## 1 Introduction  
The accurate identification and delineation of structures within medical images are essential for extracting meaningful information, aiding clinicians in making informed decisions. Traditional segmentation methods have demonstrated limitations in handling the complexity and variability inherent in biomedical images, particularly in the presence of noise and intricate anatomical details [1]. To address these challenges, probabilistic models have gained prominence for their ability to capture the uncertainty and variability in imaging data [2]. Among these models, the Denoising Diffusion Probabilistic Model (DDPM) has emerged as a promising approach with its capacity to learn intricate probability distributions and effectively denoise images. DDPM, originally developed for generative modeling, has garnered attention for its potential application in biomedical image segmentation [3]. In the realm of medical imaging, the significance of accurate image segmentation cannot be overstated. The extraction of precise information from medical images through segmentation forms the bedrock for a multitude of clinical applications that are pivotal for patient care. Accurate segmentation delineates and isolates structures of interest, such as organs, tissues, and pathological regions, providing clinicians with invaluable insights into anatomical details and disease states [3]. The reliability of diagnostic assessments, treatment planning, and therapeutic interventions hinges upon the fidelity of segmentation results [4]. Innovative methods, including graph-based processing and statistical signal processing such as Markov Random Fields (MRF) exemplified by techniques like synthetic graph coordinates [5] and fuzzy clustering with hidden Markov random field models and Voronoi tessellation [6], offer unique advantages in capturing complex relationships within image structures. Additionally, the fusion of graph-based processing and MRF models, as demonstrated in works like the hybrid ACO-ICM algorithm for MRF optimization [7], showcases the potential for improved segmentation accuracy. Furthermore, the integration of goal-driven unsupervised image segmentation methods, combining graph-based processing and MRFs [8], has demonstrated promising results. Such approaches not only enhance the precision of segmentation but also contribute to the interpretability and adaptability of the segmentation process. Traditional methods of image segmentation have long been employed in medical imaging; however, they often encounter challenges in handling the inherent complexities of biological structures and the variability present in imaging data. The need for more sophisticated and adaptive segmentation approaches has driven the exploration of advanced techniques, and probabilistic models have emerged as a promising avenue for addressing these challenges [9]. The accuracy of medical image segmentation is particularly crucial in scenarios where subtle structural details or anomalies can significantly impact clinical decisions [10]. For instance, in the detection and characterization of tumors, the delineation of precise boundaries is paramount for treatment planning and monitoring disease progression. Similarly, in anatomical studies and functional assessments, accurate segmentation lays the foundation for reliable quantitative analyses. The rationale for exploring DDPM in this context lies in its inherent capacity to capture complex dependencies in data and its adaptability to the unique challenges posed by medical images [11; 12]. As the field of medical imaging continues to evolve, there is a growing need for segmentation methods that can robustly handle variations in imaging conditions, noise levels, and the inherent heterogeneity of biological structures [13]. This review sets the stage for a comprehensive review and analysis of the use of DDPM in biomedical image segmentation.