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Abstract
3D spatial graphs play a crucial role in biological and clinical research by modeling anatomical networks such as blood vessels, neurons, and airways. However, generating 3D biological graphs while maintaining anatomical validity remains challenging, a key limitation of existing diffusion-based methods. In this work, we propose a novel 3D biological graph generation method that adheres to structural and semantic plausibility conditions. We achieve this by using a novel projection operator during sampling that stochastically fixes inconsistencies. Further, we adopt a superior edge-deletion-based noising procedure suitable for sparse biological graphs. Our method demonstrates superior performance on two real-world datasets, human circle of Willis and lung airways, compared to previous approaches. Importantly, we demonstrate that the generated samples significantly enhance downstream graph labeling performance. Furthermore, we show that our generative model is a reasonable out-of-the-box link predictior.
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2025/paper/3940_paper.pdf
SharedIt Link: Not yet available
SpringerLink (DOI): Not yet available
Supplementary Material: Not Submitted
Link to the Code Repository
https://github.com/chinmay5/semantically_consistent_graph_generation
Link to the Dataset(s)
N/A
BibTex
@InProceedings{PraChi_Semantically_MICCAI2025,
author = { Prabhakar, Chinmay AND Shit, Suprosanna AND Amiranashvili, Tamaz AND Li, Hongwei Bran AND Menze, Bjoern},
title = { { Semantically Consistent Discrete Diffusion for 3D Biological Graph Modeling } },
booktitle = {proceedings of Medical Image Computing and Computer Assisted Intervention -- MICCAI 2025},
year = {2025},
publisher = {Springer Nature Switzerland},
volume = {LNCS 15971},
month = {September},
page = {594 -- 604}
}
Reviews
Review #1
- Please describe the contribution of the paper
This work proposes a semantically consistent diffusion model for 3D biological graph generation. In particular, this work introduces a label-consistent projector that enforces semantic plausibility by stochastically correcting invalid edges during the diffusion process and proposes an edge-deletion noising scheme suitable for sparse anatomical graphs.
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
1 Visualization helps readers better understand. 2 The caption is self-contained.
- Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
1 The paper does not describe in detail the characteristics of training graphs (e.g., average number of nodes, edge class distribution, etc.). 2 Although semantic projection is well-motivated, the stochastic sampling mechanism’s convergence and efficiency tradeoffs are not analyzed. 3 The “edge-deletion only” assumption limits model flexibility. 4 In the diffusion model, it is critical to analyze the sensitivity of the diffusion rate, which is missing in the experiment. 5 Missing sufficient models in the comparison experiments.
- Please rate the clarity and organization of this paper
Satisfactory
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The authors claimed to release the source code and/or dataset upon acceptance of the submission.
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2025/en/REVIEWER-GUIDELINES.html
Please address the weakness points.
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(2) Reject — should be rejected, independent of rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
While the paper proposes a semantically consistent diffusion model for 3D biological graph generation, it falls short in several critical aspects. The training graph characteristics are insufficiently described, making it hard to assess generalizability. The convergence behavior and computational efficiency of the stochastic projection mechanism are not analyzed. Besides, the reliance on edge-deletion limits model flexibility, and the sensitivity to the diffusion rate—a crucial hyperparameter in diffusion models—is not studied. Finally, the experimental comparisons lack breadth, omitting several relevant baseline models. These omissions reduce the paper’s clarity, rigor, and reproducibility, warranting a rejection in its current form.
- Reviewer confidence
Very confident (4)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
N/A
- [Post rebuttal] Please justify your final decision from above.
N/A
Review #2
- Please describe the contribution of the paper
By restricting the edge generation process in graph generation through prior semantic information, it ensures that all edges conform to medical priors and guarantees the effectiveness of the generated results. At the same time, the edge deletion framework is very suitable for sparse biological graphs.
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
- The project method of label consistency strictly controls the semantic rationality in the edge denoising process.
- The process of edge deletion is more suitable for the generation of sparse biological graphs.
- The generated results in the experiment are excellent.
- Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
- The article mainly focuses on the generation of edges, but there is no detailed description of the generation process of nodes, which is likely to cause misunderstandings. The limitations of node generation are also mentioned in the “limitation” section, and in the experiment, it can be seen that the metrics related to nodes (such as edge length, included angle, etc.) are not advantageous enough.
- How can it be ensured that there will definitely be a process that conforms to all semantic priors during the k-times resample process? At the same time, such an edge deletion logic can only ensure that the generated edges are mostly reasonable, but it cannot ensure that all reasonable edges will be generated with a high probability.
- It is recommended that all formulas be listed in a single line like Formula 1, which is convenient for readers to locate and read. At the same time, some Es in the formula of the last paragraph of the Semantically Consistent Projection part lack the superscript hat.
- Please rate the clarity and organization of this paper
Good
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The authors claimed to release the source code and/or dataset upon acceptance of the submission.
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2025/en/REVIEWER-GUIDELINES.html
N/A
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(4) Weak Accept — could be accepted, dependent on rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
All is stated above. The article does not explain the node generation process in detail, nor does it conduct more subsequent processing on node generation, resulting in relatively weak capabilities in this regard.
- Reviewer confidence
Very confident (4)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
N/A
- [Post rebuttal] Please justify your final decision from above.
N/A
Review #3
- Please describe the contribution of the paper
The author propose a two(three)-stage generative framework for 3D biological graphs. It first generates node coordinates via continuous diffusion, followed by discrete diffusion model on edges combined with a label-consistent projector that enforces semantic constraints and structural requirements, which ensures the resulting 3D graphs are “anatomically plausible”.
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
The paper introduces a label-aware projection step so that the model can enforce application-specific rules beyond simple structural constraints. This potentially improves biological realism and utility.
- Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
Introduction:
- The authors flag “anatomical plausibility” as a major challenge but did not clearly explain what this could refer to, and it appears in the following part they just “prevents conflicting neighboring edge labels that are anatomically invalid”. It may be better to tone down, or a least, be more specific about “anatomical plausibility” at the very beginning.
Method:
- Limitations: Node positions are assumed not to co-evolve with adjacency. The graph is non-rotation-equivariant. These bring significant limitations to the model’s capacity and biological meanings.
- Does the adjacency generation have any awareness of node distances or potential collisions? It appears that the constraints are only on edge types but not unrealistic connections constrained by like maximum edge length.
- In this paper the authors aim at generating tree-like structures (airways). How does the model generate a graph with only one connected component? Any math constraints on the graph topological structure or it’s purely relying on the blackbox model itself?
- How often does the model produce conflicts in the first place? If it’s “very frequently”, the post-hoc semetic projection is essentially overwriting the model’s outputs, and the generative distribution learned by the model is meaningless.
- The correction is local, and how will that affect global topological structure?
- Please rate the clarity and organization of this paper
Satisfactory
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The authors claimed to release the source code and/or dataset upon acceptance of the submission.
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2025/en/REVIEWER-GUIDELINES.html
N/A
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(4) Weak Accept — could be accepted, dependent on rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
Overall, my biggest concern is that the performance of the framework largely depends on the post-hoc correction. Even with a totally randomly generated graph, one can still crop it into very good shape in a post-hoc fashion. If this is the case, then it will be meaningless. If the author can clarify this, I would like to give accept.
- Reviewer confidence
Very confident (4)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
Accept
- [Post rebuttal] Please justify your final decision from above.
The authors have addressed my major concerns. Although the framework has limitations, it still provides some value to this community.
Author Feedback
Dear Reviewers and Area Chairs,
We appreciate the reviewers’ valuable remarks and are encouraged by their recognition that our method can enforce application-specific complex semantic constraints (R1,R4), improve results in realism and utility (R1,R4), and edge deletion noising best suits sparse biological graph generation (R1,R3). Here, we address the raised concerns.
Node Generation (R1,R4): This work aims to enforce semantic (& structural) constraints into the edge-generation, a crucial & challenging task for biological graphs. For a fair comparison with prior work, we kept the node generation process unchanged as in [14], which is now detailed in the paper. Thus, node-level metrics stay mostly identical, whereas edge-driven metrics (node degree, semantic validity) improve, confirming the efficacy of our method. As noted in the paper, we defer the co-evolution of nodes and edges as future work, which lies beyond our current scope.
Correction Frequency (R4): In our experiments, the projection affects only ~2% of all the generated edges. These corrections offer minimal intervention to avoid error compounding in model prediction during sampling, rather than frequently overwriting the model output. Such minimal intervention distances our method from a largely post-hoc corrected random graph generator. We have added this to the paper.
Conformity & Likely Edges (R1): We refer to Theorem 1 of [9] showing that constraint-conforming processes exist in the projected space. Because we use the same noising, this result also holds for our resampling setting. We primarily rely on the diffusion model to assign a high probability to reasonable edges, which is supported by the projector module’s minimal intervention (~2%).
Non-rot. Equiv. & Dist. Aware (R4): Our model can support rot. equiv. as in [21]. But, we chose to turn it off following [14] because of orientation bias from acquisition protocols (e.g., patient position) in biological graphs (e.g., airway trees & CoW). The edge generation model uses the fixed node locations as features, making it inherently aware of distances between the nodes and potential collisions.
Tree & Local Correction (R4): As noted in our limitations, our method cannot guarantee one connected component. Following [9,14,20,21], we employ a purely data-driven (black-box) strategy for handling complex topologies. While the projector enforces local semantic validity and some global rules (e.g., tree constraint for ATM), how the local corrections affect global topology is intriguing and remains an open question. Addressing these is left as future work.
Graph Prop. & Diff. Rate (R3): #node spans [40-500] in ATM, & [13-27] in CoW. Average #edge for ATM is ~127, & ~8 for CoW. Such diversity underscores our method’s generalizability. Assuming Diff. Rate means scheduler, we found that linear & cosine with 500 & 1000 steps yield similar results; hence, we follow [21,9] and use linear with 500 steps. All details are now added.
Convergence & Efficiency (R3): Our resampling makes at most k=4 attempts to find a valid edge. Since resampling is stochastic, point-wise convergence is not meaningful. Tab 1 shows that the sampled distribution converges to the data distribution. Our projection is efficient (happens ~2% cases, takes ~0.62ms(w/) vs. ~0.55ms(w/o) per sample).
Missing Models (R3): We outperform recent strong baselines [14] (MICCAI’24) and [9] (NeurIPS’24), both capable of generating complex cyclic topologies. Regrettably, since R3 provides no reference, we cannot address this further.
Edge Deletion (R3): Compared with uniform noising [14], edge deletion [9] outperforms on 6/7 metrics for CoW and 4/7 for ATM (Tab 1), improves downstream labeling (Tab 2), and uniquely enables link prediction (Tab 3). Hence, adopting edge deletion enhances our model’s flexibility rather than limiting it.
Misc: We have improved equations (R1) and updated the intro. to be more specific on anatomical plausibility (R4) in main text.
Meta-Review
Meta-review #1
- Your recommendation
Invite for Rebuttal
- If your recommendation is “Provisional Reject”, then summarize the factors that went into this decision. In case you deviate from the reviewers’ recommendations, explain in detail the reasons why. You do not need to provide a justification for a recommendation of “Provisional Accept” or “Invite for Rebuttal”.
N/A
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Accept
- Please justify your recommendation. You may optionally write justifications for ‘accepts’, but are expected to write a justification for ‘rejects’
N/A
Meta-review #2
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Accept
- Please justify your recommendation. You may optionally write justifications for ‘accepts’, but are expected to write a justification for ‘rejects’
N/A
Meta-review #3
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Accept
- Please justify your recommendation. You may optionally write justifications for ‘accepts’, but are expected to write a justification for ‘rejects’
All reviewers acknowledged the methodological novelty and practical value of the proposed semantically consistent diffusion model for 3D biological graph generation. The authors effectively addressed reviewers’ concerns in their rebuttal. Overall, the paper makes a meaningful contribution and is recommended for acceptance.