\section{Related Works}


\paragraph{Diffusion Models for Medical Analysis.}
DDPMs \cite{ho2020denoising} have surpassed GANs in generative fidelity and are now widely adopted in medical image synthesis \cite{muller2022diffusion, khader2023denoising}. Beyond generation, diffusion models have been adapted for discriminative tasks. In segmentation, they model the joint distribution of images and masks to produce uncertainty-aware predictions \cite{amit2021segdiff, wu2024medsegdiff, wu2026volumetric}. In detection and anomaly localization, diffusion-based methods leverage reconstruction errors or latent-space signals to highlight pathological regions \cite{wolleb2022diffusion, pinaya2022fast}. These developments demonstrate the strong capability of diffusion models to capture complex structures inherent in medical data.


\paragraph{Generative Classification Frameworks.}
Current diffusion-based classifiers primarily follow two paradigms. The first treats classification as conditional generation, determining labels by evaluating the reconstruction likelihood of the input image under different class conditions \cite{favero2025conditional, li2023your}. While explainable, this reconstruction-based approach is computationally expensive due to the need for repeated sampling per class. The second paradigm, pioneered by CARD \cite{han2022card}, formulates classification as a generative process of the label vector itself ($p(y|x)$). In the medical domain, DiffMIC \cite{yang2023diffmic} and DiffMIC-v2 \cite{yang2025diffmic} adopted this strategy, introducing dual-granularity guidance to improve feature extraction. However, these methods typically impose Gaussian noise directly on One-Hot encoded labels. As noted in recent theoretical discussions \cite{hoogeboom2021argmax}, applying continuous Gaussian diffusion to discrete or simplex-constrained data introduces a fundamental geometric mismatch, potentially limiting modeling precision.

\paragraph{Diffusion on Constrained Manifolds.}
Existing diffusion methods for discrete data rely on discrete transition kernels \cite{hoogeboom2021argmax, austin2021structured} or bit-to-real relaxations \cite{chen2022analog}. Yet, a geometrically coherent mapping from the probability simplex to a continuous logit space has not been explored in medical classification. We address this gap by introducing a simplex-consistent framework that preserves the robustness benefits of Gaussian diffusion.