RecDreamer: Consistent Text-to-3D Generation via Uniform Score Distillation

We thank Reviewer X3Gz for their valuable comments. To provide comprehensive details and visual evidence of the improvements, we have included the updated manuscript in the supplementary materials. We kindly invite you to review this version, where all new comparisons and analyses are thoroughly documented.

Q1: "How does RecDreamer handle variations in complex textures or intricate details that might not be directly related to pose?"

Response: We appreciate the reviewer’s thoughtful question about handling variations in complex textures or intricate details. RecDreamer addresses this challenge through its architecture, designed to ensure pose estimation is invariant to surface textures and fine details unrelated to pose.

To achieve this invariance, we utilize a pre-trained DINOv2 [1] feature extractor, which is highly effective at separating high-level semantic content from low-level visual attributes like texture and color. In our framework, orientation score computation is performed in DINOv2’s feature space rather than the raw pixel space. This semantic-level processing inherently filters out irrelevant texture variations and intricate details, enabling the model to focus exclusively on pose-relevant structural information.

Empirical results presented in Appendix D validate this texture invariance, demonstrating that RecDreamer consistently achieves robust pose estimation across objects with diverse surface complexities and levels of detail.

• [1] Oquab et al., Dinov2: Learning robust visual features without supervision

Q2(W2): "Can the proposed method be extended or adapted to address other biases in text-to-3D generation beyond pose inconsistency?"

<em>[Note: Our response refers to new content in the revised manuscript:

• Discussions: Appendix F (Page 28, Line 1560)
  • Evidence: Figure 15 (Page 30, Line 1604)]</em>

Response: Thank you for raising this insightful question about the broader applicability of our method. Our framework is indeed generalizable and can address various biases, provided a differentiable classifier is available to identify the bias in question.

We illustrate this extensibility with an example in Appendix F, where we address gender bias in facial generation. Specifically, we observed that the prompt "A person's face" tends to produce outputs skewed towards feminine and youthful features, as shown in Fig. 15(a). To mitigate this, we applied a 2D uniform score distillation algorithm using a CLIP classifier [1] with the text labels "man" and "woman" to represent the categories. The results (Fig. 15(b)) demonstrate that this intervention successfully diversifies the output distribution, generating faces with a broader range of gender presentations, including distinct masculine features.

This experiment validates the extensibility of our method and highlights its potential for addressing other forms of bias. The key requirement is the availability of a suitable differentiable classifier for the specific bias dimension. This framework could be adapted to mitigate biases related to age, ethnicity, or stylistic preferences, offering a promising direction for future research.

• [1] Radford et al., Learning transferable visual models from natural language supervision

W3: " ... a more detailed presentation of quantitative metrics."

<em>[Note: Our response refers to new content in the revised manuscript:

• Detailed Metrics: Appendix C.1 (Page 22, Line 1142)]</em>

Response: We have restructured our discussion of evaluation metrics to improve clarity while maintaining comprehensive technical detail. The metrics are now organized into two sections: a concise overview in the main text focusing on the key roles of different losses, with detailed implementations provided in Appendix C.1. This revised presentation addresses several key aspects:

1. Generation Quality (FID and uFID):
   We measure generation quality using two variants of the Fréchet Inception Distance (FID). The standard FID quantifies the distribution gap between rendered images and outputs from the diffusion model, indicating how closely our learned model aligns with the prior distribution's quality. However, since diffusion-generated images can exhibit inherent bias, we introduce an unbiased FID (uFID) for further evaluation. Specifically, we manually label the poses of generated images and resample them according to these pose labels, removing pose bias from the evaluation. The uFID is then calculated between the rendered images and this unbiased set.

2. Geometric Consistency (Entropy-Based Metrics):
   To address geometric consistency issues, such as the Multi-Face Janus problem, we employ entropy-based metrics. These metrics operate on the principle that geometrically inconsistent models, which exhibit similar classifications across different viewpoints, will have low entropy in their averaged classification results. A lower entropy value thus indicates poorer geometric consistency, providing a targeted measure for such inconsistencies.

3. Text-Scene Alignment (CLIP Score):
   Following Reviewer wW4M's suggestion, we incorporated the CLIP score [1] as an additional metric to evaluate the alignment between text prompts and the generated scene.

This revised structure balances technical rigor with improved accessibility, offering a clear motivation and detailed implementation for each metric used in our evaluation.

• [1] Radford et al., Learning transferable visual models from natural language supervision

W4: " ... Background section is too long."

Response: Thank you for the constructive feedback. We will streamline the Background section by concentrating on essential concepts directly relevant to our technical contributions, such as the foundations of score distillation and pose-aware generation. To improve the paper’s focus and readability, we will remove peripheral background material in the next revision.

Q3(W1): "What are the computational requirements for implementing RecDreamer, and how does it perform in terms of efficiency compared to baseline methods?"

<em>[Note: Our response refers to new content in the revised manuscript:

• Runtime Performance: Appendix C.6 (Page 28, Line 1486)
  • Evidence: Table 3 (Page 28, Line 1458)
• Discussions: Appendix F (Page 28, Line 1560)]</em>

Response: Our method currently runs on a single NVIDIA RTX 4090 GPU at a resolution of $256 \times 256$. As detailed in Appendix C.6, RecDreamer requires more training time compared to baselines, primarily due to the gradient back-propagation through the UNet introduced by the rectifier function.

While RecDreamer has increased computational demands, it achieves significantly better geometric consistency than prior methods—a critical advancement in addressing persistent challenges in 3D generation. This quality-runtime trade-off is particularly valuable for applications where geometric accuracy is paramount.

Our current implementation prioritizes theoretical validation over speed optimization, but we see clear opportunities for improvement. One promising direction is a hybrid training strategy: applying USD optimization during early epochs to establish geometry, followed by lighter computation for detail refinement. Additionally, as outlined in Appendix F, we analyze the computational intensity of our method and propose solutions, such as reducing redundant gradient computations through the UNet, to streamline the distillation process.

In summary, we view the current computational overhead as an engineering challenge rather than a fundamental limitation. Ongoing work is focused on developing faster implementations while preserving the high quality that distinguishes RecDreamer.

Table 3: Runtime comparison. All measurements are reported in minutes.

• [1] https://github.com/threestudio-project/threestudio
• [2] McAllister et al., Rethinking Score Distillation as a Bridge Between Image Distributions
• [3] Wang et al., Taming Mode Collapse in Score Distillation for Text-to-3D Generation

We have carefully addressed the main concerns raised in the review.

First, we conducted a thorough evaluation of runtime performance. While our method incurs an increase in runtime, it effectively mitigates the Multi-Face Janus problem, representing a valuable trade-off in applications where geometric consistency is critical. Additionally, we have proposed potential solutions to reduce runtime in future iterations.

Second, we have expanded our comparisons to include the suggested SDS-Bridge method, incorporating relevant discussions into sections such as related work.

Given these efforts, we respectfully hope the reviewer might reconsider their assessment of our paper’s contributions. We believe these improvements have significantly strengthened our work and addressed the key concerns outlined in the initial review.

W1: "More comparison with baselines is needed."

<em>[Note: Our response refers to new content in the revised manuscript:

• Main experiment: Table 1 (Page 8, Line 378)
• User study: Table 4 (Page 28, Line 1463)
• Results: Figure 17 (Page 32, Line 1727)]</em>

Response: We sincerely thank the reviewer for this constructive suggestion, which has significantly improved our evaluation framework. In response, we have expanded our experimental comparisons to include additional state-of-the-art baselines, specifically SDS-Bridge [1] and ESD [2]. The comprehensive results of these comparisons are presented in Table 1 and Table 4, with visual examples provided in Fig. 17. These additions enhance the robustness of our evaluation and offer a more complete context for assessing our method's contributions relative to existing approaches.

Table 1: Quantitative comparison.

Table 4: User study on geometric consistency. Higher indicates better.

• [1] McAllister et al., Rethinking Score Distillation as a Bridge Between Image Distributions
• [2] Wang et al., Taming Mode Collapse in Score Distillation for Text-to-3D Generation

We thank Reviewer 1nXi for their valuable comments. To provide comprehensive details and visual evidence of the improvements, we have included the updated manuscript in the supplementary materials. We kindly invite you to review this version, where all new comparisons and analyses are thoroughly documented.

Q1(W2): "Can the authors report the runtime per sample of your method and other baselines to ensure the completeness of comparison?"

<em>[Note: Our response refers to new content in the revised manuscript:

• Runtime Performance: Appendix C.6 (Page 28, Line 1486)
  • Evidence: Table 3 (Page 28, Line 1458)
• Discussions: Appendix F (Page 28, Line 1560)]</em>

Response: Detailed runtime comparisons across different methods are provided in Appendix C.6. Our method currently requires longer computational time due to the additional gradient back-propagation through the UNet introduced by our rectifier function. We address this runtime consideration from three key perspectives:

1. Quality-Runtime Trade-off:
   While our method has a longer runtime, it achieves superior geometric consistency that is challenging to replicate with existing approaches. This trade-off is particularly valuable for applications where geometric accuracy is critical.

2. Focus on Theoretical Validation Over Optimization:
   Our current implementation prioritizes theoretical validation rather than computational efficiency. However, there are several promising directions for runtime improvement:

   • Implementing a hybrid optimization strategy: employing USD during the initial epochs to establish geometric consistency, followed by lightweight optimization for detail refinement.
   • Optimizing implementation: Our method currently lacks some of the optimization tricks used in other three-studio-based approaches [1], such as SDS-Bridge [2] and ESD [3], which employ techniques like low-resolution warmup. Incorporating these practices could significantly reduce runtime without sacrificing performance.

3. Future Algorithmic Improvements:
   As outlined in Appendix F, potential enhancements to our method include optimizing the conditional gradient back-propagation through the UNet to minimize computational overhead while maintaining high-quality outputs.

These considerations highlight both the strengths of our method and the clear pathways for reducing runtime in future work.

Table 3: Runtime comparison. All measurements are reported in minutes.

• [1] https://github.com/threestudio-project/threestudio
• [2] McAllister et al., Rethinking Score Distillation as a Bridge Between Image Distributions
• [3] Wang et al., Taming Mode Collapse in Score Distillation for Text-to-3D Generation

We sincerely thank Reviewer i678 for the constructive suggestions. We believe that the additional experiments, analysis, and explanations have significantly enhanced the quality of our submission. We hope these improvements provide sufficient justification for a higher score.

Q1(W3): " ... not feasible for users to provide consistent multi-view templates for any text prompts."

<em>[Note: Our response refers to new content in the revised manuscript:

• Template images: Appendix C.3 (Page 26, Line 1387)
  • Supporting evidence: Figure 10 (Page 25, Line 1333)
• Cross-modality: Appendix C.4 (Page 26, Line 1397)]</em>

Response: We appreciate the reviewer’s concerns and would like to emphasize that our method imposes minimal requirements on template images, both in terms of quantity and quality. Specifically:

1. Flexibility in Template Requirements:
   Our approach does not require the template images to be view-consistent or even from the same modality, making it highly practical for real-world applications. As shown in Appendix C.3 (Fig. 10(a)), we use Stable Diffusion [1] outputs as templates, without demanding high-quality or view-consistent images.

2. Support for Cross-Modality Inputs:
   We further demonstrate the flexibility of our method by supporting multiple input modalities. For instance, we achieve successful results using hand-drawn sketches for cross-modality generation, as detailed in Appendix C.4. Moreover, while not necessary, users may optionally employ multi-view image generation models [2] to generate additional viewpoints if desired, as illustrated in Fig. 10(b).

These features make our classifier-based approach lightweight and practical, requiring minimal effort from users while maintaining robust and versatile performance.

• [1] Rombach et al., High-resolution Image Synthesis with Latent Diffusion Models
• [2] Liu et al., Zero-1-to-3: Zero-shot One Image to 3D Object

W1-1: " ... prompt list is also not provided in the appendix ... "

<em>[Note: Our response refers to new content in the revised manuscript:

• Prompt list: Appendix G (Page 31, Line 1653)]</em>

Response: Thank you for the suggestion. We have provided in the Appendix G in the revised version.

W1-2: " ... recent open-sourced baseline methods ESD and JointDreamer."

<em>[Note: Our response refers to new content in the revised manuscript:

• Related works: Appendix A (Page 15, Line 756)
• Main experiment: Table 1 (Page 8, Line 378)
• User study: Table 4 (Page 28, Line 1463)]</em>

Response: Thank you for your suggestion. We have expanded our evaluation by including additional baseline methods, specifically ESD [1] and Bridge-SDS [2], which rely solely on diffusion models without requiring 3D data for fine-tuning. The quantitative results and findings from the user study are presented in Table 1 and Table 4. Regarding JointDreamer [3], while it is an important contribution in this domain, we discuss it in our related work section (Appendix A) due to its fundamentally different approach, which relies on view-aware pre-trained models.

Table 1: Quantitative comparison.

Table 4: User study on geometric consistency. Higher indicates better.

• [1] Wang et al., Taming Mode Collapse in Score Distillation for Text-to-3D Generation
• [2] McAllister et al., Rethinking Score Distillation as a Bridge Between Image Distributions
• [3] Jiang et al., JointDreamer: Ensuring Geometry Consistency and Text Congruence in Text-to-3D Generation via Joint Score Distillation

We thank Reviewer i678 for their valuable comments. To provide comprehensive details and visual evidence of the improvements, we have included the updated manuscript in the supplementary materials. We kindly invite you to review this version, where all new comparisons and analyses are thoroughly documented.

Q1(W2)-1: " ... joint distribution expression of the data and camera pose, limited explanation of the practical meaning of such a distribution."

Response: We thank the reviewer for raising this important point about the interpretation of the joint distribution. We provide the following detailed explanation to clarify its practical meaning:

The joint distribution $p(x, c)$ represents the probability of observing both a specific data point $x$ and a camera pose $c$ simultaneously. This formulation serves as a crucial mathematical connection between the data distribution $p(x)$ and the pose distribution $p(c)$. Without this joint formulation, these two distributions would remain independent, making it challenging to analyze or model their interdependence. The joint distribution enables us to derive the marginal distributions by integration: $p(c)$ can be obtained by marginalizing over $x$ ($\int p(x, c) dx$), and $p(x)$ can be obtained by marginalizing over $c$ ($\int p(x, c) dc$). This approach is particularly valuable because it allows us to impose specific constraints on the marginal distributions, such as enforcing $p(c)$ to follow a uniform distribution, while preserving the mathematical relationship between data and pose.

Q1(W2)-2: "Also, the use of a rather discrete 4-views to represent the camera pose distribution does not appear to be meaningful."

Response: We thank the reviewer for their thoughtful observation regarding our representation of the camera pose distribution. The use of four discrete perspectives in our design effectively simulates the global pose distribution, and this choice is supported by two key considerations:

1. Robustness of Score Distillation to Coarse Pose Supervision:
   Score distillation with diffusion models is inherently robust to coarse pose supervision. Our four-view approach (front-back-left-right) provides sufficient semantic guidance for the task. Unlike geometric reconstruction methods [1,2], which require precise pose estimation, score distillation relies primarily on general semantic cues to transfer pre-trained knowledge into 3D models. This robustness is evidenced by prior works such as Vanilla SDS [3] and VSD [4], which achieve effective optimization using similarly broad pose categories (e.g., "front view," "back view," "side view").

2. Objective to Mitigate Pose Bias, Not Precise Pose Control:
   Our primary goal is to address pose bias by enabling the generation of diverse poses, rather than achieving precise pose control. The four-view discretization effectively captures sufficient pose variations guided by the templates during score distillation. This approach strikes a balance between simplicity of implementation and the robustness needed for our objectives.

These considerations demonstrate that the four-view discretization represents a practical and effective design choice, ensuring diversity in pose expression while maintaining robust performance.

• [1] Mildenhall et al., NeRF: Representing Scenes as Neural Radiance Fields for View Synthesis
• [2] Kerbl et al., 3D Gaussian Splatting for Real-Time Radiance Field Rendering
• [3] Poole et al., DreamFusion: Text-to-3D Using 2D Diffusion
• [4] Wang et al., ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillation

W4-1: " ... whether score distillation with the rectified distribution could largely match the performance of the distribution fine-tuned with extra data."

<em>[Note: Our response refers to new content in the revised manuscript:

• 3D Generation: Appendix F (Page 29, Line 1560)
  • Evidence: Figure 16 (Page 30, Line 1632)]</em>

Response: We thank the reviewer for raising this important question. Our comparative analysis highlights a trade-off between geometric consistency and stylistic flexibility in methods based on score distillation, including ours, compared to approaches trained on 3D data.

To illustrate this trade-off, we present an experiment in Appendix F using a challenging prompt: "A platypus, dressed in a video game pixelated costume, steps on a pixelated surfboard and holds a squid weapon that emits 8-bit light effects." As shown in Fig. 16(a), 3D-trained methods like Tripo AI [1] excel at producing precise geometry but struggle to capture stylistic elements, such as the "pixelated" and "8-bit" effects described in the prompt. In contrast, our approach (Fig. 16(b)) successfully captures these stylistic nuances, including the digital effects, but demonstrates lower geometric consistency.

This comparison underscores the complementary strengths of these methods. While 3D-trained approaches prioritize geometric precision, score distillation methods offer greater flexibility in generating stylized outputs. These findings suggest promising directions for future work that could integrate the advantages of both approaches to achieve robust geometric consistency and stylistic versatility.

• [1] https://lumalabs.ai/genie

W4-2: " ... whether the proposed USD can enhance training-based methods."

<em>[Note: Our response refers to new content in the revised manuscript:

• 3D Generation: Appendix F (Page 29, Line 1560)
  • Evidence: Figure 16 (Page 30, Line 1632)]</em>

Response: Thank you for this insightful comment on USD's potential to enhance training-based methods. Our experimental results in Appendix F demonstrate that USD can effectively leverage the 2D prior to improve visual quality. Specifically, as shown in Fig. 16, applying USD with templates generated by Tripo AI [1] leads to meaningful enhancements in the output's visual fidelity.

While training from scratch may introduce some limitations in geometric consistency, these challenges can be addressed in future work through direct fine-tuning on 3D models, providing a promising direction for further refinement.

• [1] https://lumalabs.ai/genie

W2: " ... potential solutions to abstract or imaginary prompts."

<em>[Note: Our response refers to new content in the revised manuscript:

• Template images: Appendix C.3 (Page 26, Line 1387)
  • Supporting evidence: Figure 10 (Page 25, Line 1333)
• Cross-modality: Appendix C.4 (Page 26, Line 1397)]</em>

Response: Thank you for raising this important question regarding the handling of abstract and imaginary prompts. Our research explores innovative strategies to address such prompts, with detailed findings provided in Appendix C.3. The key components of our approach are as follows:

1. Generating Abstract and Imaginative Templates:
   As demonstrated in Fig. 10, we generate reference template images using Stable Diffusion [1]. These generated images effectively serve as templates, allowing users to select representative examples for different poses. We have also implemented an automated pipeline where the diffusion model first generates concept images in a canonical pose, which are subsequently processed by our multi-view model [2] to synthesize coherent perspectives from diverse angles.

2. Adaptability of Template Requirements:
   As shown in Fig. 10, the template images used in our pipeline do not need to be multi-view consistent or high-quality. They only require basic orientation information, making the approach highly adaptable across various applications. This flexibility allows for practical deployment in handling abstract or low-quality inputs.

3. Cross-Modal and Cross-Category Capabilities:
   Our approach incorporates the powerful feature matching capabilities of DINOv2 [3], enabling robust cross-modal generation. This allows the system to work with diverse inputs, such as sketches and stylistically varied images, and even perform cross-category generation (e.g., using cat images to generate dogs). The generated outputs maintain semantic consistency while allowing for creative transformations. An application of sketch-based generation is detailed in Appendix C.4.

These features, combined with examples extensively documented in Appendix C.3, showcase the ability of our method to handle abstract and imaginative prompts while ensuring consistent multi-view generation.

• [1] Rombach et al., High-resolution image synthesis with latent diffusion models
• [2] Liu et al., Zero-1-to-3: Zero-shot one image to 3d object
• [3] Oquab et al., Dinov2: Learning robust visual features without supervision

W3: " ... a more comprehensive review."

<em>[Note: Our response refers to new content in the revised manuscript:

• Related works: Appendix A (Page 15, Line 756)]</em>

Response: We appreciate the reviewer's suggestion regarding the literature review. We have substantially expanded our discussion of related works in Appendix A, incorporating several recent and significant contributions to the field. The additions include pivotal works on score distillation techniques as follows:

• [1] Yu et al., Text-to-3D with Classifier Score Distillation
• [2] Katzir et al., Noise-free Score Distillation
• [3] Wang et al., SteinDreamer: Variance Reduction for Text-to-3D Score Distillation via Stein Identity
• [4] Shi et al., MVDream: Multi-view Diffusion for 3D Generation
• [5] McAllister et al., Rethinking Score Distillation as a Bridge Between Image Distributions
• [6] Jiang et al., JointDreamer: Ensuring Geometry Consistency and Text Congruence in Text-to-3D Generation via Joint Score Distillation

W1: "CLIP score and human evaluation of success rate."

<em>[Note: Our response refers to new content in the revised manuscript:

• Main experiment: Table 1 (Page 8, Line 378)
• Success Rate: Appendix C.7 (Page 28, Line 1499)
  • Evidence: Table 5 (Page 28, Line 1470)
• Discussions: Appendix F (Page 28, Line 1560)]</em>

Response: Thank you for your valuable feedback regarding evaluation metrics. We have addressed both points as follows:

1. CLIP Scores [1] (Shown in Table 1):
   We have included CLIP score evaluations in the main paper. While CLIP scores measure image-text consistency, it is important to note that our method generates multi-view results, including viewpoints (e.g., back views) that may not be explicitly described in the prompt. This viewpoint diversity enhances 3D consistency but may lead to lower CLIP scores since the additional views do not strictly align with the text description.

2. Success Rate Evaluation (Shown in Table 5):
   In response to your insightful suggestion regarding human evaluation, we conducted a detailed manual assessment (described in Appendix C.7) using a structured scoring system. Specifically, we assigned a score of 1.0 for global feature inconsistency and 0.5 for local feature inconsistencies (e.g., in features like ears, hands, and feet). The results show that our method effectively resolves global inconsistencies, although challenges persist in maintaining fine-grained detail consistency. To address these challenges, future work could explore incorporating multi-view image reconstruction supervision techniques to better constrain the score distillation process. Further details on this potential direction are discussed in Appendix F.

Table 1: Quantitative comparison.

Table 5: Success rates for Janus-free generation

• [1] Radford et al., Learning transferable visual models from natural language supervision

We thank Reviewer wW4M for their valuable comments. To provide comprehensive details and visual evidence of the improvements, we have included the updated manuscript in the supplementary materials. We kindly invite you to review this version, where all new comparisons and analyses are thoroughly documented.

Q1: "Why is the VSD loss in Eq. 14 denoted as $L'\_{VSD}$ instead of $L_{VSD}$ as in Eq. 9?"

Response: The distinction between $L'\_{VSD}$ and $L\_{VSD}$ highlights a key difference in the treatment of directional prompts. In the original $L\_{VSD}$ formulation (Eq. 9), the text conditioning adapts to the camera pose, utilizing specific directional prompts (e.g., "front view," "side view") for each sampling position $q$. In contrast, the modified $L'\_{VSD}$ (Eq. 14) employs a single, fixed prompt that remains consistent across all camera poses. This simplification is denoted by omitting the directional conditioning subscript $c$ from the loss term in the modified formulation.

Q2: " ... modifying the camera sampling distribution in VSD to use the estimated p(c∣y) could yield similar or complementary effects?"

<em>[Note: Our response refers to new content in the revised manuscript:

• Related works: Appendix C.2 (Page 23, Line 1235)
• Qualitative results: Figure 9 (Page 25, Line 1306)]</em>

Response: We thank the reviewer for the insightful suggestion regarding the modification of the camera sampling distribution in VSD using the estimated $p(c|y)$. While we explored this direction extensively, as detailed in Appendix C.2 (Sampling $q$), our experiments indicate that such modifications do not result in the anticipated improvements in 3D consistency. Our analysis highlights two fundamental limitations:

1. Data Bias in the Underlying Prior:
   Adjusting the view sampling probabilities in the $q$ distribution does not address the inherent data bias in the training prior. Certain viewpoints are naturally underrepresented in the training data, and this scarcity remains a limiting factor even with modified sampling strategies.

2. Optimization Challenges from Focused Sampling:
   Experiments show that concentrating sampling on specific viewpoints introduces problematic optimization behavior. Specifically, we observe that scenes become flatter when optimization focuses too heavily on certain camera poses, leading to difficulties in convergence. Furthermore, the lack of comprehensive viewpoint supervision prevents the model from synthesizing geometrically coherent structures.

These findings suggest that the challenges inherent in the training prior and optimization dynamics cannot be resolved solely through modifications to the $q$ distribution sampling strategy. The quantitative results supporting this analysis are presented in Fig. 9.

Thanks authors for the extensive clarifications. Most of my concerns are addressed. I keep my score and remain positive for this work.

Thanks for your attention. Since Q1 and Q3 need further clarification, we will provide more details later.

Q2 "How does this process work? What is the pipeline for mask segmentation?"

Response: This is actually a trick mentions in DINOv2 [1]. To segment the images, the reviewers construct a PCA to classify the patch tokens. Specifically, images are encoded as patch features (with tensor shape $[B, C, H\*W]$). Then, PCA is applied on all the patch features ($[B\*H\*W, C]$, performed on the feature channel $C$). The first channel in the compressed feature ($[B\*H\*W, C']$, where $C' << C$) is the most distinctive component, which indicates the foreground and background in the DINO feature space. However, PCA does not specify whether the value $>0$ or $<0$ represents foreground, so we add a simple postprocessing step as discussed in Appendix B.1.3.

• [1] Oquab et al., Dinov2: Learning robust visual features without supervision