KANResDiff: Learning Local Residual Diffusion via Kolmogorov-Arnold Network for Ambiguous Medical Image Segmentation

Ambiguous 3D medical image segmentation often involves boundaries where different expert delineations are non-identical yet clinically plausible. Modeling such inter-observer variability requires a careful balance between diversity and anatomical fidelity: deterministic models preserve coherent volumetric structures but collapse expert disagreement into a single mask, while stochastic generative models can produce diverse samples but may introduce disconnected components or slice-to-slice inconsistency when generating full 3D masks from unstructured noise. We propose Volumetric Directional Diffusion (VDD), a prior-anchored diffusion framework that shifts stochastic generation from full-mask synthesis to residual boundary exploration. VDD uses a coarse consensus prediction as an anatomical anchor and learns a directional diffusion process to generate plausible boundary variations around ambiguous regions while preserving stable volumetric topology. Experiments on three multi-rater datasets, including LIDC-IDRI, KiTS21, and ISBI 2015, show that VDD improves uncertainty distribution alignment while maintaining competitive segmentation accuracy and 3D structural consistency. These results suggest that prior-anchored residual diffusion can model clinically plausible expert disagreement without sacrificing anatomical fidelity.

Image segmentation remains fundamentally limited by boundary ambiguity arising from sampling-induced information loss and inherent uncertainty in pixel-wise labeling. Although encoder-decoder architectures such as U-Net achieve strong performance, they often produce overconfident predictions that fail to capture transition-region ambiguity. To address this issue, we propose \textbf{NoiseUNet}, a simple yet effective framework that injects bounded perturbations into skip connections to regularize cross-scale feature fusion. This mechanism enforces robustness to local feature variations and promotes boundary-aware representations. Theoretically, the perturbation induces an implicit fuzzification effect, yielding soft, data-driven memberships without requiring explicit fuzzy modeling. We further introduce \textbf{ThyR}, a real-world thyroid ultrasound dataset with inherently ambiguous boundaries. Experiments demonstrate that NoiseUNet consistently improves both segmentation accuracy and boundary fidelity.

Segmentation models such as Segment Anything Model (SAM) and SAM2 achieve strong prompt-driven zero-shot performance. However, their training on natural images limits domain transfer to medical data. Consequently, accurate segmentation typically requires extensive fine-tuning and expert-designed prompts. We propose DiffuSAM, a diffusion-based adaptation of SAM2 for prompt-free medical image segmentation. Our framework synthesizes SAM2-compatible segmentation mask-like embeddings via a lightweight diffusion-prior from off-the-shelf frozen SAM2 image features. The generated embeddings are integrated into SAM2's mask decoder to produce accurate segmentations, thereby eliminating the need for user prompts. The diffusion prior is further conditioned on previously segmented slices, enforcing spatial consistency across volumes. Evaluated on the BTCV and CHAOS datasets for CT and MRI under Source-Free Unsupervised Domain Adaptation (SF-UDA) and Few-Shot settings, DiffuSAM achieves competitive performance with efficient training and inference. Code is available upon request from the corresponding author.