GeoAda: Efficiently Finetune Geometric Diffusion Models with Equivariant Adapters

W1. Rewrite

We sincerely thank the reviewer for recognizing the contributions of our work and for the constructive feedback on the writing. We will revise the paper to improve its overall flow and conciseness, and will significantly shorten the final paragraph of Section 4 to avoid redundancy.

W2.Table/Figure’s Descriptions

We sincerely thank the reviewer for their positive feedback on our experimental results and the effectiveness of our method. We also apologize for the lack of detail in the current figure and table presentations. In the revised version, we will update their captions as follows to provide a clearer and more informative description:

Figure2. Overall framework of GeoAda. A control signal C\mathcal{C}C is injected into the noised graph Gτ\mathcal{G}_\tauGτ​ and processed by an equivariant adapter block. The adapter output is added to the frozen denoiser and repeated B times to produce the final symmetry-preserving output.

Figure3.  Visualization results of our GeoAda on Malonaldehyde and Naphthalene from the MD17 dataset.

Table2. Comparisons for Molecular Dynamics prediction on MD17 dataset (all results reported by ×10−1 ). The best results are highlighted in bold. Results averaged over 5 runs. “NaN” denotes generation collapse due to numerical instability, typically observed in baseline models after fine-tuning on the original task. 

We will also include the following concise explanation of “Marg,” “Class,” and “Pred” in Section 5.1 to improve readability and facilitate interpretation of the results:

The Marginal score measures statistical alignment by computing the mean absolute error (MAE) between binned distributions of model-generated and ground-truth coordinates (or bond lengths for MD17). The Classification score is the cross-entropy of a binary classifier trained to distinguish generated trajectories from real ones, offering insight into sample realism. The Prediction score measures the mean squared error (MSE) of a sequence model trained on generated data and tested on real trajectories, reflecting the utility of generated samples for downstream prediction.  For more detailed metric definitions, please refer to Appendix 8.5.

For Tables 6 and 7, we mainly follow the evaluation metrics used in TargetDiff. We apologize for not elaborating on them in the main text due to space limitations. In the revised version, we will include detailed descriptions in the appendix.

W3. Related work

We thank the reviewer for this feedback. In the camera-ready version, we will expand the related work section to provide more comprehensive coverage of the literature. For the works you mentioned, we will include descriptions such as: "EDM introduced an SE(3)-equivariant framework for 3D molecule generation that significantly improved sample quality" and "TargetDiff further extended these models to structure-based drug design by generating molecules conditioned on protein targets through an SE(3)-equivariant processor."

W4. Typo

Thank you for your careful review and for pointing out these typos. We will correct the two errors you mentioned in Lines121& 267 & 312 in the camera-ready version. We will also thoroughly check the rest of the manuscript to ensure no similar issues remain.

Q1.Multiple Adapters

Yes, GeoAda is able to combine multiple adapters which are separately trained by composing the corresponding scores $\mathbf{s}_\theta$ produced by the adapters together during sampling. To demonstrate such potential, we provide an additional experiment on motion capture dataset by separately training two adapters that correspond to frame control (for additional 5 frames) and global type control (following our setup in Sec 5.2), respectively. The model successfully generates prolonged simulation on the new motion (running) with results of 19.10, 33.63, 50.38, 55.92,61.13,71.34 on 80 160 320 400 560 1000ms, showcasing its strong generalization towards composing different controls.

Q2.Recent Baseline

Thank you for raising this. These are highly relevant and timely papers that appeared concurrently with our work. Based on the results reported in these two papers, we summarize the key numbers as follows:

Table 5: Summary of binding affinity and molecular properties of reference molecules and molecules generated by GeoAda and baselines.

Table 6: Jensen-Shannon divergence of bond distance distributions between reference and generated molecules.

TargetDiff trains molecular generation simply conditioned on protein, and there is future work, such as IP-Diff that further adds protein and molecule interaction as additional conditions. Our work builds on the TargetDiff pipeline, taking off the protein condition during pretraining and adding trainable copy layers for Finetuning, which is the key reason why we mainly compared our result with TargetDiff and may not outperform the latest SOTA methods in every dimension.

But GeoAda consistently improves upon TargetDiff, demonstrating the effectiveness and generality. Moreover, GeoAda is modular by design and can be easily applied to other backbones, making it broadly applicable across future geometric diffusion models.

Q3. FT vs Unified guidance

We appreciate the reviewer for bringing this up — this is an insightful comparison and a key point that reinforces the motivation of our method. While methods like classifier guidance can offer strong control, they typically require training a separate predictor for each property and rely on adversarial gradients during sampling.This restricts their applicability to tasks lacking reliable property-specific classifiers and makes the generation process more prone to instability introduced by adversarial optimization.

In contrast, our fine-tuning approach employs lightweight, easily pluggable adapters without requiring additional predictors. These adapters also provide implicit regularization, reducing reward hacking risks and ensuring stable control. Moreover, our method generalizes effectively across diverse tasks—including frame, global, and subgraph control—where training-free methods may fall short.

Nonetheless, we acknowledge that both fine-tuning and guidance are complementary and promising directions. The choice between them may depend on the specific requirements of the target task.

Summary

We hope our responses sufficiently address your concerns regarding: (1) Writing Redundancy and Clarity, (2) Table and Figure Presentation, (3) Metric Definitions, (4) Related Work Coverage, (5) Minor Typos, (6) Multi Control Composition, (7) Inclusion of Recent Baselines, and (8) Fine-Tuning vs. Training-Free Guidance.

We sincerely thank the reviewer for recognizing the clarity of our framework, the relevance of our control settings, and the strong empirical performance across tasks. We truly appreciate your reconsideration of our work in light of our responses. Thank you again for your valuable and thoughtful feedback.

We sincerely appreciate your positive assessment and valuable suggestions on improving our paper. Regarding your questions, we detailed our responses below.

W1. Novelty beyond ControlNet

We agree that ControlNet is a key inspiration for our work. However, as the reviewer also mentioned, our primary contribution and novelty lie in successfully adapting and extending this paradigm to the geometric deep learning domain which is non-trivial. Our core technical innovations include:

• Designing domain-specific coupling/decoupling operators that can inject diverse geometric conditions (e.g., global, subgraphs, Frame control) into a pre-trained model.
• Ensuring the adapter architecture is equivariant, which is a fundamental requirement for most geometric tasks and not an aspect of the original ControlNet.
• Demonstrating the versatility of this approach across varied and important geometric tasks like particle /molecular dynamics, human motion, and molecular generation.

We will restructure the introduction and related work sections to more explicitly disentangle our contributions from ControlNet and highlight the unique challenges and solutions for geometric data.

W2. Experimental Details

We sincerely apologize for the lack of clarity regarding experimental details in the main paper and will revise the manuscript to include a more thorough description.

Model Architectures & Trainable Copy Strategy:

For both trajectory control and global control settings, we follow the same setup as GeoTDM [1]. The backbone model used in our method is EGTN, which is also employed for all baselines to ensure fair comparison. The original base model consists of six EGTN layers. We insert three trainable copies at layers 1, 3, and 5. That is, the model architecture becomes:

input → layer1_origin + layer1_copy → layer2_origin → layer3_origin + layer3_copy  
→ layer4_origin → layer5_origin + layer5_copy → layer6_origin → output.

For subgraph control, the base model is following the setting of TargetDiff [2], which has nine layers in total. We apply the same strategy by inserting trainable copies at layers 1, 3, 5, and 7.

We further perform an ablation study on the number of trainable copy layers in Section 5.4 and Appendix 9.3.1 (Table 20). The results show that increasing the number of trainable layers generally improves performance, but also leads to higher parameter count and computational cost, revealing a trade-off between accuracy and efficiency.

Human Motion

The Human Mocap dataset is a widely adopted benchmark for human pose prediction. Due to space limitations, the detailed dataset splits and experimental setup for our human motion experiments are provided in Appendix 8.3.1. For the input/output formats and joint selection, we closely follow the configuration used in MSR-GCN [3], taking in 10 Frames and predicting the following 25 frames.

We sincerely thank the reviewer for pointing out these sources of confusion. In the revised version of the paper, we will explicitly reference both this appendix section and the relevant prior work in the main text to enhance clarity and improve accessibility for readers.

[1] Geometric trajectory diffusion models.

[2] 3d equivariant diffusion for target-aware molecule generation and affinity prediction.

[3] MSR-GCN: Multi-Scale Residual Graph Convolution Networks for Human Motion Prediction

Q1. Subgraph Control

Thank you for raising this interesting question. In the case that the subgraph control $\mathcal{C}$ is part of the graph $\mathcal{G}$ itself, we can instead implement the coupling operator f as an identity function since the original graph is already a supergraph of the subgraph control. For the decoupling operator, we can keep it the same that extracts the nodes that need to optimize from the output of the model and discards the nodes in the subgraph control $\mathcal{C}$.

Q2. Global type Control

Yes, the coupling function $f$ is trained together with the rest of the model. In line 150 we introduce $f$ as an MLP as a general case, while we practically find that a simple linear layer already works well enough for $f$ thus having kept such a design. We will clarify this point in the final version.

Q3. Selection of Trainable copies

As mentioned in W2,

input → layer1_origin + layer1_copy → layer2_origin → layer3_origin + layer3_copy  
→ layer4_origin → layer5_origin + layer5_copy → layer6_origin → output. 

is an example of selecting the first layer of every K=2 layers. We will incorporate the corresponding clarifications into the main text in the revised version.

Q4. multiple adapters

Yes, GeoAda is able to combine multiple adapters which are separately trained by composing the corresponding scores $\mathbf{s}_\theta$ produced by the adapters together during sampling.

To demonstrate such potential, we provide an additional experiment on motion capture dataset by separately training two adapters that correspond to frame control (for additional 5 frames) and global type control (following our setup in Sec 5.2), respectively. The model successfully generates prolonged simulation on the new motion (running) with results of 19.10, 33.63, 50.38, 55.92, 61.13, 71.34 on 80 160 320 400 560 1000ms, showcasing its strong generalization towards composing different controls.

Q5. Equation (6)

Thank you for pointing out the ambiguity in Equation (6). We confirm that $\phi_h$ is a vector, and the use of the dot symbol “$\cdot$” was a typo. The intended operation is element-wise multiplication, and we will correct the symbol to “$\odot$” in the final manuscript to ensure clarity.

Q6. nan & –

Thank you for pointing out this confusion.

“NaN” indicates that the model experienced generation collapse and failed to produce valid outputs due to numerical instability. This issue was observed in certain baseline models after fine-tuning, particularly when evaluated on the original task, where they were unable to generate numerically valid samples. This further highlights the necessity of our method, which preserves stability and avoids such collapse.

The “–” in Table 1 for Prompt-Tem under the unconditional setting denotes that this baseline is not applicable. Prompt-Tem is specifically designed to match a known conditioning frame (e.g., frame 5 to frame 10), and thus cannot be meaningfully applied to unconditional generation scenarios where no such conditioning exists.

We sincerely thank the reviewer for pointing out the lack of explanation for these two cases. In the revised version, we will update the caption of Table 1 as follows to provide a clearer description:

Table 1. Comparisons on the CHARGED PARTICLES dataset (all results reported as ×10⁻¹). (↑)/(↓) indicates whether a higher/lower value is preferred. “NaN” denotes generation collapse due to numerical instability, typically observed in baseline models after fine-tuning on original task. “–” indicates that the baseline Prompt-Tem requires explicit conditioning and cannot be applied when no conditioning frame is given.

Summary

We hope our answers sufficiently address your concerns regarding: (1) Novelty Clarification, (2) Experimental Details,(3) Subgraph Control Integration, (4) Global Control MLP Training, (5)Trainable Copy Selection,(6) Multiple Adapter Composition, (7) Equation. 6 Notation, and (8)“NaN” and “–” Clarification.

We also sincerely thank the reviewer for the positive feedback on both the technical soundness of our approach and the breadth of our experimental validation. We truly appreciate your reconsideration of our work in light of our responses. Thank you once again for your valuable insights.

Thank you for your detailed review and valuable feedback. We have addressed your concerns below and hope these clarifications will assist you in re-evaluating and update the score:

W1. Sensitive Results

Thank you for pointing this out — this is indeed an important aspect. To better quantify the impact of architectural choices, we’ve conducted ablation study on the number of trainable copy layers, reported in Section 5.4 and Appendix 9.3.1 (Table 20). The results show that increasing the number of trainable layers generally improves performance, but also introduces additional parameters and computational cost, highlighting a trade-off between accuracy and efficiency.

We further ablated the architectural design of our adapters in Section 5.4 and Appendix 9.3.2. Specifically, we evaluated two variants to assess the role of the equivariant zero convolution: (1) replacing it with standard Gaussian-initialized convolutions, and (2) replacing each trainable copy block with a single convolution layer. Both modifications resulted in noticeable performance degradation, emphasizing the importance of zero initialization and the proposed structural design for stable and effective fine-tuning.

We apologize for not presenting these results more clearly in the main paper due to space limitations. In the revised version, we will include key tables and results in the main text to improve clarity and visibility.

W2. Usage details

We apologize for the confusion, and we completely agree that parameter analysis is important. As mentioned in Section 5.4, we report the number of tunable parameters for different tuning strategies in Appendix 9.3, Table 21. Specifically, Full Fine-Tuning involves 1,418,252 tunable parameters (~5.41 MB), whereas GeoAda only requires 711,791 tunable parameters (~2.72 MB), effectively reducing the parameter count by half. Despite this reduction, GeoAda achieves better or comparable performance on downstream tasks while also preserving performance on the original task, avoiding issues such as model forgetting or collapse. We will make sure to highlight this quantitative analysis more clearly in the main text of the revised version.

W3. OOD result

Evaluating robustness to OOD controls is indeed a valuable aspect. We further evaluate our model on OOD task involving frame control on Charged Particle setting conditioning on 5 frames to predict the next 20 frames.

These results highlight the strong OOD generalization and downstream performance of GeoAda.

W4. Feature

Thank you for this suggestion. To provide deeper insight into the behavior of the adapters, we generated visualizations comparing the outputs of the original (frozen) network, the trainable copy, and the ground truth during inference. These comparisons help illustrate how the adapter modifies the generation trajectory and captures control-relevant structures. Due to the rebuttal policy restricting figures, we are unable to include these results here, but we will incorporate them in the camera-ready version to support a more comprehensive understanding of the model's effect.

Q1. Metrics Descriptions in Main Paper

We fully agree that these metrics should be better introduced in the main text to offer more background for the reader. In the revised version, we will include the following concise explanation of “Marg,” “Class,” and “Pred” in Section 5.1 to improve readability and facilitate interpretation of the results:

The Marginal score measures statistical alignment by computing the mean absolute error (MAE) between binned distributions of model-generated and ground-truth coordinates (or bond lengths for MD17). The Classification score is the cross-entropy of a binary classifier trained to distinguish generated trajectories from real ones, offering insight into sample realism. The Prediction score measures the mean squared error (MSE) of a sequence model trained on generated data and tested on real trajectories, reflecting the utility of generated samples for downstream prediction.  For more detailed metric definitions, please refer to Appendix 8.5.

Q2. NaN

“NaN” indicates that the model experienced generation collapse and failed to produce valid outputs due to numerical instability. This issue was observed in certain baseline models after fine-tuning, particularly when evaluated on the original task, where they were unable to generate numerically valid samples. This further highlights the necessity of our method, which preserves stability and avoids such collapse. We sincerely thank the reviewer for pointing out the lack of explanation for these two cases. In the revised version, we will update the caption of Table 1 as follows to provide a clearer description:

Table 1. Comparisons on the CHARGED PARTICLES dataset (all results reported as ×10⁻¹). (↑)/(↓) indicates whether a higher/lower value is preferred. “NaN” denotes generation collapse due to numerical instability, typically observed in baseline models after fine-tuning on the original task. “–” indicates that the baseline Prompt-Tem  requires explicit conditioning and cannot be applied when no conditioning frame is given.

Q3. Backbone & Pretrained Model

We sincerely apologize for the lack of clarity regarding experimental details in the main paper and will revise the manuscript to include a more thorough description.

For both frame control and global control settings, we follow the same setup as GeoTDM [1]. The backbone model used in our method is EGTN, which is also employed for all baselines to ensure fair comparison. The original base model consists of six EGTN layers. We insert three trainable copies at layers 1, 3, and 5. That is, the model architecture becomes:

input → layer1_origin + layer1_copy → layer2_origin → layer3_origin + layer3_copy  
→ layer4_origin → layer5_origin + layer5_copy → layer6_origin → output.

For subgraph control, the base model is following the setting of TargetDiff [2], which has nine layers in total. We apply the same strategy by inserting trainable copies at layers 1, 3, 5, and 7.

[1] Geometric trajectory diffusion models.

[2] 3d equivariant diffusion for target-aware molecule generation and affinity prediction.

Q4. Change FT with Downstream

Thank you for this valuable suggestion to improve clarity! We will replace “FT” with “Downstream” in all tables in the revised version.

Q5. Subgraph Control on Pretrain

On the subgraph control task, all baseline methods are trained from scratch on the downstream CrossDocked dataset with protein pocket conditions. In contrast, our method is first pretrained on unconditional datasets (QM9 and GEOM-Drugs) and then fine-tuned on the downstream task, demonstrating GeoAda’s effectiveness and generalizability. Therefore, we do not report baseline performance on QM9 or GEOM-Drugs. However, this does not affect our conclusions, as our method is designed to preserve performance on the pretraining dataset while enabling effective adaptation to new tasks.

Summary

We hope our answers sufficiently address your concerns regarding: (1) Sensitive study Results, (2) Parameter Efficiency, (3) OOD Robustness, (4) Adapter Behavior Visualization, (5) Metric Descriptions, (6) “NaN” Clarification, (7) Pretrained Backbone and Architecture, (8) Table Label Clarity, and (9) Subgraph Control results on pretrain.

We also sincerely thank the reviewer for the positive feedback on the motivation, theoretical soundness, and practical relevance of our method, as well as the recognition of our strong and diverse experimental results. We truly appreciate your reconsideration of our work in light of our responses. Thank you once again for your valuable insights.

We sincerely appreciate your positive assessment and valuable suggestions on improving our paper. Regarding your questions, we detailed our responses below.

W1. Novelty beyond ControlNet

We agree that ControlNet is a key inspiration for our work. However, our primary contributions and novelty lie in successfully adapting and extending this paradigm to the geometric deep learning domain which is non-trivial. Our core technical innovations include:

• Designing domain-specific coupling/decoupling operators that can inject diverse geometric conditions (e.g., global, subgraphs, Frame control) into a pre-trained model.
• Ensuring the adapter architecture is equivariant, which is a fundamental requirement for most geometric tasks and not an aspect of the original ControlNet.
• Demonstrating the versatility of this approach across varied and important geometric tasks like particle /molecular dynamics, human motion, and molecular generation. We will restructure the introduction and related work sections to more explicitly disentangle our contributions from ControlNet and highlight the unique challenges and solutions for geometric data.

W1.Typos

Thank you for your careful review and for pointing out these typos. We will correct the two errors you mentioned in Lines 51 & 138 in the camera-ready version. We will also thoroughly check the rest of the manuscript to ensure no similar issues remain.

Q1. Notation in Eq. (7)

Thank you for this insightful question. You are correct that our adapter acts on intermediate activations, not just the final layer, as shown in Figure 2, where the adapter $s_{\theta', \phi}$ processes the control $\mathcal{C}$ in addition to the original inputs $(\mathcal{G}_\tau, \tau)$.

We use the notation in our loss function to express the high-level training objective in a clear and compact way: This formula defines the overall goal, training the adapter $s_{\theta', \phi}$ to produce a corrective signal that is added to the frozen model’s $\epsilon_\theta$ prediction.
The layer-by-layer additions in our architecture are the concrete mechanism to achieve this high-level objective.

We acknowledge this distinction could be clearer and will revise Section 3.2 to explicitly connect the objective function with its layer-wise architectural implementation.

Summary

We hope our answers address your concerns. Thanks again for recognizing our contribution to this important and challenging topic, as well as the effectiveness of our approach and the comprehensiveness of our evaluation.