Causal Deciphering and Inpainting in Spatio-Temporal Dynamics via Diffusion Model

W1: Thank you for your careful review. We appreciate your attention to detail and will correct this typo to accurately reflect the use of front-door adjustment in the abstract.

W2: Thank you for your valuable feedback. For each original spatio-temporal sequence, we enhance the data by first identifying causal regions using a Vision Transformer. We then apply diffusion inpainting to fine-tune the data and fill the identified environmental parts. After inpainting, we perform sampling with a probability ppp to mix the original sequences with the augmented sequences. This process ensures that the generated data maintains spatial and temporal coherence, resulting in high-quality, coherent spatio-temporal sequences.

W3: Thank you for your suggestion. We have supplemented our paper with additional experiments comparing our method with NuwaDynamics. The results demonstrate that our method achieves similar or better performance with only 2 sequences, whereas Nuwa requires 4-5 sequences. This clearly shows the superior quality and efficiency of our generation process.

We selected MAE as the reference metric, and it is evident that our proposed CaPaint outperforms Nuwa across the board. It is worth mentioning that Nuwa requires generating 4 and 5 augmented sequences per spatio-temporal sequence for TaxiBJ+ and KTH, respectively, to achieve its results. In contrast, we only needed to generate 2 sequences to surpass Nuwa's performance. This is because Nuwa can only mix local information around the environment, whereas our method can consider and fill in global details, generating higher-quality data. This aligns with the background of our paper, which addresses data scarcity and uneven sensor collection.

Q1: Thank you for your insightful question. We have provided an example of the inpainting technique in Appendix F. CaPaint effectively fills the environmental regions of the images based on their data distribution. We fine-tuned the Stable Diffusion model on our datasets, enabling it to learn the spatio-temporal data distributions accurately.

The key factors influencing the performance of the inpainting technique in these contexts include:

1. Data Distribution: The model's ability to understand and replicate the inherent distribution of the spatio-temporal data.
2. Model Fine-tuning: The extent to which the Stable Diffusion model has been fine-tuned on the specific datasets to capture the nuances of the data.
3. Environmental Region Identification: The accuracy in identifying and masking the environmental patches that need inpainting.
4. Causal and Non-causal Patch Distinction: The precision in distinguishing between causal and non-causal patches to ensure that the inpainting enhances the model’s generalizability and interpretability

Q2: Thank you for your question. We briefly analyzed this in Section 4.4 of our experiments. Traditional data augmentation methods indeed disrupt spatio-temporal characteristics, leading to two possible outcomes:

1. Data Only Augmentation: If only the data is augmented without corresponding changes to the labels, there is a significant decline in performance due to the loss of spatio-temporal coherence.
2. Data and Label Augmentation: If both the data and labels are augmented together, the performance only slightly declines. This is because augmenting both preserves some of the spatio-temporal characteristics, maintaining a level of coherence between the input data and the expected output.

By retaining some of the intrinsic spatio-temporal properties through coordinated augmentation of both data and labels, the performance remains relatively stable.

Q3: Thank you for your question. As shown in Figure 7 of our experiments section, even when maintaining an equal amount of training data, CaPaint demonstrates superior performance compared to the original backbone model. For instance, when comparing 50% original data with 25% original data combined with 25% augmented data, CaPaint's MAE and MSE are lower than those of the original backbone. This indicates that CaPaint effectively enhances model generalizability by leveraging the augmented data.

I believe my response has addressed your concerns. If you have any further questions, please feel free to let me know. Thank you!

Q1: In line 39-44, the authors lack discussion of why the causality and interpretability of models can improve generalization capabilities when dealing with the uneven, insufficient data collection.

Answer:

1. When data is sparse, models may learn shortcut solutions from biased data, as noted in several studies [1-3]. These shortcuts can significantly interfere with causal discovery, which relies on counterfactual reasoning to understand the underlying mechanisms that generate the observed data. In spatio-temporal domains, this issue is particularly critical as the temporal dependencies and spatial correlations are more complex and often underexplored. Traditional approaches have primarily focused on spatio-temporal graphs, but our work extends this to spatio-temporal continuity in image data (video data), a relatively underexplored area. By addressing these gaps, we provide a more robust foundation for understanding and predicting spatio-temporal dynamics, ultimately enhancing the model's ability to generalize from incomplete or biased datasets.
2. Interpretability and causality are strongly correlated. Discovering patterns in model and data predictions is crucial for identifying causality and enhancing interpretability. This process allows us to understand how different variables interact and contribute to the observed outcomes. In our work, we leverage self-supervision and employ global perception by introducing inpainting to dynamically fill in potentially biased areas. This approach ensures that the model can make informed predictions based on a more comprehensive understanding of the underlying data distribution, thus achieving interpretability. This interpretability, grounded in solid causal theory, allows us to make sense of the model's decisions, facilitating better generalization and robustness, especially in scenarios with uneven and insufficient data collection.
3. To help readers better understand the relationship between data scarcity, causality, and interpretability, we have cited more relevant literature in the paper. These citations not only provide a historical context for the technical developments in this area but also highlight the critical correlation between data scarcity, causality, and interpretability. By grounding our discussion in established research, we illustrate how our approach aligns with and advances current understanding, providing a clearer picture of how addressing causality and interpretability can significantly improve generalization capabilities in spatio-temporal data analysis.

Q2: In the left side of Fig.4, the visualizations of finer details are small and not clear enough, so it would be more informative to zoom in on local details of the image.

Answer: Thank you for pointing this out. We appreciate your feedback and recognize the importance of clear and detailed visualizations. To address this issue, we will provide zoomed-in versions of the local details for different datasets to offer a clearer and more informative visualization. To improve the readability of the paper, we have re-arranged the layout of Figure 4. We have enlarged the relevant images and fonts to make it easier for readers to view the finer details. Additionally, we have systematically refined the layout of the entire paper, which includes adjustments to image sizes, fonts, and tables to enhance overall readability**.Upon acceptance, we will include these additional results and enhanced visualizations in the appendix for ease of reference.** This will ensure that all visual details are accessible and that the readers can fully appreciate the improvements and performance of our proposed method.

I believe my response has addressed your concerns. If you have any further questions, please feel free to let me know. Thank you!

Reference:

[1] Causal Attention for Interpretable and Generalizable Graph Classification.

[2] Enhancing Out-of-distribution Generalization on Graphs via Causal Attention Learning.

[3] Reinforced causal explainer for graph neural networks.

Answer(Q1): Thank you for your feedback. We respectfully disagree with the assessment that our method lacks novelty. Our work presents significant improvements and innovations over NuwaDynamics.

1. Conceptual Difference:
   • Our proposed method employs a different approach to causal adjustments, utilizing front-door adjustment rather than back-door adjustment as in NuwaDynamics. Back-door adjustment requires traversing and repeatedly sampling all environmental patches, leading to exponential complexity: ${\cal O}( {T \times {\cal N}_E^{{\cal M}\left( {\rm{*}} \right)}} )$
   • In contrast, our method with front-door adjustment avoids the need for repeated sampling of all environmental patches, reducing the complexity to linear levels: $\cal{O}(T \times {\cal N}_E)$
   • This significant reduction in complexity provides practical advantages, especially in large-scale data processing and real-time applications, by substantially lowering computational resource requirements.
2. Different Methodology:
   • Our approach involves the use of generative models, specifically diffusion inpainting methods, for causal interventions. After fine-tuning the model, it achieves a global awareness of the data, enabling effective inpainting of environmental regions. In contrast, NuwaDynamics can only perceive local information around the surrounding areas.
   • Traditionally, Diffusion Models (DMs) were utilized to generate high-quality synthetic images in the field of Computer Vision (CV). Inspired by the powerful generation capability of DMs given an input picture, we incorporate generative models like DMs into spatio-temporal video data analysis for data augmentation, without harming its efficiency greatly. Our key insight lies in addressing the challenge of data sparsity, and the experimental results have demonstrated that our method achieves significant improvements. This is a substantial innovation in this field.
3. Broad Applicability:
   • Our CaPaint method effectively addresses the issue of exponential complexity found in NuwaDynamics, resulting in more efficient processing. Furthermore, the spatio-temporal data sequences generated by our method are of higher quality, enhancing the robustness and generalizability of the model. This allows CaPaint to be applied in various scenarios, making it advantageous for practical applications and deployment in the industry.

By addressing these aspects, we hope to clarify the distinct advantages and innovations of our method compared to existing approaches.

Answer(Q2): Thank you for your suggestion. Our CaPaint and Nuwa approaches inherently differ in their focus on front-door and back-door adjustments, respectively. Back-door adjustment, as used in Nuwa, requires traversing and repeatedly sampling as many environmental patches as possible, which leads to fundamentally different experimental setups. In contrast, front-door adjustment, which we employ, only needs to perceive the overall environment and fill in the environmental parts. This eliminates the need for repeatedly sampling numerous environmental patches, which is one of the key advantages of our method.

Additionally, in the experimental section of our paper, we have provided a comparison between our method and Nuwa under our settings. The results show that our method outperforms Nuwa across different datasets. This demonstrates the robustness and effectiveness of our approach.

To better explore the results of our method and Nuwa under the same settings, we followed your suggestion to align the experimental setup with that of Nuwa. Additionally, our experiments introduced backbones that have been updated in recent years, meaning the backbones we used are newer than those in Nuwa. Due to limited time and resources, we selected overlapping backbones such as SimVP and PredRNN-V2, and overlapping datasets,TaxiBJ+ and KTH for comparison, setting the environmental ratio to 15% for testing.

We selected MAE as the reference metric, and it is evident that our proposed CaPaint outperforms Nuwa across the board. It is worth mentioning that Nuwa requires generating 4 and 5 augmented sequences per spatio-temporal sequence for TaxiBJ+ and KTH, respectively, to achieve its results. In contrast, we only needed to generate 2 sequences to surpass Nuwa's performance. This is because Nuwa can only mix local information around the environment, whereas our method can consider and fill in global details, generating higher-quality data. This aligns with the background of our paper, which addresses data scarcity and uneven sensor collection.

In summary, our more advanced concept is fundamentally different from Nuwa and is more advantageous for practical applications. I believe my response has addressed your concerns. If you have any further questions, please feel free to let me know. Thank you!

• Details on computational efficiency or scalability of the proposed method are not provided, leaving it as a potential limitation for practical applications.

Thank you for your valuable feedback. We appreciate your concern regarding the computational efficiency and scalability of our proposed method.

1: We leverage the attention mechanism for causal deciphering, which does not introduce additional parameters. This ensures that our model remains efficient without incurring extra computational overhead. 2: In the Introduction, we briefly analyze the computational efficiency of our method. Specifically, traditional backdoor adjustment requires traversing and repeatedly sampling all environmental patches, leading to exponential complexity: ${\cal O}( {T \times {\cal N}_E^{{\cal M}\left( {\rm{*}} \right)}} )$. In contrast, our CaPaint method employs front-door adjustment, which eliminates the need for repeated sampling of all environmental patches. This improvement reduces the complexity to linear levels: $\cal{O}(T \times {\cal N}_E)$.

Reduction in Complexity: Our approach substantially reduces the complexity of the optimal spatio-temporal causal discovery process from exponential to quasi-linear levels. By performing targeted interventions only on identified environmental patches rather than the entire dataset, we achieve significant computational savings.

Scalability: This reduction in complexity ensures efficient causal interventions, making our method more practical and scalable for real-world applications. Our method has been tested across multiple benchmark datasets (FireSys, SEVIR, Diffusion Reaction System (DRS), KTH, and TaxiBJ+), demonstrating its robustness and effectiveness in enhancing model performance.

Practical Applications: By implementing these enhancements, CaPaint provides a robust framework for spatio-temporal dynamics with improved computational efficiency and scalability. This makes it suitable for deployment in various real-world scenarios where data scarcity and computational efficiency are critical concerns.

• More visualization of the prediction results should be included even in supplementary material.

Thank you for your suggestion. In the main body of the paper, we have presented the visualization results for the SEVIR and TaxiBJ+ datasets. Additionally, we have included the visualization results for the KTH and DRS datasets in Appendix I and J, respectively. Although these visualizations are not in the supplementary material section, they are provided in the appendix. Furthermore, Appendix F also showcases the visualization of the inpainting effects of our CaPaint method on the SEVIR dataset.While we believe these visualizations adequately demonstrate the performance advantages of incorporating CaPaint, we are continuously updating our results to include more comprehensive visualizations. Specifically, we plan to add:

1. Visualizations for More Datasets: We will supplement the visualizations with results from the FireSys dataset.
2. Visualizations for Different Backbones: We will include visualization results using different backbone models.
3. Comparisons with Different Augmentation Methods: We will provide comparisons of visualizations using various augmentation methods.

Upon acceptance, we will include these additional results in the appendix for ease of reference. These updates will ensure that our paper provides a comprehensive overview of the performance improvements achieved by our method and its applicability to a wide range of datasets and model architectures.

I believe my response has addressed your concerns. If you have any further questions, please feel free to let me know. Thank you!