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The authors present a method for performing topology optimization using a diffusion model framework. Building upon prior work [Maze & Ahmed, 2023], this submission introduces three additional physics-based features - displacement maps, principal stress lines, and strain energy density - to guide the generation process. The authors argue that enriching the diffusion model with these physical signals leads to results that better approximate classical topology optimization outcomes. Additionally, a connectivity-preserving loss is proposed to reduce floating regions in the output.
作者提出了一种使用扩散模型框架进行拓扑优化的方法。在前文[Maze & Ahmed, 2023]的基础上，本文引入了三个额外的基于物理的特征——位移图、主应力线和应变能密度——来指导生成过程。作者认为，利用这些物理信号丰富扩散模型，可以获得更接近经典拓扑优化结果的结果。此外，作者还提出了一种保持连通性的损失函数，以减少输出中的浮动区域。

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The length is fine but the presentation lack of details in some sense - see my detail comments below.
长度还可以，但呈现在某种意义上缺乏细节 - 请参阅下面的详细评论。

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Some self-learning based topology optimization works are missed.
一些基于自学习的拓扑优化工作被遗漏了。

TOuNN: Topology Optimization using Neural Networks, Structural and Multidisciplinary Optimization 63, 3 (2021), 1135–1149.
TOuNN：使用神经网络进行拓扑优化，结构和多学科优化 63, 3 (2021), 1135–1149。
FRC-TOuNN: Topology Optimization of Continuous Fiber Reinforced Composites using Neural Network, Computer-Aided Design 156 (2023), 103449.
FRC-TOuNN：基于神经网络的连续纤维增强复合材料拓扑优化，计算机辅助设计 156 (2023)，103449。
Simultaneous topology optimization of differentiable and non-differentiable objectives via morphology learning: stiffness and cell growth on scaffold, Advanced Intelligent Discovery, 2025.
通过形态学习同时对可微分和不可微分目标进行拓扑优化：支架上的刚度和细胞生长，高级智能发现，2025 年。
Neural co-optimization of structural topology, manufacturable layers, and path orientations for fiber-reinforced composites, SIGGRAPH 2025.
纤维增强复合材料的结构拓扑、可制造层和路径方向的神经协同优化，SIGGRAPH 2025。

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Parameters for reproduction are not provided, which may be solved if authors can provide the source code of their implementation.
没有提供复制的参数，如果作者可以提供其实现的源代码，这个问题可能会得到解决。

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See my detail comments below.
请参阅下面我的详细评论。

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n/a  无

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The fundamental technical contribution is limited.
基础技术贡献有限。

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markdown  降价

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While the idea of integrating physical cues into generative diffusion models is interesting, I have several significant concerns regarding the technical novelty, generalizability, and methodological justification of the work. My detailed comments are as follows:

1. Technical Contribution and Originality
The authors list four key contributions, but in my view, the actual novelty is limited:
- The overall framework (Contribution 2) is closely based on existing work by [Maze & Ahmed, 2023], with a standard U-Net-based diffusion architecture that is widely used in image generation tasks. There is little novelty in the architecture or training strategy.
- The proposed connectivity-preserving loss (Contribution 3) seems to be a patch for addressing floating regions—a known issue in generative models. It is unclear why this issue cannot be resolved via density thresholding or by directly optimizing for connected components within the learned field. The added loss term appears minor and ad hoc.
- Contribution 4 does not constitute a technical contribution; it simply describes dataset augmentation.
- The introduction of physical feature maps (Contribution 1) is potentially useful, but no rigorous analysis or ablation study is provided to understand their actual impact (see Point 4 below).

2. Generality and Dataset Dependence
The diffusion-based method, as described, appears highly data-dependent and limited in generalizability:
- It is unclear whether the model trained on a specific dataset (e.g., rectangular 2D domains from [Maze & Ahmed, 2023]) can generalize to different domain geometries, dimensionalities (e.g., 3D), or material parameters.
- The method seems restricted to learning a narrow family of solutions, and no experiments are provided to support claims of broader applicability.

3. Supervised Learning vs. Physics-Based Self-Learning
The authors opt for a supervised learning pipeline using pre-generated optimization results. However, there is no justification provided for choosing supervised learning over self-supervised or reinforcement learning approaches that embed FEA directly in the loop (e.g., physics-informed self-learning or gradient-based differentiable simulation).
- Are there computational advantages in training time or inference speed?
- Is your method more scalable or efficient than self-learning frameworks?
These comparisons / justifications are essential but are currently missing.

4. Lack of Ablation and Redundancy in Feature Maps
Section 3.1 introduces three physical signals (displacement, stress lines, and strain energy density) as conditional features. However:
- No ablation study is provided to assess the individual or combined impact of these signals.
- There is potential redundancy, particularly between displacement and strain energy density, which are physically related. An analysis of their relative contributions would improve the paper's clarity and depth.

5. Simplistic Examples and Missing Experimental Details
The examples used in the paper are overly simplistic and lack critical details:
- Boundary conditions and volume fraction constraints are not clearly defined.
- It is unclear whether the method can generalize to different volume fraction ratios. This is a core aspect of topology optimization and should be explicitly tested.
- A study showing structural variation with fixed boundary conditions and varying volume fractions would significantly strengthen the evaluation.

Conclusion
While the idea of embedding physical fields into a generative model for topology optimization is appealing, the current submission falls short in several key areas:
- Limited technical novelty.
- Lack of rigorous evaluation and ablation.
- Poor justification for the learning framework choice.
- Simplistic experiments without sufficient detail.

Given these issues, I believe the submission is clearly below the acceptance threshold for SIGGRAPH, whether for the conference or journal track. I therefore recommend rejection.

While the idea of integrating physical cues into generative diffusion models is interesting, I have several significant concerns regarding the technical novelty, generalizability, and methodological justification of the work. My detailed comments are as follows:
虽然将物理线索整合到生成扩散模型中的想法很有趣，但我对该研究的技术新颖性、普遍性和方法论的合理性有几个重大的担忧。我的具体意见如下：

1. Technical Contribution and Originality
   技术贡献与原创性
   The authors list four key contributions, but in my view, the actual novelty is limited:
   作者列出了四个主要贡献，但在我看来，实际的新颖性是有限的：

• The overall framework (Contribution 2) is closely based on existing work by [Maze & Ahmed, 2023], with a standard U-Net-based diffusion architecture that is widely used in image generation tasks. There is little novelty in the architecture or training strategy.
  整体框架（贡献 2）与 [Maze & Ahmed, 2023] 的现有工作紧密相关，采用了在图像生成任务中广泛使用的标准 U-Net 扩散架构。在架构和训练策略上几乎没有创新之处。
• The proposed connectivity-preserving loss (Contribution 3) seems to be a patch for addressing floating regions—a known issue in generative models. It is unclear why this issue cannot be resolved via density thresholding or by directly optimizing for connected components within the learned field. The added loss term appears minor and ad hoc.
  提出的连通性保留损失（贡献 3）似乎是解决浮动区域问题的补丁——浮动区域是生成模型中的一个已知问题。目前尚不清楚为什么这个问题不能通过密度阈值或直接优化学习域内的连通分量来解决。新增的损失项似乎很小且是临时性的。
• Contribution 4 does not constitute a technical contribution; it simply describes dataset augmentation.
  贡献 4 不构成技术贡献；它只是描述了数据集增强。
• The introduction of physical feature maps (Contribution 1) is potentially useful, but no rigorous analysis or ablation study is provided to understand their actual impact (see Point 4 below).
  物理特征图（贡献 1）的引入可能很有用，但没有提供严格的分析或消融研究来了解其实际影响（见下文第 4 点）。

1. Generality and Dataset Dependence
   通用性和数据集依赖性
   The diffusion-based method, as described, appears highly data-dependent and limited in generalizability:
   如上所述，基于扩散的方法似乎高度依赖数据并且普遍性有限：

• It is unclear whether the model trained on a specific dataset (e.g., rectangular 2D domains from [Maze & Ahmed, 2023]) can generalize to different domain geometries, dimensionalities (e.g., 3D), or material parameters.
  目前尚不清楚在特定数据集（例如，[Maze & Ahmed, 2023] 的矩形二维域）上训练的模型是否可以推广到不同的域几何、维度（例如，三维）或材料参数。
• The method seems restricted to learning a narrow family of solutions, and no experiments are provided to support claims of broader applicability.
  该方法似乎仅限于学习一小类解决方案，并且没有提供任何实验来支持更广泛适用性的主张。

1. Supervised Learning vs. Physics-Based Self-Learning
   监督学习与基于物理的自学习
   The authors opt for a supervised learning pipeline using pre-generated optimization results. However, there is no justification provided for choosing supervised learning over self-supervised or reinforcement learning approaches that embed FEA directly in the loop (e.g., physics-informed self-learning or gradient-based differentiable simulation).
   作者选择使用预先生成的优化结果构建监督学习流程。然而，他们并未提供任何理由来支持选择监督学习，而非将有限元分析 (FEA) 直接嵌入循环中的自监督学习或强化学习方法（例如，基于物理信息的自学习或基于梯度的可微分模拟）。

• Are there computational advantages in training time or inference speed?
  训练时间或推理速度方面是否存在计算优势？
• Is your method more scalable or efficient than self-learning frameworks?
  您的方法是否比自学习框架更具可扩展性或更高效？
  These comparisons / justifications are essential but are currently missing.
  这些比较/理由很重要，但目前却缺失。

1. Lack of Ablation and Redundancy in Feature Maps
   特征图缺乏消融和冗余
   Section 3.1 introduces three physical signals (displacement, stress lines, and strain energy density) as conditional features. However:
   第3.1节介绍了三个物理信号（位移、应力线和应变能密度）作为条件特征。然而：

• No ablation study is provided to assess the individual or combined impact of these signals.
  没有提供消融研究来评估这些信号的单独或组合影响。
• There is potential redundancy, particularly between displacement and strain energy density, which are physically related. An analysis of their relative contributions would improve the paper's clarity and depth.
  存在潜在的冗余，尤其是在位移和应变能密度之间，它们之间存在物理联系。分析它们的相对贡献将有助于提升论文的清晰度和深度。

1. Simplistic Examples and Missing Experimental Details
   示例过于简单，缺少实验细节
   The examples used in the paper are overly simplistic and lack critical details:
   论文中使用的例子过于简单，缺乏关键细节：

• Boundary conditions and volume fraction constraints are not clearly defined.
  边界条件和体积分数约束没有明确定义。
• It is unclear whether the method can generalize to different volume fraction ratios. This is a core aspect of topology optimization and should be explicitly tested.
  目前尚不清楚该方法是否可以推广到不同的体积分数比。这是拓扑优化的核心方面，应该进行明确的测试。
• A study showing structural variation with fixed boundary conditions and varying volume fractions would significantly strengthen the evaluation.
  一项显示具有固定边界条件和不同体积分数的结构变化的研究将大大加强评估。

Conclusion  结论
While the idea of embedding physical fields into a generative model for topology optimization is appealing, the current submission falls short in several key areas:
虽然将物理场嵌入到拓扑优化生成模型中的想法很有吸引力，但目前提交的方案在几个关键领域存在不足：

• Limited technical novelty.
  技术新颖性有限。
• Lack of rigorous evaluation and ablation.
  缺乏严格的评估和消融。
• Poor justification for the learning framework choice.
  学习框架选择的理由不充分。
• Simplistic experiments without sufficient detail.
  实验过于简单，缺乏足够的细节。

Given these issues, I believe the submission is clearly below the acceptance threshold for SIGGRAPH, whether for the conference or journal track. I therefore recommend rejection.
鉴于这些问题，我认为该投稿明显低于 SIGGRAPH 的接受门槛，无论是会议还是期刊。因此，我建议拒绝。

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The paper introduces a diffusion model guided by Multiphysics features for topology optimization. The authors propose a connectivity-preserving loss function aimed at reducing floating material in the generated designs. The use of diffusion models and topology-aware loss functions for topology optimization has been explored extensively, as acknowledged through the citations. As such, the novelty of this work is not clearly articulated, and in its current form, it lacks sufficient contribution to warrant publication.
本文介绍了一种基于多物理场特征的扩散模型，用于拓扑优化。作者提出了一种保持连通性的损失函数，旨在减少生成设计中的浮动材料。扩散模型和拓扑感知损失函数在拓扑优化中的应用已被广泛探索，这一点已在引文中得到确认。因此，本文的新颖性尚未清晰阐述，且就其目前的形式而言，其贡献不足以保证发表。

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the exposition and presentation are clear
阐述和呈现清晰

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All the relevant papers are discussed
所有相关论文均已讨论

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Yes  是的

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Yes  是的

None  没有任何

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Not suitable for either  都不适合

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markdown  降价

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The paper introduces a diffusion model guided by Multiphysics features for topology optimization. The authors propose a connectivity-preserving loss function aimed at reducing floating material in the generated designs. The use of diffusion models and topology-aware loss functions for topology optimization has been explored extensively, as acknowledged through the citations. As such, the novelty of this work is not clearly articulated, and in its current form, it lacks sufficient contribution to warrant publication.
To assist the authors in strengthening their work, I offer the following comments:

1. The authors claim that their method produces high-performing and manufacturable designs without additional postprocessing. However, the method does not guarantee topological correctness, which casts doubt on the manufacturability of the predictions.

2. The model is trained on a 64×64 grid, which is a relatively low resolution. At this scale, traditional methods such as SIMP can compute optimal designs in under two seconds on a standard PC. It is unclear why a complex and resource-intensive deep learning pipeline would be preferred over such efficient traditional methods unless the benefits are demonstrated on higher-resolution (e.g., 256×256) or 3D problems.

3. The justification for using a mask M in the connectivity loss function is unclear. If M represents a corrected version of the ground truth with no floating materials, why not directly compare the prediction with this corrected design? Additionally, since the gradient of the loss may be zero where M is zero, it is unclear how the model learns from such regions. A theoretical or empirical justification for the effectiveness of this masking strategy would be valuable.

4. Diffusion models are known for high inference times. The authors should report and compare the inference time of their method with other state-of-the-art approaches to demonstrate practical viability.

The paper introduces a diffusion model guided by Multiphysics features for topology optimization. The authors propose a connectivity-preserving loss function aimed at reducing floating material in the generated designs. The use of diffusion models and topology-aware loss functions for topology optimization has been explored extensively, as acknowledged through the citations. As such, the novelty of this work is not clearly articulated, and in its current form, it lacks sufficient contribution to warrant publication.
本文介绍了一种基于多物理场特征的扩散模型，用于拓扑优化。作者提出了一种保持连通性的损失函数，旨在减少生成设计中的浮动材料。扩散模型和拓扑感知损失函数在拓扑优化中的应用已被广泛探索，这一点已在引文中得到确认。因此，本文的新颖性尚未清晰阐述，且就其目前的形式而言，其贡献不足以保证发表。
To assist the authors in strengthening their work, I offer the following comments:
为了帮助作者加强他们的工作，我提出以下评论：

1. The authors claim that their method produces high-performing and manufacturable designs without additional postprocessing. However, the method does not guarantee topological correctness, which casts doubt on the manufacturability of the predictions.
   作者声称，他们的方法无需额外的后处理即可生成高性能且可制造的设计。然而，该方法并不能保证拓扑的正确性，这使得人们对预测的可制造性产生了怀疑。
   
   
2. The model is trained on a 64×64 grid, which is a relatively low resolution. At this scale, traditional methods such as SIMP can compute optimal designs in under two seconds on a standard PC. It is unclear why a complex and resource-intensive deep learning pipeline would be preferred over such efficient traditional methods unless the benefits are demonstrated on higher-resolution (e.g., 256×256) or 3D problems.
   该模型在 64×64 网格上训练，分辨率相对较低。在这种规模下，像 SIMP 这样的传统方法可以在标准 PC 上在两秒内计算出最优设计。目前尚不清楚，为什么复杂且资源密集型的深度学习流程会比如此高效的传统方法更受青睐，除非其优势能够在更高分辨率（例如 256×256）或 3D 问题上得到体现。
   
   
3. The justification for using a mask M in the connectivity loss function is unclear. If M represents a corrected version of the ground truth with no floating materials, why not directly compare the prediction with this corrected design? Additionally, since the gradient of the loss may be zero where M is zero, it is unclear how the model learns from such regions. A theoretical or empirical justification for the effectiveness of this masking strategy would be valuable.
   在连接损失函数中使用掩码 M 的理由尚不清楚。如果 M 代表了没有浮动材料的校正版本，为什么不直接将预测与校正后的设计进行比较？此外，由于在 M 为零的地方，损失函数的梯度可能为零，因此模型如何从这些区域学习尚不清楚。对这种掩码策略的有效性进行理论或经验论证将非常有价值。
   
   
4. Diffusion models are known for high inference times. The authors should report and compare the inference time of their method with other state-of-the-art approaches to demonstrate practical viability.
   扩散模型以高推理时间而闻名。作者应报告其方法与其他最先进方法的推理时间，并进行比较，以证明其实际可行性。

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This paper proposes a diffusion-based generative model for generating minimum-compliance structures in topology optimization (TO) problems. The main idea is to condition a standard UNet-based diffusion model on TO-specific physical quantities, e.g., displacement fields. Furthermore, to avoid floating materials, the paper introduces a regularization term in the diffusion model's training loss to encourage connectivity. The paper evaluates the proposed method on a standard TO dataset and compares its performance with three existing generative models for TO. The experiments show that the proposed generative model achieves smaller errors, and several ablation studies confirm the efficacy of the newly introduced components in the model.
本文提出了一种基于扩散的生成模型，用于在拓扑优化 (TO) 问题中生成最小柔顺结构。其主要思想是将基于 UNet 的标准扩散模型与 TO 特定的物理量（例如位移场）进行条件化。此外，为了避免浮动材料，本文在扩散模型的训练损失函数中引入了正则化项以促进连通性。本文在标准 TO 数据集上评估了所提出的方法，并将其性能与三种现有的 TO 生成模型进行了比较。实验表明，所提出的生成模型实现了更小的误差，多项消融研究证实了模型中新引入组件的有效性。

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I feel that the technical method in the paper can really benefit from a more precise, quantitative description, e.g., by adding key equations, notations, and pseudocode. I also suggest the paper consider adding a background section reviewing 1) the minimum-compliance problem setup in TO and 2) the standard diffusion model.
我认为论文中的技术方法如果能更精确、更量化地描述，例如添加关键方程、符号和伪代码，将会受益匪浅。我还建议论文考虑增加一个背景部分，回顾 1）TO 中的最小合规性问题设置；2）标准扩散模型。

The output insets in Figs. 1 and 2 look quite noisy, but the output in Fig. 4 looks much cleaner. Which of them represents the output from your trained diffusion model?
图 1 和图 2 中的输出插图看起来噪声很大，但图 4 中的输出看起来干净得多。哪一个代表了你训练好的扩散模型的输出？

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OK.  好的。

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The high-level idea in this paper is straightforward, and I don't see anything that is fundamentally wrong.
本文的高层思想很简单，我没有发现任何根本错误。

The text does not present too many low-level algorithmic and implementation details. Instead, the paper presents its codebase in the supplementary materials. Therefore, reproducibility should not be a big deal for people familiar with both TO and diffusion models.
正文并未过多地展示底层算法和实现细节。相反，论文在补充材料中展示了其代码库。因此，对于熟悉 TO 和扩散模型的人来说，可重复性应该不是什么大问题。

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The quantitative results reported in the tables look OK to me. I wish the paper could report more qualitative results, e.g., more visualization of the generated structures and a supplementary video showing progressive results from the diffusion model during and after training.
我觉得表格中报告的定量结果还不错。我希望论文能报告更多定性结果，例如，对生成的结构进行更多可视化，并附上一个补充视频，展示扩散模型在训练期间和训练后的进展结果。

It looks like all LD values reported in the table are zero, which seems to indicate that it is not an effective metric for comparing these methods.
看起来表中报告的所有 LD 值都是零，这似乎表明它不是比较这些方法的有效指标。

None  没有任何

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Conference, if the paper can be accepted. Please see my explanation of rating below.
如果论文能被接受，请提交会议审核。请参阅下文我对评级的解释。

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markdown  降价

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One thing that I like about this paper is that it explores a modern generative method in the context of the minimum-compliance problem in TO. I think this is a promising research direction because diffusion models bring in a new view to this classic problem, i.e., interpreting optimal structures as a learnable probabily distribution. Although this is not the first paper in this topic (Maze and Ahmed 23 is a closely related work), the physics guidence in this paper leads to an improved performance over the baselines. Therefore, I think the paper has made some technical contributions in this relatively new topic and may inspire follow-up works.

On the other hand, the paper also has some weaknesses:
1. The experiments focus on 2D examples exclusively. It is unclear whether the method is scalable to 3D examples. Training a 3D diffusion model for high-resolution TO results might be non-trivial.
2. I'd welcome more visualization of the current results in the experiment section.
3. The paper could also benefit from some real-world validation, e.g., by 3D-printing some designs generated from the diffusion model.
4. I am also curious to see some "failure cases", e.g., showing a generated design and/or its performance that deviate a lot from the "ground-truth" design optimized from SIMP. Some discussions on what boundary conditions/load conditions may trigger such failure cases would also shed more light on the capability of the proposed model.

One thing that I like about this paper is that it explores a modern generative method in the context of the minimum-compliance problem in TO. I think this is a promising research direction because diffusion models bring in a new view to this classic problem, i.e., interpreting optimal structures as a learnable probabily distribution. Although this is not the first paper in this topic (Maze and Ahmed 23 is a closely related work), the physics guidence in this paper leads to an improved performance over the baselines. Therefore, I think the paper has made some technical contributions in this relatively new topic and may inspire follow-up works.
我喜欢这篇论文的一点是，它在 TO 的最小合规性问题背景下探索了一种现代生成方法。我认为这是一个很有前景的研究方向，因为扩散模型为这个经典问题带来了新的视角，即将最优结构解释为可学习的概率分布。虽然这不是该主题的第一篇论文（Maze 和 Ahmed 23 是一篇密切相关的工作），但本文中的物理指导使其性能优于基线。因此，我认为这篇论文在这个相对较新的主题上做出了一些技术贡献，并可能启发后续的研究。

On the other hand, the paper also has some weaknesses:
另一方面，该论文也存在一些不足之处：

1. The experiments focus on 2D examples exclusively. It is unclear whether the method is scalable to 3D examples. Training a 3D diffusion model for high-resolution TO results might be non-trivial.
   实验仅针对二维样本。尚不清楚该方法是否可以扩展到三维样本。训练一个用于高分辨率 TO 结果的三维扩散模型可能并非易事。
2. I'd welcome more visualization of the current results in the experiment section.
   我欢迎在实验部分对当前结果进行更多可视化。
3. The paper could also benefit from some real-world validation, e.g., by 3D-printing some designs generated from the diffusion model.
   该论文还可以从一些现实世界的验证中受益，例如通过 3D 打印一些由扩散模型生成的设计。
4. I am also curious to see some "failure cases", e.g., showing a generated design and/or its performance that deviate a lot from the "ground-truth" design optimized from SIMP. Some discussions on what boundary conditions/load conditions may trigger such failure cases would also shed more light on the capability of the proposed model.
   我也非常期待看到一些“失败案例”，例如，生成的设计和/或其性能与基于 SIMP 优化的“真实”设计存在很大偏差。关于哪些边界条件/负载条件可能触发此类失败案例的讨论，也能更好地阐明所提模型的性能。

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This paper introduces a diffusion model for topology optimization that incorporates physics-based constraints as guidance mechanisms. Unlike its predecessor, TopoDiff, the model employs hierarchically placed cross-attention modules to steer the denoising process, instead of classifier-based guidance. They demonstrate through in- and out-of-distribution experiments that their method outperforms existing methods such as TopoDiff, TopologyGAN and DOM in generating designs with compliance values closer to the ground truth.
本文介绍了一种用于拓扑优化的扩散模型，该模型将基于物理的约束作为指导机制。与其前身 TopoDiff 不同，该模型采用分层放置的交叉注意力模块来控制去噪过程，而非基于分类器的指导。通过分布内和分布外实验，他们证明该方法在生成符合度值更接近真实值的设计方面优于 TopoDiff、TopologyGAN 和 DOM 等现有方法。

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The paper is generally well-written and easy to follow. However, some concepts are either not clearly defined or omitted entirely. That being said, I find their meaning can often be inferred from the context. More specifically:

- A minor point: the use of the term multi-physics is confusing. In the literature, it typically refers to systems that simulate multiple physical phenomena simultaneously (e.g., elasticity and heat). In this work, however, it refers to multiple physical fields.

- The term PSL is described but lacks a mathematical definition. Figure 2 indicates that it is a 3-component scalar vector per pixel. What does each scalar represent? Why not simply use the independent values of the stress tensor?

- I assume all physical fields are computed using a finite element method package. From the text, it appears the analysis is limited to linear elasticity. Are these fields evaluated point-wise at the center of each cell?

- Possibly a typo? Figure 2 depicts the volume fraction as a scalar field rather than a single scalar value.

- Shouldn't the output of Figure 2 be the denoised sample?

- Is MHG-Diff in Table 4 also guided?

- I find the distinction between global and local physical fields confusing. Since all these fields are interrelated, it is unclear what it means for the energy density to be a global characteristic and the displacements to be a local characteristic. I can understand that applying these features to the specified layers may produce more satisfying results. However, I find the explanation provided somewhat vague and not supported by results, as it is not evident how changing the hierarchy influences the outcomes shown in Table 4. I consider this point especially important, given the emphasis placed on this hierarchy as a key contribution.

The paper is generally well-written and easy to follow. However, some concepts are either not clearly defined or omitted entirely. That being said, I find their meaning can often be inferred from the context. More specifically:
这篇论文总体写得很好，易于理解。然而，有些概念要么定义不明确，要么完全被忽略了。话虽如此，我发现它们的含义通常可以从上下文中推断出来。更具体地说：

• A minor point: the use of the term multi-physics is confusing. In the literature, it typically refers to systems that simulate multiple physical phenomena simultaneously (e.g., elasticity and heat). In this work, however, it refers to multiple physical fields.
  一个小问题：“多物理场”这个术语的使用容易让人困惑。在文献中，它通常指同时模拟多种物理现象（例如弹性和热）的系统。然而，在本文中，它指的是多个物理场。
  
  
• The term PSL is described but lacks a mathematical definition. Figure 2 indicates that it is a 3-component scalar vector per pixel. What does each scalar represent? Why not simply use the independent values of the stress tensor?
  术语“PSL”已被描述，但缺乏数学定义。图 2 表明它是每个像素的 3 分量标量矢量。每个标量代表什么？为什么不直接使用应力张量的独立值呢？
  
  
• I assume all physical fields are computed using a finite element method package. From the text, it appears the analysis is limited to linear elasticity. Are these fields evaluated point-wise at the center of each cell?
  我假设所有物理场都是使用有限元方法程序包计算的。从文本来看，分析似乎仅限于线性弹性。这些场是在每个单元的中心逐点计算的吗？
  
  
• Possibly a typo? Figure 2 depicts the volume fraction as a scalar field rather than a single scalar value.
  可能是打字错误？图 2 将体积分数描述为标量场，而不是单个标量值。
  
  
• Shouldn't the output of Figure 2 be the denoised sample?
  图 2 的输出不应该是去噪样本吗？
  
  
• Is MHG-Diff in Table 4 also guided?
  表 4 中的 MHG-Diff 是否也有指导意义？
  
  
• I find the distinction between global and local physical fields confusing. Since all these fields are interrelated, it is unclear what it means for the energy density to be a global characteristic and the displacements to be a local characteristic. I can understand that applying these features to the specified layers may produce more satisfying results. However, I find the explanation provided somewhat vague and not supported by results, as it is not evident how changing the hierarchy influences the outcomes shown in Table 4. I consider this point especially important, given the emphasis placed on this hierarchy as a key contribution.
  我发现全局和局部物理场之间的区别令人困惑。由于所有这些场都是相互关联的，因此能量密度作为全局特征、位移作为局部特征的含义尚不明确。我可以理解，将这些特征应用于指定的层可能会产生更令人满意的结果。然而，我发现提供的解释有些模糊，而且没有得到结果的支持，因为改变层级结构如何影响表4中显示的结果并不明显。鉴于层级结构作为一项关键贡献被强调，我认为这一点尤为重要。

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I am ok with the references provided. Perhaps other reviewers with greater expertise in this specific area can offer more insightful feedback regarding the citations.
我对提供的参考文献没有意见。或许其他在该领域更专业的审阅者可以针对引用提供更有见地的反馈。

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The paper looks reproducible. While I am not an expert in generative models, my understanding is that this work adapts existing image synthesis techniques to the context of topology optimization, and thus builds on well-known methods. I have a couple of questions:

- Section 3.3 states that it is preferable to include data with floating material during training, as such samples are said to contain useful information. However, these cases may actually be suboptimal, since floating material often indicates that the iterative optimization failed to find a reasonable material distribution within the given budget. The optimal solution could differ significantly. What useful information can the network realistically extract from such flawed samples? If presented with the same boundary conditions during inference, would the network reproduce the flawed design, without the floating material?

- I wonder under what circumstances the compliance of the generated structure is lower than that of the ground truth, as mentioned in Section 4.4. Do these designs comply with the specified material budget?

The paper looks reproducible. While I am not an expert in generative models, my understanding is that this work adapts existing image synthesis techniques to the context of topology optimization, and thus builds on well-known methods. I have a couple of questions:
这篇论文看起来具有可复现性。虽然我不是生成模型方面的专家，但我的理解是，这项工作将现有的图像合成技术应用于拓扑优化的背景下，因此建立在众所周知的方法之上。我有几个问题：

• Section 3.3 states that it is preferable to include data with floating material during training, as such samples are said to contain useful information. However, these cases may actually be suboptimal, since floating material often indicates that the iterative optimization failed to find a reasonable material distribution within the given budget. The optimal solution could differ significantly. What useful information can the network realistically extract from such flawed samples? If presented with the same boundary conditions during inference, would the network reproduce the flawed design, without the floating material?
  第 3.3 节指出，在训练过程中最好包含含有浮动材料的数据，因为这类样本被认为包含有用的信息。然而，这些情况实际上可能并非最优，因为浮动材料通常表明迭代优化未能在给定的预算内找到合理的材料分布。最优解可能会有很大差异。网络实际上能从这些有缺陷的样本中提取出哪些有用的信息？如果在推理过程中呈现相同的边界条件，网络是否会在没有浮动材料的情况下重现有缺陷的设计？
  
  
• I wonder under what circumstances the compliance of the generated structure is lower than that of the ground truth, as mentioned in Section 4.4. Do these designs comply with the specified material budget?
  我想知道在什么情况下，生成的结构的柔顺性会低于真实值的柔顺性，如4.4节所述。这些设计是否符合指定的材料预算？

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The paper is well validated against related generative models, particularly TopoDiff, TopologyGAN, and DOM. However, the intended benchmark or objective relative to traditional "iterative" topology optimization methods is unclear. Since the analysis is based on linear elasticity with 64×64 resolution samples, it is uncertain how much slower conventional methods truly are compared to the network’s inference time. Providing runtime comparisons with a standard SIMP implementation would help establish a clear performance baseline.
该论文已针对相关生成模型（尤其是 TopoDiff、TopologyGAN 和 DOM）进行了充分验证。然而，相对于传统“迭代”拓扑优化方法，其预期基准或目标尚不明确。由于分析基于 64×64 分辨率样本的线性弹性，因此尚不确定传统方法与网络推理时间相比究竟慢多少。提供与标准 SIMP 实现的运行时比较将有助于建立清晰的性能基准。

Additionally, building on the last point in the "Clarity of Exposition" section, it remains unclear how much the proposed physical fields, and their specific arrangement, impact the network’s final performance. For example, how beneficial is the chosen hierarchy compared to alternative configurations? Does incorporating PSL provide a significant improvement over using only energy density and von Mises stress, as in TopoDiff? More specifically, which performance gains can be attributed to changes in the network architecture, and which stem from the choice of physical fields? Moreover, why is von Mises stress used as a direct input while PSL is employed as a guidance mechanism? Given the physical similarity between these two fields, this choice is somewhat unclear.
此外，基于“阐述清晰度”部分的最后一点，目前尚不清楚所提出的物理场及其具体排列对网络最终性能的影响程度。例如，与其他配置相比，所选的层级结构有多大优势？与仅使用能量密度和冯·米塞斯应力（例如 TopoDiff 中）相比，加入 PSL 是否能带来显著的改进？更具体地说，哪些性能提升可以归因于网络架构的变化，哪些源于物理场的选择？此外，为什么冯·米塞斯应力被用作直接输入，而 PSL 被用作引导机制？鉴于这两个场在物理上的相似性，这种选择有些不明确。

Lastly, how does the choice of guidance inputs affect the final results? It seems that, during testing, these inputs were chosen from optimized samples. However, in practical applications, such information is not available a priori, and it would presumably require the user to estimate the expected behavior in order to provide valid inputs.
最后，引导输入的选择如何影响最终结果？在测试过程中，这些输入似乎是从优化样本中选择的。然而，在实际应用中，此类信息并非先验可得，可能需要用户估计预期行为才能提供有效的输入。

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No issues  没有问题

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While the paper provides an incremental improvement over existing work, its practical applicability appears limited in its current form. From the perspective of structural optimization, it is difficult to discern concrete contributions beyond the development of the diffusion model or to extract insights that are applicable in practice. In particular, its applicability is confined to 2D structures at a 64×64 resolution, relying on additional input data that traditional topology optimization methods can directly compute, with the flexibility to handle different geometries.
虽然该论文在现有研究的基础上取得了一些进展，但其实际应用性在目前的形式下似乎有限。从结构优化的角度来看，除了扩散模型的开发之外，很难发现具体的贡献，也很难提取出适用于实践的洞见。具体而言，其适用性仅限于 64×64 分辨率的二维结构，依赖于传统拓扑优化方法能够直接计算的额外输入数据，并且能够灵活地处理不同的几何结构。