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Volumetric Directional Diffusion: Anchoring Uncertainty Quantification in Anatomical Consensus for Ambiguous Medical Image Segmentation

Chao Wu, Kangxian Xie, Mingchen Gao

TL;DR

Volumetric Directional Diffusion provides clinicians with anatomically coherent uncertainty maps, enabling safer decision-making and mitigating risks in downstream tasks, and achieves state-of-the-art uncertainty quantification while remaining highly competitive in segmentation accuracy against deterministic upper bounds.

Abstract

Equivocal 3D lesion segmentation exhibits high inter-observer variability. Conventional deterministic models ignore this aleatoric uncertainty, producing over-confident masks that obscure clinical risks. Conversely, while generative methods (e.g., standard diffusion) capture sample diversity, recovering complex topology from pure noise frequently leads to severe structural fractures and out-of-distribution anatomical hallucinations. To resolve this fidelity-diversity trade-off, we propose Volumetric Directional Diffusion (VDD). Unlike standard diffusion models that denoise isotropic Gaussian noise, VDD mathematically anchors the generative trajectory to a deterministic consensus prior. By restricting the generative search space to iteratively predict a 3D boundary residual field, VDD accurately explores the fine-grained geometric variations inherent in expert disagreements without risking topological collapse. Extensive validation on three multi-rater datasets (LIDC-IDRI, KiTS21, and ISBI 2015) demonstrates that VDD achieves state-of-the-art uncertainty quantification (significantly improving GED and CI) while remaining highly competitive in segmentation accuracy against deterministic upper bounds. Ultimately, VDD provides clinicians with anatomically coherent uncertainty maps, enabling safer decision-making and mitigating risks in downstream tasks (e.g., radiotherapy planning or surgical margin assessment).

Volumetric Directional Diffusion: Anchoring Uncertainty Quantification in Anatomical Consensus for Ambiguous Medical Image Segmentation

TL;DR

Volumetric Directional Diffusion provides clinicians with anatomically coherent uncertainty maps, enabling safer decision-making and mitigating risks in downstream tasks, and achieves state-of-the-art uncertainty quantification while remaining highly competitive in segmentation accuracy against deterministic upper bounds.

Abstract

Equivocal 3D lesion segmentation exhibits high inter-observer variability. Conventional deterministic models ignore this aleatoric uncertainty, producing over-confident masks that obscure clinical risks. Conversely, while generative methods (e.g., standard diffusion) capture sample diversity, recovering complex topology from pure noise frequently leads to severe structural fractures and out-of-distribution anatomical hallucinations. To resolve this fidelity-diversity trade-off, we propose Volumetric Directional Diffusion (VDD). Unlike standard diffusion models that denoise isotropic Gaussian noise, VDD mathematically anchors the generative trajectory to a deterministic consensus prior. By restricting the generative search space to iteratively predict a 3D boundary residual field, VDD accurately explores the fine-grained geometric variations inherent in expert disagreements without risking topological collapse. Extensive validation on three multi-rater datasets (LIDC-IDRI, KiTS21, and ISBI 2015) demonstrates that VDD achieves state-of-the-art uncertainty quantification (significantly improving GED and CI) while remaining highly competitive in segmentation accuracy against deterministic upper bounds. Ultimately, VDD provides clinicians with anatomically coherent uncertainty maps, enabling safer decision-making and mitigating risks in downstream tasks (e.g., radiotherapy planning or surgical margin assessment).
Paper Structure (14 sections, 8 equations, 3 figures, 3 tables)

This paper contains 14 sections, 8 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Preliminaries and Forward Process of VDD
  4. Preliminaries and Forward Process of VDD
  5. Reverse Trajectory and $y_0$-Parameterization
  6. Experiments
  7. Dataset and Evaluation Metrics
  8. Results
  9. Balancing Anatomical Fidelity and Generative Diversity
  10. Visualizing Topological Consistency
  11. Multi-Planar Visual Analysis
  12. Ablation Study
  13. Clinical Applicability: Inference Efficiency
  14. Conclusion

Figures (3)

  • Figure 1: Overview of the proposed Volumetric Directional Diffusion (VDD) framework. The pipeline consists of three main stages: (1) Anatomical Anchoring: A deterministic 3D U-Net is trained on the consensus of divergent expert annotations to extract a coarse anatomical prior $\hat{y}$. (2) Directional Forward Process: Unlike the original DDPM that diffuses towards isotropic Gaussian noise, VDD anchors the forward trajectory towards the anatomical prior. (3) Reverse Process: A denoising 3D U-Net predicts the noise $\epsilon_\theta$, which is reparameterized to recover the clean boundary $\hat{y}_0^\theta$ via a boundary-aware objective.
  • Figure 2: 3D visual comparison of uncertainty quantification on highly ambiguous LIDC-IDRI nodules. From left to right, the four blocks represent: (1) Ground Truth, (2) CCDM, (3) DiffOSeg, and (4) VDD (Ours).
  • Figure 3: Visual comparison of uncertainty maps among VDD, Prob Unet and VDD(Gaussian)