Qwen3-Embedding-8B

Action tokenizers play a central role in autoregressive vision-language-action (VLA) models, determining both the targets for policy training and the executable commands recovered from predicted tokens. Their fidelity is commonly evaluated using pointwise reconstruction metrics such as mean squared error (MSE), yet small individual errors do not fully characterize how faithfully action adjustments across demonstrations are preserved. After compression, similar actions may still cluster around a representative motion, while the adjustments needed for different contexts are diminished, distorted, or even reversed. We introduce physical rank consistency (PRC) to measure how well tokenization preserves local physical distance rankings after reconstruction. Evaluating decoded actions provides a common reference across token vocabularies and decoder architectures, complementing pointwise accuracy with a measure of relational fidelity. We further present ActionPiece, which preserves physical action relationships through joint supervision of representation learning and quantization. Physical rank preservation supervises near-far ordering in encoder and quantized feature distances, while quantization regularization applies the same ordering to codeword assignment distributions. Both objectives augment reconstruction, producing discrete action tokens for standard autoregressive policy learning and execution through a frozen decoder. Under the same Qwen3-VL-4B policy training setup, ActionPiece achieves 94.8% on LIBERO and 68.8% on unseen LIBERO-Plus, with additional evaluations reaching 71.9% on SimplerEnv and 51.5% across VLA-Arena L0-L2. Component ablations show that the two objectives jointly improve PRC and policy success, demonstrating the value of physical relationship supervision for action tokenization.

The separation of cardiovascular sounds is a critical task in biomedical signal processing. In this paper, we introduce XVAE-WMT1, an unsupervised explainable generative AI algorithm combining a variational autoencoder (VAE) with explainable AI (XAI), wavelet-based inputs, a post-hoc output mask, and temporal consistency (TC) loss. Unlike existing supervised and VAE-based methods that rely on Short-Time Fourier Transform (STFT) and ignore latent interpretability, XVAE-WMT requires no paired clean recordings and integrates a Continuous Wavelet Transform (CWT) front-end for superior time-frequency localization. We assessed the latent space interpretability via different metrics, with SHAP (SHapley Additive exPlanations) enabling dimensionality reduction to the top 75% of latent features while preserving separation quality. Evaluated across two datasets using Signal-to-Distortion Ratio (SDR), Signal-to-Interference Ratio (SIR), and Signal-to-Artifacts Ratio (SAR), XVAE-WMT attains 26.8 dB SDR, 32.8 dB SIR, and 28.6 dB SAR.

Vision-language models (VLMs) are increasingly deployed on consumer hardware where input images are degraded by compression, camera shake, and poor lighting. In such settings, a reliable uncertainty signal matters more than raw accuracy, because it determines when a system should defer rather than answer. We evaluate two small open-weight VLMs -- Qwen2-VL-2B-Instruct and SmolVLM-Instruct -- across six realistic photographic degradations at three severity levels, comparing two confidence signals: the confidence the model states in natural language, and the model's own mean token probability over its generated answer. Across 3,800 predictions, we find a large and consistent gap. Verbalized confidence in Qwen2-VL is almost constant (mean 0.87-0.90 across all conditions) and detects its own errors at chance level (AUROC 0.39-0.75, typically ~0.50), while internal token probability from the same model separates correct from incorrect answers with AUROC 0.92-0.99. In SmolVLM, verbalized confidence proved largely unobtainable: across three prompt templates, only one of five pilot attempts produced a parseable confidence value, while internal probability again yielded above-chance error detection (AUROC 0.54-0.92). Both models fail in the same place: under severe underexposure, accuracy collapses (0.99->0.22 for Qwen2-VL, 0.97->0.42 for SmolVLM) while both confidence signals barely move, and internal error-detection falls to chance. We conclude that small VLMs encode usable self-knowledge that their verbalized output does not express, that internal probability is therefore the better deferral signal in constrained deployment, and that neither signal should be trusted under severe low-light conditions.

Mirror Theory proposes that an intelligent system should be studied not only by what it represents, but by what coherent continuations it can sustain under repeated reflection. We make this claim operational through \emph{viable path entropy} (VPE), a finite-budget measure of verified continuation capacity. Given a mirror state, a rollout protocol, a verifier, and a mode map, VPE decomposes bounded capability into two parts: the probability of reaching a viable continuation and the diversity of verified continuation modes reached among successful rollouts. This paper restores the full theoretical scaffold behind the measure: intuition as local underdetermining constraint, taste as invariant-selecting pressure, reflection as taste-guided resolution of underdetermination, and geometry as the learned structure that makes future reflection stable. We then instantiate the theory in language-model reasoning experiments on GSM8K. Across Qwen2.5-Instruct models, 32 sampled rollouts per problem, and two reflection horizons, increasing the token budget from 96 to 160 substantially expands verified reachability, reduces zero-reachability, increases verified-mode entropy, and improves smoothed VPE. At 160 tokens, Qwen2.5-1.5B realizes the strongest mirror horizon among the tested models, even though Qwen2.5-3B has more parameters. This shows that mirror horizon is not parameter count, but accessible verified continuation capacity under a bounded reflection protocol. The result supports Mirror Theory as a measure-level account: capability is the structure of viable continuations made reachable, not merely one-shot accuracy or pass@k.

Uncertainty quantification for visual language models (VLMs) conventionally targets the answer token distribution. We provide the first three-family empirical characterisation of answer entropy behaviour in thinking-mode VLMs. Running four models on identical POPE adversarial samples, we find three qualitatively distinct patterns: Qwen3-VL-8B-Thinking shows complete collapse (ans H AUROC = 0.492); GLM-4.1V-9B-Thinking shows no collapse (0.716); and InternVL3-8B shows selective thinking (chains on only 50% of samples, ans H = 0.675 full / 0.602 thinking-only). Across all three thinking-mode models, thinking chain entropy outperforms answer entropy on the subset where chains are generated (0.647, 0.759, 0.608 vs. 0.492, 0.716, 0.602 respectively), suggesting chain signals are the more reliable predictor whenever chains are present. This holds strongly for Qwen and GLM, but with only marginal and statistically unreliable advantage for InternVL3 (n_FP = 17). A 300-sample VQAv2 pilot confirms chain entropy (0.680) outperforms answer entropy (0.595) on VQAv2 questions, with the gap largest for free-form answers (0.733 vs. 0.467). On harder reasoning tasks (HallusionBench) both Qwen models show moderate signal (approx. 0.64), consistent with incomplete pre-commitment on difficult questions. We additionally document structured abstention affecting 12-22% of queries with asymmetry toward absent-object queries, and a practical abstention gate raising accuracy from 71.0% to 93.8% at 62.7% coverage with no additional inference cost.

We present SimpleSearch-VL, an efficient, reliable, and practical framework for multimodal agentic search. Its core idea is to improve the agent's own search-and-verification process rather than scaling data, tools, or auxiliary model components. For efficiency, Factorized Adaptive Rollout (FAR) improves sampling efficiency by forming more informative training groups while using redundant samples to mitigate long-tail latency and expose hard samples. For reliability, SimpleSearch-VL performs evidence-verified reasoning, explicitly using chain-of-thought verification to assess the relevance of retrieved visual and textual cues to the original context. For practicality, SimpleSearch-VL keeps a lightweight tool interface and performs webpage self-summary within the agent, requiring no additional external dependencies. With only 5K supervised tool-interleaved trajectories and 2K RL data, SimpleSearch-VL improves Qwen3-VL agentic baselines by 15.8 and 16.0 average points for the 8B and 30B-A3B variants, respectively. The SimpleSearch-VL-30B-A3B model further achieves performance competitive with agentic Gemini-3-Pro.

Existing embedding models are inherently static: they encode text segments in isolation, ignoring their surrounding context and temporal order. This paper introduces EvoEmbedding, a novel embedding model that generates evolvable representations for retrieval. It is tailored for long-context scenarios, where information is dynamic, sequential, and requires continuous state tracking. Our design is simple: EvoEmbedding maintains a continuously updated latent memory as it sequentially processes inputs, and uses it alongside the raw content to jointly generate evolvable embeddings. Consequently, for the same query, our model adapts its representation to retrieve distinct targets based on the evolving context, going beyond static semantic search. To equip the model with this capability, we construct EvoTrain-180K, a diverse dataset for the joint optimization of latent memory and retrieval. Furthermore, we introduce a memory queue to prevent representation collapse during recurrent encoding, alongside segment-batching techniques that tackle significant length variance and accelerate training by 3.8$\times$. Extensive experiments show that our model not only outperforms larger-scale specialists (e.g., Qwen3-Embedding-8B and KaLM-Embedding-Gemma3-12B) across a range of long-context retrieval benchmarks, but also generalizes well to downstream tasks (e.g., personalization) with contexts 10$\times$ longer than its training window. Notably, EvoEmbedding seamlessly integrates into agentic workflows to boost performance. For instance, a naive RAG pipeline equipped with our model surpasses dedicated agentic memory systems. Project Page: https://clare-nie.github.io/EvoEmbedding/.

Spatial reasoning remains a persistent challenge for multimodal large language models (MLLMs). Existing approaches largely rely on large-scale, statically curated datasets, where all training samples are treated uniformly regardless of the model's evolving capabilities. This static paradigm is inherently data-inefficient: training capacity is often spent on samples that are either trivial or overly difficult for the model at its current stage. To address this limitation, we propose Ouroboros-Spatial, a self-evolving training framework in which the model plays dual roles as a proposer and a solver. In each iteration, a frozen proposer generates spatial question-answer (QA) pairs from 3D scene metadata and raw video frames, together with executable code for deriving reliable ground truth. A learnable solver is then fine-tuned on the accepted samples, and its per-sample prediction confidence is used as a difficulty signal. This signal is fed back to the proposer in the next iteration, guiding it to generate questions better matched to the solver's current capabilities. Through this closed-loop design, the training distribution co-evolves with model ability, reducing redundant trivial examples while filtering out ambiguous or uninformative samples with limited learning value. Across six spatial reasoning benchmarks, Ouroboros-Spatial substantially improves Qwen3-VL-4B and Qwen3-VL-8B while using an order of magnitude fewer training examples than recent large-scale curated datasets. On VSI-Bench, it yields absolute gains of 9.9 and 6.8 points for the 4B and 8B models, respectively, enabling both to outperform a wide range of strong open-source and proprietary baselines.

Semiconductor lithography inspection requires reliable detection of small pattern defects such as bridge, burr, pinch, and contamination. In this study, we propose a two-stage vision-language framework that combines initial defect detection with prediction refinement. In the first stage, Qwen3-VL is fine-tuned with LoRA as a vision-language adapter to predict defect counts, defect categories, and normalized bounding boxes from lithography images. However, direct fine-tuning may still produce common test-time errors, including false positives, missed defects, and incorrect defect types. To address this limitation, the second stage trains a refinement module using first-stage prediction failures and their corrected labels, allowing the model to review and revise initial outputs. By learning from cases where the initial adapter fails, the refinement process improves defect inference beyond single-stage fine-tuning.

General-purpose VLMs remain unreliable for biomedical research because valid answers in scientific papers depend on evidence split across figures, tables, charts, captions, and referring text. Existing post-training pipelines are bottlenecked by costly expert annotation and by synthetic data that drops this evidence structure. We present Ryze, a fully automated system that converts raw biomedical papers into an evidence-enriched training set and a domain-specialized VLM. Ryze synthesizes QA pairs with complete supporting evidence (visual element, caption, extracted structure, and referring paragraphs), reduces layout and OCR errors via chart/table-aware extraction and LLM-based cleansing, and applies a progress-gated post-training strategy combining supervised fine-tuning with reinforcement learning. Starting from Qwen3-VL-8B, Ryze produces BioVLM-8B at under USD 200, achieving 48.0% weighted accuracy on LAB-Bench, outperforming the base model by +12.6 percentage points (pp) and surpassing GPT-5.2 by +3.8 pp. We release Ryze as open source together with the trained BioVLM-8B model.

EgoCross evaluates multimodal large language models on egocentric video question answering under substantial domain shift, where test videos come from surgery, industrial assembly, extreme sports, and animal-mounted cameras rather than ordinary daily-life scenes. In the source-limited track, the base model is fixed to Qwen3-VL-4B, while the official task-specific support set contains only 20 training samples. This setting makes the challenge less about model scaling and more about exposing the right visual, temporal, and answer-selection cues to a constrained model. Our key observation is that the frozen baseline model is not simply incapable of these rare scenarios; rather, it often fails to transfer its existing visual-language knowledge to the new task format without an appropriate interface. We therefore use a domain-wise inference strategy that treats the four target domains separately and designs different input, prompting, and answer-mapping procedures according to each domain's task characteristics. These strategies make the rare egocentric scenes more interpretable to the VLM by emphasizing the cues that matter for each domain. The resulting system is nearly training-free: surgery, and animal questions are answered with the base Qwen3-VL-4B model, while XSports and industry use only the official SFT checkpoint trained for two epochs on the provided 20 training samples. On the final evaluation, this simple strategy reaches 66.98% overall accuracy, suggesting that careful domain-aware inference can compensate for limited base-model strength and recover much of the ability already present in the baseline model.

Embodied intelligence is often studied through specialized models for individual tasks such as manipulation or navigation, resulting in fragmented capabilities and limited generalization across tasks, environments, and robot embodiments. In this work, we study whether heterogeneous embodied decision-making problems can be unified within a single vision-language-action model. We present Qwen-VLA, a unified embodied foundation model that extends Qwen's vision-language modeling stack from perception, understanding, and reasoning to continuous action and trajectory generation through a DiT-based action decoder. Qwen-VLA is trained with a large-scale joint pretraining recipe over diverse data sources, including robotics manipulation trajectories, human egocentric demonstrations, synthetic simulation data, vision-and-language navigation data, trajectory-centric supervision, and auxiliary vision-language data. To support multiple robot platforms, we introduce embodiment-aware prompt conditioning, where robot-specific textual descriptions specify the current embodiment and control convention. We further cast manipulation, navigation, and trajectory prediction into a unified action-and-trajectory prediction framework, enabling transferable visual grounding, spatial reasoning, and continuous action generation across robot morphologies, task families, and environments. Experiments on manipulation, navigation, and trajectory-centric benchmarks show consistent multi-task performance and out-of-distribution generalization under variations in scene layout, background, lighting, object configuration, and robot embodiment. Qwen-VLA-Instruct achieves 97.9% on LIBERO, 73.7% on Simpler-WidowX, 86.1%/87.2% on RoboTwin-Easy/Hard, 69.0% OSR on R2R, 59.6% SR on RxR, 76.9% average OOD success in real-world ALOHA experiments, and 26.6% zero-shot success on DOMINO dynamic manipulation.

Vision-language models with extended reasoning succeed on complex problems, but many real-world problems require external tools that internal reasoning alone often cannot resolve. Agentic reasoning therefore interleaves two behaviors with a structural asymmetry: thinking (the self-contained default) and tool use (a high-variance auxiliary acting). We refer to this asymmetry as the Thinking-Acting Gap. Under standard RL recipes like GRPO, the gap manifests as two diagnostic symptoms during training: tool use is attempted on only ~30% of rollouts, and when attempted, the tool-using rollouts within a group are all-wrong on ~40% of questions, suppressing the learning signal at the tool calls that needed it. We propose AXPO (Agent eXplorative Policy Optimization): for each all-wrong tool-using subgroup, AXPO fixes the thinking prefix and resamples the tool call and its continuation, paired with uncertainty-based prefix selection. Across nine multimodal benchmarks and three scales of Qwen3-VL-Thinking, SFT+AXPO outperforms SFT+GRPO at average (+1.8pp Pass@1 and +1.8pp Pass@4 at 8B on average) and 8B with SFT+AXPO surpasses the 32B Base on Pass@4 with 4 times fewer parameters.

Visual impairment affects hundreds of millions of people worldwide, severely limiting their ability to navigate urban environments safely and independently. While wearable assistive devices offer a promising platform for real-time hazard detection, existing approaches rely on task-specific vision pipelines that lack flexibility and generalizability. In this work, we propose an event map framework based on visual question answering that leverages Vision-Language Models (VLMs) for pedestrian scene description and hazard identification across diverse real-world environments, using a three-level hierarchical query structure to enable fine-grained scene understanding without task-specific retraining. Model responses are aggregated into a weighted risk scoring system that maps street segments into four discrete safety categories, producing navigable risk-aware event maps for route planning. To support evaluation and future research, we introduce a geographically diverse dataset spanning 20 cities across six continents, comprising over 800 annotated images and 18,000 answered questions. We benchmark four VQA architectures -ViLT, LLaVA, InstructBLIP, and Qwen-VL- and find that generative Multimodal Large Language Models (MLLMs) substantially outperform classification-based approaches, with Qwen-VL achieving the best overall balance of precision and recall. These results demonstrate the viability of MLLMs as a flexible and generalizable foundation for assistive navigation systems for visually impaired people.

Vision-language models typically reason over post-ISP RGB images, although RGB rendering can clip, suppress, or quantize sensor evidence before inference. We study whether grounding improves when the visual interface is moved closer to the underlying camera measurement. We formulate measurement-grounded vision-language learning and instantiate it as PRISM-VL, which combines RAW-derived Meas.-XYZ inputs, camera-conditioned grounding, and Exposure-Bracketed Supervision Aggregation for transferring supervision from RGB proxies to measurement-domain observations. Using a quality-controlled 150K instruction-tuning set and a held-out benchmark targeting low-light, HDR, visibility-sensitive, and hallucination-sensitive cases, PRISM-VL-8B reaches 0.6120 BLEU, 0.4571 ROUGE-L, and 82.66% LLM-Judge accuracy, improving over the RGB Qwen3-VL-8B baseline by +0.1074 BLEU, +0.1071 ROUGE-L, and +4.46 percentage points. These results suggest that part of VLM grounding error arises from information lost during RGB rendering, and that preserving measurement-domain evidence can improve multimodal reasoning.

Video-language models (VLMs) face rapid inference costs as visual token counts scale with video length. For example, 32 frames at $448{\times}448$ resolution already yield >8,000 visual tokens in Qwen3-VL, making LLM prefill the dominant throughput bottleneck. Existing methods often rely on global similarity or attention-guided compression, incurring offsets to their gains. We propose \textbf{Temporal Token Fusion (TTF)}, a training-free, plug-and-play pre-LLM token compression framework that exploits structured temporal redundancy in video. TTF automatically selects an anchor frame, then for each subsequent frame, performs a local window similarity search (e.g.,$3\times 3$), fusing tokens that exceed a threshold. The compressed sequence maintains positional consistency across both prefill and decoding through coordinate realignment, enabling seamless integration with existing VLM pipelines. On Qwen3-VL-8B with threshold t=0.70, TTF removes about 67% of visual tokens while retaining 99.5% of the baseline accuracy and introducing only ${\approx}0.16$,GFLOPs of matching overhead. Overall, TTF offers a practical, efficient solution for video understanding. The code is available at \href{https://github.com/Cominder/ttf}{https://github.com/Cominder/ttf}

Open-world referring segmentation requires grounding unconstrained language expressions to precise pixel-level regions. Existing multimodal large language models (MLLMs) exhibit strong open-world visual grounding, but their outputs remain limited to sparse bounding-box coordinates and are insufficient for dense visual prediction. Recent MLLM-based segmentation methods either directly predict sparse contour coordinates, struggling to reconstruct continuous object boundaries, or rely on external segmentation foundation models such as the Segment Anything Model (SAM), introducing substantial architectural and deployment overhead. We present Qwen3-VL-Seg, a parameter-efficient framework that treats the MLLM-predicted box as a semantically grounded structural prior and decodes it into pixel-level referring segmentation. At its core, a lightweight box-guided mask decoder combines multi-scale spatial feature injection, spatial-semantic query construction, box-guided high-resolution pixel fusion, and iterative mask-aware query refinement, introducing only 17M parameters (about 0.4% of the base model). For scalable open-world training, we construct SA1B-ORS, an SA-1B-derived dataset with two subsets: SA1B-CoRS (category-oriented samples) and SA1B-DeRS (descriptive, instance-specific samples). For evaluation, we curate ORS-Bench, a manually screened benchmark with in-distribution and out-of-distribution subsets covering diverse referring expression types. Extensive experiments on referring expression segmentation, visual grounding, and ORS-Bench show that Qwen3-VL-Seg performs strongly across closed-set and open-world settings, with clear advantages on language-intensive instructions and strong out-of-distribution generalization. Evaluations on general multimodal benchmarks further show that the model broadly preserves general-purpose multimodal competence after segmentation-oriented adaptation.

Function association is a useful process for binary reverse engineers. Search tools exist to perform association at scale, but they do not utilize the full range of capabilities that AI-enabled search provides. Prior work has explored the development of embedding models for association between certain reverse engineering code representations, but that work does not cover bidirectional association between source code and decompiled, stripped code with standard preprocessing requirements. To bridge this gap, we formalize this function association problem and evaluate the extent to which embedding models can bidirectionally associate between these two representations. To improve model performance at this task, we fine-tune a Qwen3-Embedding model with contrastive learning. We find that our new model outperforms other models on all function association baselines by a substantial margin and generalizes to a constant-algorithm association task it is not explicitly trained on.

Transformer inference often requires a large KV cache, especially for long-context language modeling and multimodal generation. Existing compression methods usually reduce cache cost by selecting, evicting, quantizing, or compressing cached tokens, or by reducing the visual-token sequence before language-model inference. We introduce sub-token routing, a KV-compression method that adds a finer control axis inside retained tokens. It splits each retained value vector into groups and keeps only selected groups, while leaving query and key states unchanged. The method is designed to work after token-level reduction. First, a token-reduction method determines which tokens are retained. Then, sub-token routing compresses the value states inside those retained tokens. Experiments under matched KV budgets show that adding sub-token routing improves token-level reduction performance in both LLM and VLM settings, including Quest on LLaMA-2-7B and Qwen2.5-7B, and FastV/VisionZip across LLaVA and Qwen-VL models. The gains are larger at smaller KV budgets, suggesting that value-group routing is especially useful when further token removal becomes costly. Overall, token-level reduction and sub-token routing provide complementary ways to reduce KV cost.

Multimodal instruction tuning is often compute-inefficient because training budgets are spread across large mixed image-video pools whose utility is highly uneven. We present Goal-Driven Data Optimization (GDO), a framework that computes six sample descriptors for each candidate and constructs optimized 1$\times$ training subsets for different goals. Under a fixed one-epoch Qwen3-VL-8B-Instruct training and evaluation recipe on 8 H20 GPUs, GDO uses far fewer training samples than the Uni-10x baseline while converging faster and achieving higher accuracy. Relative to the fixed 512k-sample Uni-10x baseline, GDO reaches the Uni-10x reference after 35.4k samples on MVBench, 26.6k on VideoMME, 27.3k on MLVU, and 34.7k on LVBench, while improving Accuracy by +1.38, +1.67, +3.08, and +0.84 percentage points, respectively. The gains are largest on MVBench and MLVU, while LVBench improves more modestly, consistent with its ultra-long-video setting and the mismatch between that benchmark and the short-video/image-dominant training pool. Across MinLoss, Diverse, Temp, and Temp+, stronger temporal emphasis yields steadily better long-video understanding behavior. Overall, GDO provides a goal-driven data optimization framework that enables faster convergence with fewer training samples under a fixed training protocol. Code is available at https://github.com/rujiewu/GDO.

Focusing on low-resource languages is an essential step toward democratizing generative AI. In this work, we contribute to reducing the multimodal NLP resource gap for Romanian. We translate the widely known Flickr30K dataset into Romanian and further extend it for visual question answering by leveraging open-source LLMs. We demonstrate the usefulness of our datasets by fine-tuning open-source VLMs on Romanian visual question answering. We select VLMs from three widely used model families: LLaMA 3.2, LLaVA 1.6, and Qwen2. For fine-tuning, we employ the parameter-efficient LoRA method. Our models show improved Romanian capabilities in visual QA, as well as on tasks they were not trained on, such as Romanian image description generation. The seven-billion-parameter Qwen2-VL-RoVQA obtains top scores on both tasks, with improvements of +2.29% and +4.45% in BERTScore F1 on VQA and captioning, respectively, over its original version. Finally, the models show substantial reductions in grammatical errors compared to their original forms, indicating improvements not only in language understanding but also in Romanian fluency.

We propose RT (Refine Thought), a method that can enhance the semantic reasoning ability of text embedding models. The method obtains the final semantic representation by running multiple forward passes of the text embedding model. Experiments show that RT achieves significant improvements on semantic reasoning tasks in BRIGHT and the person-job matching benchmark PJBenchmark, while maintaining consistent performance on general-purpose semantic understanding tasks such as C-MTEB. Our results indicate that RT is effective because it further activates the semantic reasoning ability learned during pretraining by decoder-only text embedding models (e.g., Qwen3-Embedding-8B). RT can be seen as a test-time inference method.

Recent progress in large-scale reinforcement learning (RL) has notably enhanced the reasoning capabilities of large language models (LLMs), especially in mathematical domains. However, current multimodal LLMs (MLLMs) for mathematical reasoning often rely on one-to-one image-text pairs and single-solution supervision, overlooking the diversity of valid reasoning perspectives and internal reflections. In this work, we introduce MathV-DP, a novel dataset that captures multiple diverse solution trajectories for each image-question pair, fostering richer reasoning supervision. We further propose Qwen-VL-DP, a model built upon Qwen-VL, fine-tuned with supervised learning and enhanced via group relative policy optimization (GRPO), a rule-based RL approach that integrates correctness discrimination and diversity-aware reward functions. Our method emphasizes learning from varied reasoning perspectives and distinguishing between correct yet distinct solutions. Extensive experiments on the MathVista's minitest and Math-V benchmarks demonstrate that Qwen-VL-DP significantly outperforms prior base MLLMs in both accuracy and generative diversity, highlighting the importance of incorporating diverse perspectives and reflective reasoning in multimodal mathematical reasoning.