td><td>47.1%</td><td>17.4%</td><td>36.1%</td><td>51.5%</td><td>41.9%</td><td>53.3%</td><td>81.0%</td><td>38.3%</td><td>48.7%</td></tr><tr><td>RANKCLIP</td><td>78.4%</td><td>56.6%</td><td>42.4%</td><td>23.4%</td><td>40.2%</td><td>60.6%</td><td>40.6%</td><td>53.4%</td><td>79.6%</td><td>47.7%</td><td>52.3%</td></tr></table>
+
+![](images/31d7130f45b1d82da3a58469ac680f37ad1eeb69df1a93def1b4b015c0546910.jpg)  
+Table 3. Linear probing accuracy on 10 downstream datasets using a ViT backbone.  
+Figure 3. Effect of  $\lambda_{1}$  and  $\lambda_{2}$  on zero-shot classification (ImageNet1K) and retrieval (MSCOCO).
+
+improvements are less pronounced compared to zero-shot classification. This smaller margin of improvement may be attributed to the increased complexity of retrieval tasks, which require fine-grained image-text alignment across varying resolutions and object details - challenges distinct from the more direct pattern recognition in classification.
+
+# 4.4. Robustness to Distribution Shifts
+
+To evaluate the robustness of RANKCLIP under distribution shifts, we test all approaches on three variants of ImageNetV2 [45] and ImageNet-R [22], which assess resilience to different real-world deviations from ImageNet1K. As shown in Table 2, RANKCLIP consistently outperforms all baselines, achieving the highest accuracy across all datasets. These results indicate that RANKCLIP not only improves standard zero-shot classification but also enhances adaptation to real-world distribution shifts.
+
+# 4.5. Linear Probing
+
+We further assess whether the advantages of ranking consistency persist when supplemented with in-domain supervision. Specifically, we apply linear probing, where pretrained encoders remain fixed while a logistic regression
+
+classifier is trained on domain-specific datasets. We evaluate on 10 standard image classification benchmarks, including CIFAR-10, CIFAR-100, DTD [9], FGVG-Aircraft [33], Food101 [1], GTSDB [52], OxfordPets [40], SST2 [50], STL-10 [10], and SVHN [37]. As shown in Table 3, RANKCLIP achieves the highest average accuracy, demonstrating that ranking consistency enhances generalization even with additional in-domain supervision.
+
+# 5. Ablation Studies
+
+# 5.1. Different Weights of RANKCLIP Loss
+
+In Eq. (8), we define the RANKCLIP loss as a linear combination of the original contrastive loss and the in-modal and cross-modal ranking consistency losses, weighted by  $\lambda_{1}$  and  $\lambda_{2}$ , respectively. In §3.5, we introduce a training strategy that adaptively adjusts  $\lambda_{1}$  and  $\lambda_{2}$  at different stages of training. In this section, we analyze the impact of these weights and demonstrates that adaptive weighting further enhances RANKCLIP's performance. Notice that all model variants follow the same pretraining setup detailed in Appendix A. As shown in Fig. 3, RANKCLIP outperforms CLIP even with fixed  $\lambda_{1}$  and  $\lambda_{2}$ , highlighting the effectiveness of ranking consistency. And the adaptive weighting strategy further boosts accuracy by preventing the underutilization of ranking consistency at low weights and avoiding disruptions to contrastive learning at high weights.
+
+# 5.2. Different Data Sizes
+
+To assess the scalability of RANKCLIP, we trained both CLIP and RANKCLIP on 500k, 750k, 1M, and 3M text-image pairs from CC3M, as well as 15M pairs from YFCC15M, following the procedure in Appendix A. Fig. 4 compares their performance on zero-shot top-1 classifica
+
+![](images/a59e84a4cf5c6fc6742860b82a89dfd5bce782a26d1d87ab88745c44ffcbc592.jpg)  
+Figure 4. Ablation studies of CLIP and RANKCLIP trained with different data sizes. Left: zero-shot top-1 classification accuracy on ImageNet1K with various data sizes randomly sampled from CC3M. RANKCLIP consistently outperforms CLIP with significant margins. Right: zero-shot top-1 classification accuracy on ImageNet1K (horizontal axis) and ImageNet1K-R (vertical axis). RANKCLIP demonstrates better robustness as well as accuracy.
+
+![](images/2b36aa2075c9fe495932ca5c5fd21b998d81326c6c303daac59adcba2f33297c.jpg)
+
+<table><tr><td rowspan="3">Method</td><td rowspan="3">Vision Backbone</td><td rowspan="2" colspan="3">ImageNet1K</td><td colspan="6">MSCOCO</td><td rowspan="3">Linear Probing Avg. Acc.</td></tr><tr><td colspan="3">Image-to-Text Retrieval</td><td colspan="3">Text-to-Image Retrieval</td></tr><tr><td>Top-1</td><td>Top-3</td><td>Top-5</td><td>R@1</td><td>R@5</td><td>R@10</td><td>R@1</td><td>R@5</td><td>R@10</td></tr><tr><td>CLIP [43]</td><td rowspan="2">RN50</td><td>21.6%</td><td>36.9%</td><td>44.9%</td><td>15.6%</td><td>36.4%</td><td>48.4%</td><td>6.7%</td><td>15.2%</td><td>20.1%</td><td>64.2%</td></tr><tr><td>RANKCLIP</td><td>30.9%</td><td>49.4%</td><td>57.6%</td><td>19.5%</td><td>42.6%</td><td>54.8%</td><td>7.5%</td><td>16.2%</td><td>21.6%</td><td>68.9%</td></tr><tr><td>CLIP [43]</td><td rowspan="2">ViT-B/32</td><td>20.7%</td><td>35.0%</td><td>42.4%</td><td>11.9%</td><td>29.4%</td><td>40.8%</td><td>5.1%</td><td>12.9%</td><td>17.9%</td><td>60.7%</td></tr><tr><td>RANKCLIP</td><td>26.2%</td><td>41.4%</td><td>48.9%</td><td>13.8%</td><td>33.8%</td><td>45.9%</td><td>6.0%</td><td>13.6%</td><td>18.6%</td><td>61.3%</td></tr></table>
+
+Table 4. Zero-shot evaluation of CLIP and RANKCLIP trained with different vision backbones (ResNet-50 (RN50) and ViT-B/32) on ImageNet1K classification, MSCOCO cross-modal retrievals, and linear probing. “R@k” denotes Recall@k.
+
+tion accuracy for ImageNet1K (left) and averaged linear probing results (middle), where RANKCLIP consistently outperforms CLIP. Full, non-averaged linear probing results are provided in Appendix 7. Notably, the performance gains of RANKCLIP become more pronounced as dataset size scales from  $1\mathrm{m}$  to  $15\mathrm{m}$ , highlighting its superior scalability, which is critical for language-image pretraining.
+
+Fig. 4 (right) further illustrates RANKCLIP's robustness across different dataset sizes. The horizontal axis represents top-1 accuracy on standard ImageNet1K, while the vertical axis shows accuracy on ImageNet1K-R. The black diagonal  $(y = x)$  denotes ideal robustness, with deviations below it indicating degradation under distribution shifts. RANKCLIP remains well above the red baseline, which represents typical in-distribution to out-of-distribution generalization [35], and stays close to the ideal line, demonstrating strong robustness.
+
+# 5.3. Different Backbones: RN50 vs. ViT
+
+We compare RANKCLIP and CLIP across ResNet-50 (RN50) and ViT-B/32 backbones to assess its generalization performance and overall robustness. As shown in Table 4, RANKCLIP consistently outperforms CLIP across all evaluated tasks. Specifically, for zero-shot classification on ImageNet1K, RANKCLIP improves top-1 accuracy by  $+9.3\%$  with RN50 and  $+5.5\%$  with ViT-B/32, demonstrating its fundamentally stronger feature learning capabilities.
+
+In cross-modal retrieval, RANKCLIP achieves  $+3.9\%$  in image-to-text and  $+0.8\%$  in text-to-image with RN50, with smaller but consistent gains for ViT-B/32. RANKCLIP also improves linear probing accuracy by  $+4.7\%$  with RN50 and  $+0.6\%$  with ViT-B/32, confirming its advantage in representation learning. While both architectures benefit, RN50 sees the largest gains, a result suggesting that ranking consistency particularly enhances the hierarchical feature extraction process in CNNs.
+
+# 6. Analysis
+
+# 6.1. Modality Gap
+
+We analyze the modality gaps of CLIP and RANKCLIP by visualizing 250 text-image pair embeddings, reduced to two dimensions using UMAP [34], and presenting a histogram of the gaps. The modality gap [29] refers to the separation between text and image embeddings in multimodal models, hindering joint representation learning. This gap, inherent from initialization and reinforced by contrastive learning in CLIP, challenges effective language-image modeling. Recent studies [27, 38, 51] suggest that reducing this gap improves multimodal representations and downstream performance. As shown in Fig. 6, RANKCLIP exhibits a significantly smaller modality gap than CLIP, demonstrating that our ranking consistency approach effectively enhances text-image alignment.
+
+![](images/e001b595e7648a8a2d8bd15a564d13f68b6d1c226f65c23265035c56578fc121.jpg)  
+Caption: A painting of a table with fruit on top of it
+
+# 6.2. Alignment and Uniformity
+
+Beyond reducing modality gap, effective contrastive learning should ensure a broad and uniform distribution over a hypersphere [56]. These objectives – similarity and uniformity – are quantified by alignment and uniformity scores, respectively. Following Goel et al. [19] and the notations in §3, we compute the alignment score  $S_{\mathrm{A}}$  and uniformity score  $S_{\mathrm{U}}$  as:
+
+$$
+S _ {\mathrm {A}} = \frac {1}{N} \sum_ {j = 1} ^ {N} \hat {I} _ {j} ^ {T} \hat {T} _ {j}, \tag {9}
+$$
+
+$$
+S _ {\mathrm {U}} = \log \left(\frac {1}{N (N - 1)} \sum_ {j - 1} ^ {N} \sum_ {k = 1, j \neq k} ^ {N} \exp^ {- \hat {I} _ {j} ^ {T} \hat {T} _ {k}}\right) \tag {10}
+$$
+
+where  $N$  is the number of text-image pairs.  $S_{\mathrm{A}}$  captures the average cosine similarity between corresponding text and image embeddings, while  $S_{\mathrm{U}}$  measures how evenly embeddings are spread across the space. High alignment indicates strong correlation between paired embeddings, whereas low uniformity suggests diverse and efficient embedding distribution—desirable for tasks like retrieval. As shown in Table 5, CLIP achieves stronger alignment but suffers from poor uniformity, leading to redundant representations. On the other hand, RANKCLIP along with two of its ablated version,  $\mathrm{RANKCLIP}_I$  and  $\mathrm{RANKCLIP}_C$  presents much better balance between alignment and uniformity. These results further suggest that optimizing solely for alignment or uniformity does not necessarily translate to better task performance.
+
+![](images/6029461dbf5afd29185a0c4409dcf981f34f0ec9939e18d6432fa43a4ab6e660.jpg)  
+Figure 5. For a given text query, we present the top ten most semantically relevant images (ordered from left to right) obtained through both CLIP and RANKCLIP. In comparison to CLIP, our approach consistently retrieves images that more comprehensively align with the textual description, maintaining this advantage even after the correct reference image appears in the ranked results.
+
+![](images/70c8ce0199c7bfd605095ae5a8a3ba529f5fea4ed4471374544fdaeeeacb6853.jpg)  
+Figure 6. Scatter and histograms plots illustrating modality gaps of (a) CLIP and (b) RANKCLIP.
+
+<table><tr><td></td><td colspan="2">CIFAR-10</td><td colspan="2">CIFAR-100</td><td colspan="2">ImageNet1K</td></tr><tr><td></td><td>SA</td><td>SU</td><td>SA</td><td>SU</td><td>SA</td><td>SU</td></tr><tr><td>CLIP</td><td>0.28</td><td>-0.19</td><td>0.28</td><td>-0.18</td><td>0.33</td><td>-0.19</td></tr><tr><td>RANKCLIP</td><td>0.23</td><td>-0.14</td><td>0.26</td><td>-0.13</td><td>0.29</td><td>-0.13</td></tr><tr><td>RANKCLIPc</td><td>0.23</td><td>-0.13</td><td>0.24</td><td>-0.12</td><td>0.29</td><td>-0.14</td></tr><tr><td>RANKCLIPI</td><td>0.25</td><td>-0.15</td><td>0.28</td><td>-0.14</td><td>0.32</td><td>-0.17</td></tr></table>
+
+Table 5. Alignment and uniformity scores of CLIP, RANKCLIP, RANKCLIP $_C$  and RANKCLIP $_I$  indicate the solely cross-modal and in-modal rank loss.
+
+# 6.3. Qualitative Examples
+
+Class activation maps. To further examine the effects of ranking consistency, we visualize class activation maps
+
+![](images/002172d1d24a3021c222dd4ae1c1ce63531e03ec7a87d832e312021962627e99.jpg)  
+Figure 7. Class activation maps for RANKCLIP and CLIP on different objects in the caption from MSCOCO. RANKCLIP has more precise responses to some nouns compared to CLIP and can accurately locate the region related to the noun.
+
+(CAMs) [47] for RANKCLIP and CLIP in Fig. 7. The results show that RANKCLIP consistently attends to more semantically relevant regions in the images. For example, when given the caption 'An airport filled with planes sitting on tarmac', CLIP mistakenly highlights surrounding areas, whereas RANKCLIP focuses precisely on the planes. Similar improvements are observed across other examples, demonstrating that RANKCLIP better aligns textual descriptions with visual concepts. This suggests that ranking consistency enhances fine-grained feature learning, leading to more localized and accurate visual grounding.
+
+Text-to-image retrieval. Fig. 5 compares text-to-image retrieval results from RANKCLIP and CLIP. Given a query, we display the top-ranked images retrieved by each model. RANKCLIP consistently retrieves more semantically aligned images, even beyond the correct reference image. Regarding the qualitative example in Fig. 5, CLIP retrieves a table with fruit but overlooks the intended painting of fruits. Moreover, RANKCLIP consistently retrieves more relevant results: in the top 10 results, CLIP includes clear mismatches such as a cat sitting on a table or a motorcycle instead of a sink. This demonstrates RANKCLIP's
+
+ability to capture fine-grained semantic distinctions, thereby reinforcing its distinct advantage in retrieval tasks that demand a precise and nuanced understanding of the queries.
+
+# 7. Conclusion
+
+In this paper, we introduce RANKCLIP, a novel language-image pretraining method that integrates ranking consistency into the contrastive learning paradigm. RANKCLIP aims to better understand the complex many-to-many relationships in diverse text-image pairs by optimizing a self-supervised, list-wise rank loss. Through extensive experiments, including zero-shot classification, robustness to distribution shifts, linear probing, and zero-shot image-text retrieval, RANKCLIP not only enhances performance but also improves model robustness and semantic comprehension, outperforming the baseline CLIP and another state-of-the-art model ALIP. Our ablation studies and analyses further demonstrate and interpret the significance of each component of RANKCLIP in boosting performance and understanding across modalities. We believe that the methodologies and principles of RANKCLIP will inspire further research and lead to the development of models with a deeper understanding of the intricate interactions between visual and textual data.
+
+# Acknowledgements
+
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