  Medical image segmentation is a crucial task that relies on the ability to
accurately identify and isolate regions of interest in medical images. Thereby,
generative approaches allow to capture the statistical properties of
segmentation masks that are dependent on the respective structures. In this
work we propose a conditional score-based generative modeling framework to
represent the signed distance function (SDF) leading to an implicit
distribution of segmentation masks. The advantage of leveraging the SDF is a
more natural distortion when compared to that of binary masks. By learning the
score function of the conditional distribution of SDFs we can accurately sample
from the distribution of segmentation masks, allowing for the evaluation of
statistical quantities. Thus, this probabilistic representation allows for the
generation of uncertainty maps represented by the variance, which can aid in
further analysis and enhance the predictive robustness. We qualitatively and
quantitatively illustrate competitive performance of the proposed method on a
public nuclei and gland segmentation data set, highlighting its potential
utility in medical image segmentation applications.
