Recent research in tabular data synthesis has focused on single tables, whereas real-world applications often involve complex data with tens or hundreds of interconnected tables. Previous approaches to synthesizing multi-relational (multi-table) data fall short in two key aspects: scalability for larger datasets and capturing long-range dependencies, such as correlations between attributes spread across different tables. Inspired by the success of diffusion models in tabular data modeling, we introduce $\textbf{C}luster$ $\textbf{La}tent$ $\textbf{Va}riable$ $guided$ $\textbf{D}enoising$ $\textbf{D}iffusion$ $\textbf{P}robabilistic$ $\textbf{M}odels$ (ClavaDDPM). This novel approach leverages clustering labels as intermediaries to model relationships between tables, specifically focusing on foreign key constraints. ClavaDDPM leverages the robust generation capabilities of diffusion models while incorporating efficient algorithms to propagate the learned latent variables across tables. This enables ClavaDDPM to capture long-range dependencies effectively. Extensive evaluations on multi-table datasets of varying sizes show that ClavaDDPM significantly outperforms existing methods for these long-range dependencies while remaining competitive on utility metrics for single-table data.
Paper
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Peer review
Summary
The paper tackles the problem of synthetic data generation in tabular formats and particularly focuses on data generation in multi-relational (multi-table) setups like relational databases. Whereas existing tabular diffusion models work only on single tables, the proposed ClavaDDPM extends the DDPM framework to support many relational tables linked via primary-foreign keys. In the hierarchy of parent-child tables, child tables contain keys from parent tables, and ClavDDPM conditions the generative process of child entries on their parent entries (grouped by the foreign key). To enable this, the model learns latent variables (expressed as GMMs) corresponding to the groups of foreign keys. Capturing the hierarchy of parent-child relations enables learning quite deep, long-range dependencies between k-hop neighbors in the relational schema. Experimentally, ClavaDDPM outperforms existing non-diffusion baselines both in terms of effectiveness and efficiency.
Strengths
**S1.** The problem of synthetic data generation is of growing importance in the era of large, data-hungry models whose quality depends on the quality of training data. Besides, synthetic generation enables upsampling of a small custom dataset (with possible private and sensitive data) for fine-tuning backbone models. In the world of relational databases, most databases consist of multiple linked tables that have to be modeled jointly to capture data dependencies. ClavaDDPM is the first tabular DDPM that supports generation conditioned on multiple tables (organized in several hierarchy levels) and can be used on real-world datasets. **S2.** The idea of learning latent variables with classifier guidance for grouped keys is rather clever. In addition, the model supports both numerical and categorical data as well as attempts to model the generative process for tables with several parents. Conditioning on several parent tables, the authors propose soft matching of latents (conditioned on each parent separately) via approximate nearest neighbor search. **S3.** Compelling experimental results - ClavaDDPM was compared against existing non-diffusion multi-table models (PrivLava and Synthetic Dava Vault), the authors also adapted single-table baselines CTGAN and TabDDPM in several versions as baselines. Ablation studies are informative. **S4.** The paper is well-written and structured, I enjoyed reading the manuscript.
Weaknesses
**W1.** The idea of long-range dependencies in relational tables has been introduced in the beginning and highlighted in the experiments, but the main part (Section 4) does not go into the details. Perhaps Section 4.2 could expand on long-range modeling mapping to the example hierarchy from Figure 1. **W2.** No discussion of the limitations, e.g., how long the training took; inference on the datasets takes several days. The checklist mentions “the second paragraph of the Conclusion” but this section in the manuscript has only one paragraph.
Questions
**Q1.** Most of the reported numbers (total variation distance between synthetic and real data) are in the higher 95%+ range which makes it hard to distinguish the quality of new models. Are there any other metrics close to real-world tasks that could be of use? For instance, TabDDPM and others report the quality of CatBoost/XGBoost and other standard tabular ML algorithms trained on the synthetic data. Comments: * Line 206: Typo in LavaDDPM * Captions of Tables 1 and 2 could also mention what the reported metrics are.
Rating
7
Confidence
3
Soundness
3
Presentation
4
Contribution
3
Limitations
There is no discussion of the limitations.
Summary
This paper proposes the new ClavaDDPM approach to address the scalability and long-range dependency challenges in tabular data synthesis. ClavaDDPM uses clustering labels to model inter-table relationships, particularly focusing on foreign key constraints, and employs diffusion models' robust generation capabilities along with efficient algorithms to propagate learned latent variables across tables. Evaluations demonstrate ClavaDDPM's superior performance in capturing long-range dependencies and competitive utility metrics for single-table data.
Strengths
$\bullet$ The manuscript is commendably well-structured, with a logical flow that effectively guides the reader through the paper. The clarity in writing and the organization of content significantly enhance the reader's comprehension and the overall quality of the presentation. $\bullet$ The authors have conducted a thorough experimental validation, which is a significant strength of the paper. The meticulous detailing of experimental procedures, including data handling, model training, and evaluation metrics, greatly contributes to the reproducibility and credibility of the study. $\bullet$ The topic of the paper addresses a highly relevant issue in the field, which is a strong point. The research aligns well with current trends and challenges in the domain, ensuring that the findings will be of interest to a broad audience and have potential applications in real-world scenarios.
Weaknesses
$\bullet$ The manuscript exhibits a lack of punctuality and standardization in the presentation of mathematical formulas, leading to potential ambiguity in interpretation. Key terms are not consistently defined upon first use, and there is a misuse of symbols that may confuse readers. Additionally, the placement of table names appears to be incorrect in some instances, further detracting from the paper's clarity. It is essential to standardize the notation and ensure consistent definitions and proper placement of table names for better readability. $\bullet$ The assumptions made in the model section require more rigorous justification. The authors should provide a more detailed explanation of why these assumptions are reasonable and how they contribute to the validity of the model. This will strengthen the theoretical foundation of the work and enhance the credibility of the proposed approach. $\bullet$ The paper would benefit from an analysis of the model's complexity, particularly in the context of large-scale databases. Given the increasing size and complexity of real-world databases, understanding how the proposed model scales and performs under such conditions is crucial. Including a complexity analysis will provide insights into the model's practicality and efficiency. $\bullet$ The ablation study regarding the cluster number 'k' lacks necessary granularity. A more fine-grained investigation is needed to understand the impact of varying 'k' on the model's performance and to identify the optimal settings for different scenarios. This will provide a clearer understanding of the model's behavior and its adaptability to various contexts. $\bullet$ The section on the multi-relational synthesis problem, currently placed in the appendix, should be relocated to the main body of the paper. This will improve the flow of the paper and make it easier for readers to follow the synthesis process and understand its relevance to the overall work. Integrating this section into the main text will enhance the coherence and comprehensiveness of the paper.
Questions
See the above weaknesses.
Rating
4
Confidence
3
Soundness
2
Presentation
3
Contribution
2
Limitations
No.
Summary
This paper proposes ClavaDDPM to address two key deficiencies in multi-table data generation: scalability for larger datasets and capturing long-range dependencies, such as correlations between attributes across different tables. This approach utilizes cluster labels as intermediaries to model relationships between tables, paying special attention to foreign key constraints. The authors elaborated on the proposed method, made some assumptions, conducted some experiments for evaluation, and performed some analysis about the results.
Strengths
1. The paper proposes an efficient framework to generate multi-relational data that preserves long-range dependencies between tables, and proposes relation-aware clustering for modeling parent-child constraints. 2. The paper applies a matching technique based on approximate nearest neighbor search as a general solution to the problem of multi-parent relation synthesis for a child table with multiple parents.
Weaknesses
1. I have some concerns about the assumptions made in the paper, which seem to be somewhat inconsistent with the scenarios in real world settings. Please refer to Questions 1 and 2 for details. 2. There may be some clarifications needed in the experimental section. Meanwhile, the analysis of the experimental results does not cover some key points. Please refer to Questions 3-6 for details. 3. There are some problems with the writing and formatting of this paper. Please refer to Questions 7-8 for details. Also, there are some confusing statements in the paper, which hinder the readability of the paper. Please refer to Questions 9-10 for details.
Questions
1. The paper assumes that there are parent-child relationships between different tables and the relationships are known. I However, in real life, the relationships may be very complex and may not be known in advance. In this case, how can ClavaDDPM handle it? 2. The i.i.d. assumption in Section 4.1 seems too strong, because the child rows corresponding to different primary keys may not be independent in real-world scenarios. If this is the case, does the theoretical analysis in the paper still hold? 3. Please clarify why you selected CTGAN over newer or state-of-the-art models like CTAB-GAN, TabSyn, and CoDi mentioned in the related work for your experiments. 4. The reason for the absence of average agree rate in the last two columns of Table 2 remains unclear. Additionally, it is not specified what NA represents. Moreover, there is a lack of clarity regarding the calculation method and formula used to determine the agree rate in this experiment. 5. I feel a bit confused about why TabDDPM converges so slowly on the Instacart05 and Movie Lens datasets. The authors of TabDDPM stated in their work that TabDDPM can converge quickly with a 2080Ti GPU. In addition, I noticed that the Berka dataset seems to be larger than those two datasets. Could you kindly provide an explanation as to why TabDDPM exhibits convergence on this larger dataset, while failing to do so on the two smaller datasets? 6. Are the evaluation metrics used in the experiment widely used in the field or are they proposed by the authors? I haven't seen similar metrics in related works. If they are proposed by the authors, why don't you use metrics from other papers, such as the relative error used in PrivLava [1] or more comprehensive metrics used in TabSyn [2]? 7. There are some typos in the paper: “LavaDDPM” in line 206, “Dnorm” in the caption of Table 1, “The experiment result show…” in line 355. 8. Page 18's experimental results table lacks a caption. 9. In Section 5.2, you referred to additional results in Appendix 5.3, which is missing from the paper. Please provide the mentioned experimental results. 10. In the checklist, you said that you discussed the limitations and future work in the second paragraph of the conclusion section, but there is no relevant discussion in the conclusion of the paper, not even the second paragraph, which is confusing. Reference: [1] K. Cai, X. Xiao, and G. Cormode. Privlava: synthesizing relational data with foreign keys under differential privacy. Proceedings of the ACM on Management of Data, 1(2):1–25, 2023. [2] H. Zhang, J. Zhang, B. Srinivasan, Z. Shen, X. Qin, C. Faloutsos, H. Rangwala, and G. Karypis. Mixed-type tabular data synthesis with score-based diffusion in latent space. arXiv preprint arXiv:2310.09656, 2023.
Rating
3
Confidence
3
Soundness
2
Presentation
2
Contribution
2
Limitations
n/a
Reference List and Table 2
**Reference** [1] K. Cai, X. Xiao, and G. Cormode. Privlava: synthesizing relational data with foreign keys under differential privacy. Proceedings of the ACM on Management of Data, 1(2):1–25, 2023. [2]N. Patki, R. Wedge, and K. Veeramachaneni. The synthetic data vault. In 2016 IEEE international conference on data science and advanced analytics (DSAA), pages 399–410. IEEE, 2016. [3] F. Li, B. Wu, K. Yi, and Z. Zhao. Wander join: Online aggregation via random walks. In Proceedings of the 2016 International Conference on Management of Data, pages 615–629,2016. [4] C. Ge, S. Mohapatra, X. He, and I. F. Ilyas. Kamino: constraint-aware differentially private data synthesis. Proc. VLDB Endow., 14(10):1886–1899, jun 2021. [5] T. Stadler, B. Oprisanu, and C. Troncoso. Synthetic data – anonymisation groundhog day. In 31st USENIX Security Symposium (USENIX Security 22), pages 1451–1468, Boston, MA, Aug. 2022. USENIX Association. [6] A. Kotelnikov, D. Baranchuk, I. Rubachev, and A. Babenko. Tabddpm: Modellingtabular data with diffusion models. In International Conference on MachineLearning, pages 17564–17579. PMLR, 2023. [7] H. Zhang, J. Zhang, B. Srinivasan, Z. Shen, X. Qin, C. Faloutsos, H. Rangwala, and G. Karypis. Mixed-type tabular data synthesis with score-based diffusion in latent space. arXiv preprint arXiv:2310.09656, 2023. $\quad$ **Table 2: ClavaDDPM vs ClavaTabsyn** |Berka|Overall|Col Shape|0-hop|Cardinality|1-hop| |-|-|-|-|-|-| |ClavaTabsyn|93.39|88.65|92.83|93.47|98.59| |ClavaDDPM|96.29|94.56|94.12|97.55|98.93|
Please read and respond to the rebuttal
Dear reviewers, First of all, thank you for your service to the ML community. Writing high-quality reviews and engaging with authors' responses is essential to a healthy ML research community. It is essential that you read the rebuttals and provide a response and/or follow-up questions within the next few days. This will allow the authors sufficient time to react. While a detailed response addressing all points is not necessary, at a minimum, you should indicate you have read and considered the review and whether you will maintain or revise your score. Please also take the time to read the other reviews. I want to thank you again, and I look forward to following the discussions here.
Summary
This work addresses the challenges inherent in generating multi-relation tabular data and proposes a novel generation method based on hidden random variables. The approach analysis correlations between primary and foreign keys between tables by predicting hidden variables associated with these keys within simultaneous tables. These hidden random variables are inferred using Denoising Diffusion Probabilistic Models (DDPM) grounded in stochastic processes. The method is elaborated from two-table linkage generation to multi-table linkage generation, with a step-by-step explanation of the approach. Comprehensive experiments are conducted to demonstrate the practical effectiveness of the proposed method.
Strengths
This paper highlights the extensive dependencies between different tables in the process of multi-relation tabular data synthesis and introduces an innovative approach by analyzing the relationships between primary keys and foreign keys using hidden variables. The proposed ClavaDDPM process is well-articulated and has demonstrated promising results across several datasets. Additionally, the subsequent analysis of hidden variables enhances the credibility of this work.
Weaknesses
Although this work attempts to elaborate on its theoretical framework with substantial content, the notation system and descriptive symbols used do not conform to standard academic mathematics conventions (see sections 3. Background and 4.1 Notations). The marks in equation are not uniform (Eq.2). Furthermore, several key formulas lack thorough proofs (for example, Formula 8). The proof of this key formula would be best placed in the appendix. Additionally, Formula 3 from a previous study lacks supporting evidence; a brief explanation of its proof process or an indication of its rationale is necessary. The validity of the method “we introduce latent random variables c such that g is independent of y conditioned on c” also requires theoretical verification.
Questions
Question 1: In line 79 to 85, the author mention table with R and relation with R. Is this means that a relation in Relational Database is a table in this paper? Since the relations are model as edges of graph. Question 2: According to the paper content, the author mention that “the primary key of table serves as the unique identifier for each row in the table”. And in section 4.1 the rows in parent table can suitable i.i.d assumption. If every row is unique, how rows can be suitable independent and identification distributions? Question 3: From the perspective of learning latent variable method alone, what are the advantages of CLavaDDPM proposed in this paper compared with other studies?
Rating
5
Confidence
3
Soundness
3
Presentation
2
Contribution
3
Limitations
The authors adequately addressed the limitations.
Rebuttal to the Questions
**A1: Terminologies of table** Yes, a relation is a table. In this paper, we primarily adhere to the terminology used in relational database literature, where a “table” is formally referred to as a “relation”, and multi-relational synthesis corresponds to multi-table synthesis. Consequently, our notation slightly differs from previous works that only consider single tables, such as TabDDPM[2] and TabSyn[3]. To be clear, we used “tables” and “relations” interchangeably in the paper. Specifically, we model “relations” or “tables” as nodes and “foreign key constraints” as edges, consistent with relational database terminology. We apologize for any confusion and will clarify this further in the revised version. $\quad$ **A2:I.i.d. assumptions** We fully understand your concern. In our work, the term “unique identifier” refers to a unique ID for a row and is not related to the data distribution itself. Below is an example table: |Primary key(id)|Gender|Country| |-|-|-| |2|M|US| |3|F|UK| In this table, the primary key (unique identifier) is simply an ID, while the actual data distribution involves attributes like (gender, country). By i.i.d., we mean that the distribution of $(gender, country)$ is independent. When modeling, the primary key is not included as part of the data but is used solely for enforcing foreign key constraints. For example, if a child table row has a foreign key value of $3$, it refers to the row $(F, UK)$ in the parent table. The value $3$ is not passed into the diffusion model and is assigned additionally. Similarly, previous works in tabular data synthesis, such as SDV, PrivLava, and TabDDPM, treat keys as identifiers rather than data, with key values not being passed into the model. We will clarify this in our revised version to prevent further confusion. $\quad$ **A3: Latent variable learning** In the context of tabular data synthesis, PrivLava[4] is the only prior work that has learned latent variables (excluding the works that directly adopt latent generative models, which do not explicitly learn latent variables). Compared to PrivLava, our approach is agnostic to data domain size and has faster convergence. PrivLava's latent learning is marginal-based, making it applicable only to predefined fixed domains (they primarily support integers). Additionally, their use of the EM algorithm is slow and prone to convergence issues in practice. Our experiments in Section 5, Table 1, demonstrate that their method fails to converge on many real-world datasets. Importantly, our method (diagonal covariance GMM) enforces our independence assumption and aligns with our theoretical analysis. In Section 4.1, Equation 7, we assume that child table groups $g$ are independent of parent row $y$, conditioned on latent variable $c$. Thus, we learn latent variable $c$ such that its distribution supports this assumption. As mentioned in Section 4.3.1, we use a GMM with diagonal covariances in the joint space of $(X, Y)$. This ensures that, when the GMM is properly trained, the covariance between $X$ and $Y$ is zero in each Gaussian cluster with centroid $c$. Consequently, conditioned on $c$, $g$ and $y$ will tend to be independent, as $g$ is a collection of $X$. While more advanced latent learning methods, such as VQVAE[5], could perform latent learning and quantization simultaneously, we considered them during development but identified potential trade-offs in terms of runtime. Currently, the runtime of the latent learning phase is negligible compared to other phases, and VQVAE lacks synergy with our theoretical assumptions. Nevertheless, as noted at the end of Section 4.3.1, we are open to exploring the impact of other latent learning methods in future work.
Rebuttal to the Weakness
>Although this work attempts to elaborate on its theoretical framework with substantial content, the notation system and descriptive symbols used do not conform to standard academic mathematics conventions (see sections 3. Background and 4.1 Notations). **R: Non-standard notations** Thank you for pointing this out. We acknowledge that our notation differs slightly from the standard. In probability theory, capital letters typically denote random variables, while lower case letters represent their actual values. We modified this convention to distinguish between row data and table data. For example, we use $x$ to denote a row of a child table and $X$ to denote the entire child table. To avoid conflicts, we use bold letters $\mathbf{x}$ and $\mathbf{X}$ to represent the corresponding random variables. To clarify this further, we will describe our design choices in detail and ensure consistency throughout the manuscript in the revised version. $\quad$ >The marks in equation are not uniform (Eq.2) **R: Non-uniform marks** We obtained Equation 2 from the Background section of TabDDPM[2]. We would greatly appreciate it if you could point out the specific issues with the notation or formality, and we are more than happy to make any necessary improvements. $\quad$ >Furthermore, several key formulas lack thorough proofs (for example, Formula 8). The proof of this key formula would be best placed in the appendix. **R: Proofs for formula** We agree with your observation that this is a key formula in our work. The derivation is based on Equation 7. Due to space constraints, we provided only a brief one-line expansion in the main paper. We appreciate your suggestion and will include a detailed proof in the appendix. $\quad$ >Formula 3 from a previous study lacks supporting evidence; a brief explanation of its proof process or an indication of its rationale is necessary. **R: Formula 3** Formula 3 is directly adopted from previous work [1], which was derived using Bayes' theorem. Due to space limitations, we were unable to provide a more detailed explanation in the main paper and included only the result. However, we appreciate your point and will add a more detailed background section in the appendix of the revised version. Additionally, we will briefly mention the Bayesian modeling rationale in the main paper. $\quad$ >The validity of the method “we introduce latent random variables c such that g is independent of y conditioned on c” also requires theoretical verification. **R: Validity of assumption** This is a valid concern. In fact, ClavaDDPM adopts a Bayesian modeling paradigm, where we make certain Bayesian assumptions and let the trained models enforce those assumptions. Therefore, we chose GMM with diagonal covariance, which by design learns latent variables $c$ that enforce conditional independence between $g$ and $y$ (with covariance being zero). We will include a more detailed demonstration of this aspect in the appendix to better address the theoretical foundations.
References
[1] P. Dhariwal and A. Nichol. Diffusion models beat gans on image synthesis. Advances in neural information processing systems, 34:8780–8794, 2021. [2] A. Kotelnikov, D. Baranchuk, I. Rubachev, and A. Babenko. Tabddpm: Modelling tabular data with diffusion models. In International Conference on Machine Learning, pages 17564–17579. PMLR, 2023. [3] H. Zhang, J. Zhang, B. Srinivasan, Z. Shen, X. Qin, C. Faloutsos, H. Rangwala, and G. Karypis. Mixed-type tabular data synthesis with score-based diffusion in latent space. arXiv preprint arXiv:2310.09656, 2023. [4] K. Cai, X. Xiao, and G. Cormode. Privlava: synthesizing relational data with foreign keys under differential privacy. Proceedings of the ACM on Management of Data, 1(2):1–25, 2023. [5] Razavi, Ali, Aaron Van den Oord, and Oriol Vinyals. "Generating diverse high-fidelity images with vq-vae-2." Advances in neural information processing systems 32 (2019).
Thank you, after reading the responses to this and other reviews my concerns are resolved and I remain positive about the work.
Thank you for your time and effort in reviewing our work as well as the rebuttal. We greatly appreciate your constructive feedback and the positive score you've given, which encourages us to further refine the research.
Dear reviewer, Please respond to the rebuttal as is expected of you as a NeurIPS reviewer asap! Thanks
Dear reviewer, Please respond to the rebuttal and provide substantive arguments and, in particular, more concrete strengths and weaknesses of the paper. Unless you update your line of argument, I will not be able to take your review into account in the decision making process.
Thank you for your detailed responses and efforts to address my concerns. I appreciate the clarifications provided, particularly regarding the assumptions in your approach. However, after careful consideration, I have decided to maintain my original score. I believe there are still several areas that require further attention: Reference to Appendix A Notation Summary: I suggest adding explicit references to the notation summary provided in Appendix A within the main text. This will help readers navigate the mathematical formulations more effectively and avoid potential confusion. Issues with Equations 5-9: I noticed that there are some missing symbols in Equations 5 through 9, which result in these equations not being properly formatted. Addressing these inconsistencies is crucial for the clarity and accuracy of your mathematical presentation. Visualization of Label Clustering and Table Relationships: It would be beneficial to include some visualizations that illustrate the relationship between label clustering and table structures. Such visual results would provide additional empirical evidence and enhance the understanding of your approach. Clarification on Mathematical Deduction: You mentioned that you provided a mathematical deduction to strengthen the theoretical foundation of your approach. Could you clarify where and how this deduction is presented in the paper? A clearer explanation or more detailed description would be helpful in understanding the rigor of your theoretical contributions. I hope these suggestions help further refine your work. Thank you again for your dedication and for considering my feedback. I look forward to seeing the final version of your paper.
Thank you for your response and we appreciate your comments that help refine our paper. $\quad$ > Reference to Appendix A Notation Summary Thank you for your feedback. To ensure clarity and consistency, we have included a paragraph at the beginning of Section 4.1 that introduces the relevant notations, such as parent/child tables, the entire database, and the distinctions between data and random variables. This section is complemented by a running example using a subset of the Berka dataset. We appreciate your suggestion and will add a reference to Appendix A for further clarification. $\quad$ > Issues with Equations 5-9 We would greatly appreciate it if you could point out any specific missing symbols or inconsistencies in Equations 5-9. This would help us further improve the clarity and accuracy of our work. $\quad$ >Visualization of Label Clustering and Table Relationships Thank you for your suggestions. We will consider adding some visualizations in the appendix to enhance understanding in the revised version. $\quad$ >Clarification on Mathematical Deduction The mathematical derivation spans from Equation 5 to Equation 10, where we derive a probability expression for the parent-child scenario under the assumptions we have applied. The final expression (Equation 10) illustrates the distribution modeled by each component in the ClavaDDPM framework. We believe this strengthens the theoretical foundations of our work, as previous approaches in tabular data synthesis, such as TabDDPM and TabSyn, do not explicitly provide the probability assumptions they rely on or clarify the distributions they model, instead solving the problem in a purely end-to-end manner. - Equation 5 is a direct result of the i.i.d. assumption on $(g_j, y_j)$. - Equation 6 is based on conditional probability. - Equation 7 introduces an independence assumption we are making. - Equation 8 is a series of conditional probability expansions of Equation 6, given Equation 7. - Equation 9 expands the conditional foreign key group distribution by introducing the group size variable, which directly extends a part of Equation 8. - Equation 10 presents the final expression of the parent-child distribution we are modeling, incorporating the independence assumptions introduced in our work. This final expression involves three probability distributions, each representing a learnable component of the ClavaDDPM framework: - $p(y, c)$ is the augmented parent distribution, modeled by training a parent diffusion model. - $p(s|c)$ is the conditional group size distribution, calculated through frequency counting. - $p(x|c)$ is the conditional child distribution, modeled using classifier-guided diffusion. We are happy to provide further details and welcome any specific recommendations to improve clarity.
Additional comment on question 9
We would like to additionally address question 9, where the mentioned experiment results are actually located in Appendix D.1. It was a typo for reference and we will fix it in the revision.
Decision
Accept (poster)