  Diffusion models have shown impressive performance for image generation,
often times outperforming other generative models. Since their introduction,
researchers have extended the powerful noise-to-image denoising pipeline to
discriminative tasks, including image segmentation. In this work we propose a
conditional score-based generative modeling framework for medical image
segmentation which relies on a parametric surface representation for the
segmentation masks. The surface re-parameterization allows the direct
application of standard diffusion theory, as opposed to when the mask is
represented as a binary mask. Moreover, we adapted an extended variant of the
diffusion technique known as the "cold-diffusion" where the diffusion model can
be constructed with deterministic perturbations instead of Gaussian noise,
which facilitates significantly faster convergence in the reverse diffusion. We
evaluated our method on the segmentation of the left ventricle from 65
transthoracic echocardiogram videos (2230 echo image frames) and compared its
performance to the most popular and widely used image segmentation models. Our
proposed model not only outperformed the compared methods in terms of
segmentation accuracy, but also showed potential in estimating segmentation
uncertainties for further downstream analyses due to its inherent generative
nature.
