Response to Weakness 2

W2. Potentially Unfair Comparisons: The experimental comparisons may be somewhat skewed ...

We appreciate the reviewer’s comments and recognize the inherent challenges in achieving completely fair comparisons in OOD settings, especially as we are pioneering this new area of research.

First, prior works can only realize conditional generation with scalar-type properties. To verify the effectiveness of our framework, we adapt these works to be able to generate target samples steered by the number of rings. We acknowledge that, given the exploratory nature of our work, achieving entirely fair comparisons may be unrealistic due to the absence of established baselines.

In fact, these geometry elements are the targets we aim to generate, so evaluating the partition of these elements in the output when they are taken as input may not be as fair.

In response to the question, "These geometry elements are the targets we aim to generate, so evaluating the partition of these elements in the output when they are taken as input may not be as fair."

Evaluating the partition of input geometric elements in the output when they are taken as input is critical to evaluating the performance of our framework. The geometric elements are encoded in a way that can steer the generation. Only when the generated output indeed contains the input geometric elements can we verify that our framework can successfully encode the input geometric elements and use the encoded information to steer the generation toward the sparse regions.

As linker design fundamentally is a special case of fragment-based generation, we also conducted a toy experiment on this task to verify the effectiveness of our framework. In particular, in this experiment, all algorithms (DiffLinker, LinkerNet, and our method) received the same geometric elements, and we believe this is a fair comparison scenario. As shown in Table 6, our experiments revealed that existing approaches exhibit limitations in OOD (data-sparse regions) linker design. The experimental results indicate that existing linker design methods fall short in linking OOD fragments, achieving a validity below 50%. These results demonstrate that our method shows promising performance in fragment linking within the OOD context.

We understand that our explanation might not fully address your comment. You could provide further details or specify the aspects that are unclear. We would be glad to further offer a more targeted explanation.

We appreciate the reviewer’s acknowledgment of the strengths of our work. We are glad that the reviewer recognizes the value and practical importance of our research, finds our results promising, and commends the organization of our code. Below, we address the reviewer’s concerns.

Response to Weakness 1

Ambiguous Statements: The definitions of $p_{\\theta}(\\mathbf{z}\_{\\mathbf{x}},\\mathbf{z}\_{\\mathbf{h}},\\mathbf{f}\_{x}, \\mathbf{f}\_{\\mathbf{h}})$ and $\\epsilon\_{\\theta}(\\mathbf{z}\_{\\mathbf{x}},\\mathbf{z}\_{\\mathbf{h}},\\mathbf{f}\_{\\mathbf{x}}, \\mathbf{f}\_{\\mathbf{h}})$ are unclear ...

We appreciate the reviewer’s comments.

1. The term $p\_{\\theta}(\\mathbf{z}\_{\\mathbf{x},t-1}, \\mathbf{z}\_{\\mathbf{h},t-1}|\\mathbf{z}\_{\\mathbf{x},t}, \\mathbf{z}\_{\\mathbf{h},t},\\mathbf{f}\_{\\mathbf{x}},\\mathbf{f}\_{\\mathbf{h}})$ represents the conditional reverse process of our diffusion model, analogous to $p\_{\\theta}(x\_{t-1}|x\_{t})$ in DDPM. The key distinction is that our model is additionally conditioned on encoded physical priors $\\mathbf{f}\_{\\mathbf{x}}$ and $\\mathbf{f}\_{\\mathbf{h}}$. Besides, $\\boldsymbol{\\epsilon}\_{\\theta}(\\mathbf{z}\_{\\mathbf{x},t}, \\mathbf{z}\_{\\mathbf{h},t},\\mathbf{f}\_{\\mathbf{x}},\\mathbf{f}\_{\\mathbf{h}},t)$ denotes the denoising network, which incorporates these physical priors as extra inputs.

2. Given fragment inputs $\\mathcal{G}^{f}=\\langle\\mathbf{x}^{f},\\mathbf{h}^{f}\\rangle$ and the corresponding learned physical prior $\\mathcal{F}=\\langle\\mathbf{f}\_{\\mathbf{x}},\\mathbf{f}\_{\\mathbf{h}}\\rangle$, we concatenate $\\mathbf{f}\_{\\mathbf{x}}$ and $\\mathbf{f}\_{\\mathbf{h}}$ to the node features $\\mathbf{z}\_{h}$. For instance, with node features $\\mathbf{z}\_{h} \\in \\mathbb{R}^{N \\times d}$, $\\mathbf{f}\_{\\mathbf{x}} \\in \\mathbb{R}^{N' \\times 3}$, and $\\mathbf{f}\_{\\mathbf{h}} \\in \\mathbb{R}^{N' \\times 1}$, the EGNN within the denoising network $\\boldsymbol{\\epsilon}\_{\\theta}$ receives noisy coordinates $\\mathbf{z}\_{x} \\in \\mathbb{R}^{N \\times 3}$ and concatenated features $\\mathbf{z}\_{h} \\in \\mathbb{R}^{N \\times (d+3+1+1)}$ (including a extra one-dimensional time-step embedding). Since the number of fragments $N'$ is smaller than the number of molecules $N$, zeros are padded to $\\mathbf{f}\_{\\mathbf{x}}$ and $\\mathbf{f}\_{\\mathbf{h}}$. We supplemented this explanation to the revised manuscript on Page 6.

3. Regarding Figure 1, we agree that the physical prior is indeed a latent point cloud. However, in our specific implementation, this latent point cloud is concatenated into the node features to guide the generation process. Thus, we chose to depict it as a representation to effectively convey our concept.

We thank you for your time and effort for reviewing our works.

Response to minor comments

In 2.2, line 160, a weight is defined, but it is not used anywhere.

We appreciate the reviewer's careful review. The weight defined here is used in the diffusion loss, as illustrated in Eq. (17) on page 14.

Response to Weakness a

a. Overly complicated and pompous presentation considering the method ...

We appreciate the reviewer’s comment. Technically, we concur that the proposed method utilizes a learned embedding to steer the generation process. Conceptually, this embedding is derived from the sub-structures of a molecule, such as scaffolds and ring structures. Those sub-structures typically are stable backbones for designing bespoke properties, which could be treated as critical physical prior information. We would like to clarify that our intention is not to obscure the simplicity of the method; instead, we aim to convey our ideas accurately and transparently.

Response to Weakness b

b. Proofs on the equivariance are presented as new, yet are simple (trivial?) extensions of well-known proofs in the field ...

We appreciate the reviewer’s recognition of our proofs as new and simple. We acknowledge that our proofs are related to but different from existing works. The work by Kohler et al. established that a transformation is H-invariant under certain constraints. In contrast, our proof specifically addresses SE(3)-invariance. Furthermore, the main difference is that our framework's training loss satisfies invariance when conditioned on equivariant representations. This aspect has not been considered or proven before, serving as the core theoretical foundation of our work. For clarity, we have included a discussion of previous works in the revised manuscript. We added citations to this work and supplemented extra discussion in the revised manuscript.

Response to Weakness c

c. While the proposed method beats a range of baselines ...

In fact, we agree with the reviewer that all work on molecule generation, including ours, is not practical enough. Among all baselines, ours has achieved SOTA performance in commonly used benchmarking datasets, including the GEOM-DRUG and QM9 datasets, as well as real-world applications in linker design. Our work can help push forward the frontier in this area.

Moreover, we are aware that the complete QM9 dataset may not serve as an ideal benchmark for molecular generation, as it consists of a comprehensive enumeration of elements H, C, N, O, and F. To address this issue, we have divided the dataset based on data scarcity, specifically focusing on the frequency of scaffolds and ring structures. Thus, while QM9 may not be suitable for training a real-world molecular generator, it remains an effective benchmark for comparing different algorithms.

Response to Question 1

I do not understand the statement that molecular stability is close to 0% on the GEOM-DRUG baseline ...

We appreciate the reviewer’s astute observation. The reported 0% molecular stability on the GEOM-DRUG dataset indeed reflects the results of the methods evaluated in the OOD generation task, highlighting both the challenges of the dataset and the limitations of existing OOD generation methods. While our proposed method has not yet achieved optimal performance, we believe that the transition from zero to 11.4% represents a significant improvement. We acknowledge the difficulties associated with this task and plan to investigate larger molecular datasets in future work.

We are grateful that the reviewer acknowledges the strengths of our work. We are glad that the reviewer found that our work is interesting and opens up new exploration and opportunities for AI for drug discovery and our paper is well-written and clear. We address the reviewer's concerns below.

Response to Weakness 1

The practical implications and real-world application scenario ...

We appreciate the reviewer’s comment. In drug discovery, OOD generation is crucial due to challenges related to data scarcity and the need for novel compounds. First, training a molecular generator typically requires a substantial amount of molecular data. However, for specific tasks, particularly those related to emerging diseases, available data may be insufficient [1]. Second, an effective molecular generator should avoid replicating the training data [2]; OOD generation enables models to create molecular structures that were not present in the training dataset.

[1] Klarner, Leo, et al. "Context-guided diffusion for out-of-distribution molecular and protein design." ICML: (2024).

[2] Walters, W. Patrick, and Mark Murcko. "Assessing the impact of generative AI on medicinal chemistry." Nature biotechnology 38.2 (2020): 143-145.

Response to Weakness 2

The paper primarily focuses on OOD generation related to shifts on molecule fragments ...

We appreciate the reviewer’s insightful comment. We acknowledge the limitation you point out and have addressed it in the limitation section of our paper. In our future work, we will actively explore methods to extract the general structure of fragments that represent distribution shifts but are not given, thereby enhancing the generalizability of our approach.

We also would like to clarify the significance of our work. Scaffolds/fragments are crucial in drug design as they provide a stable backbone that can be decorated with different functional groups to optimize the molecule's properties. Providing pre-defined scaffolds/fragments helps explore the chemical space efficiently and generate novel compounds with desired characteristics. Therefore, molecule generation given pre-defined scaffolds/fragments is an important task with wide applications.

Response to Major Question 4

Major Q4. Following the previous question ...

We sincerely appreciate the reviewer's insightful comment. First, the model indeed could work with disconnected scaffolds. Second, we can conjecture that the proposed method can also work with incomplete scaffolds as incomplete scaffolds and complete scaffolds share the same representation methods. For the reviewer's suggested task, we would like to explore relevant real-world tasks that provide an increasing proportion of the fragments and extend our frameworks as our future work.

Response to Major Question 5

Major Q5. As mentioned in "limitations" ...

It is possible. As mentioned in response to Major Question 4, our framework is agnostic to the detailed structure of the input scaffold as long as it can be presented in geometric point clouds.

Response to Minor Question 1

Minor Q1. The authors name the prior as ''physical''...

We appreciate the reviewer's insight regarding the prior being derived from the 3D structure of the fragments/scaffolds. Generally, scaffolds are crucial in drug design as they provide a stable backbone that can be decorated with different functional groups to optimize the molecule's properties. In this context, scaffolds or input 3D structures are critical physical information. Specifically, this physical knowledge serves as a prior in guiding OOD generation in data-sparse regions; thereby, we use physical priors to denote these input 3D structures.

Response to Minor Question 3

Minor Q3. As $f_{h}$ only has 1 dimension per atom ...

Thank you for your insightful question. Regarding the latent dimensionality of $\mathbf{f}_{\mathbf{h}}$, we adhere to previous studies on the latent representation of geometric point clouds. Research indicates that a smaller latent dimensionality is beneficial for effectively representing geometric information. In response to your concern, we conducted experiments on this parameter and presented the results below.

The experimental results demonstrate that the dimensionality of the latent atomic features $\mathbf{f}_{\mathbf{h}}$ has a minimal impact on performance, with $k=1$ yielding the best results. This finding is consistent with observations in GeoLDM [1], which also confirmed that a small latent dimensionality for atomic features remains representative of reconstructing the whole molecule.

[1] Xu, Minkai, et al. "Geometric latent diffusion models for 3d molecule generation." International Conference on Machine Learning. PMLR, 2023.

Response to Minor Question 4

Minor Q4. How is the atom number determined when sampling $z_{x,T}$, $z_{h,T}$ ?

We determine the atom number based on established methodologies from the literature. The number of atoms is sampled from the distribution derived from the entire dataset. Additionally, we exclude any sizes that fall below the size of input fragments.

We are pleased that the reviewer acknowledges the strengths of our work. We appreciate that the reviewer found that our target issue is challenging and underexplored, results are promising across various tasks, analysis is comprehensive, and the metrics are beneficial for future works. We address the reviewer's concerns as follows.

Response to Weakness 1 and Major Question 2

W1. From the presented generation examples, the scaffold seems to constitute a large proportion of the molecule...

Major Q2. Since the scaffold information is provided as a condition ...

In response to Weakness 1 and Major Question 2: We concur that the scaffold constitutes a significant portion of the molecule, which could be modified to create various derivatives with different properties. We would like to clarify that our diffusion model is trained in a way that it can sample the targeted molecules during the generation process rather than generate new samples based on modifications over any scaffolds. As verified with our experiments, our framework can generate samples containing specific scaffolds, which are rare in the dataset, as shown in Tables 4 and 5. Our experiments could be strong evidence showing the transferability from the dense region to the sparse regions.

In response to the Fig. 11 and the calculation of proportion and coverage. There are indeed slight alterations in the output compared to the input ring structure depicted in Fig. 11. But these outputs are our desired molecules as long as they contain the target ring number in the context of ring-structure generation tasks. Specifically, the proportion is defined as the percentage of generated molecules that contain the desired ring numbers among the valid samples. However, the coverage metric is not applicable in this context, as each ring structure represents a unique target distribution. Furthermore, in scaffold-based generation tasks, both coverage and proportion are calculated when the output molecule accurately incorporates the desired scaffold.

Response to Weakness 2

W2. The actual application of the method is somewhat limited as a pre-defined scaffold structure needs to be provided to the model...

In response to Weakness 2: Scaffolds are crucial in drug design as they provide a stable backbone that can be decorated with different functional groups to optimize the molecule's properties. Providing pre-defined scaffolds helps explore the chemical space efficiently and generate novel compounds with desired characteristics. Therefore, molecule generation given pre-defined sub-structures is an important task with wide applications.

Response to Major Question 1 and Minor Question 2

Q. For molecules with a large number of rings ...

In response to Major Question 1 and Minor Question 2: We began by analyzing the dataset to identify and filter out molecules containing more than ten rings, which are in sparse regions (all fewer than 100 samples). We then extracted the ring structures from these selected molecules; the extracted ring structures are used as input for generating new molecules with more than ten rings. This process ensures that these molecules in sparse regions are not provided for training.

Response to Major Question 3

Major Q3. For linker design tasks, the initial structures are two molecular fragments ...

In linker design tasks, the initial structures consist of multiple molecular fragments, all fed into the equivariant autoencoder. The intuition of using an equivariant autoencoder is to learn expressive representations of the fragments, which are used to steer the linking process toward OOD generation. We did not define scaffolds for this task. Instead, we directly use the molecular fragments as the input of the autoencoder.