Cyclic Discrete Diffusion: A Novel Multi-Class Segmentation Refinement Technique

We cast image segmentation refinement as a \textit{discrete} diffusion process. To solve this task we introduce Cyclic Discrete Diffusion (CDD), a novel forward–reverse formulation with a cyclic label topology that maps a discrete label set to the uniform distribution and back. Instead of injecting Gaussian noise as is done for continuous diffusion, CDD evolves segmentation masks through label jumps: at each step, every pixel either remains in its current class or jumps to the next label with a fixed rate. This jump-or-stay mechanism defines a finite-state Markov process with bounded forward and reverse steps, featuring analytically consistent and tractable reverse dynamics. CDD operates natively in a multi-class label space, enabling joint refinement of all classes in a single pass without requiring class-wise decomposition, as commonly needed in prior binary refinement approaches. The proposed formulation admits a finite and controllable number of refinement steps, for which we provide a theoretical characterization based on spectral gap analysis. We evaluate CDD across diverse segmentation tasks, including multi-class semantic, instance-level, and binary segmentation refinement. Our method consistently improves both region accuracy and boundary quality across multiple backbones and datasets.