Unrestrained Simplex Denoising for Discrete Data. A Non-Markovian Approach Applied to Graph Generation

Abstract: Denoising models such as Diffusion or Flow Matching have recently advanced generative modeling for discrete structures, yet most approaches either operate directly in the discrete state space, causing abrupt state changes. We introduce simplex denoising, a simple yet effective generative framework that operates on the probability simplex. The key idea is a non-Markovian noising scheme in which, for a given clean data point, noisy representations at different times are conditionally independent. While preserving the theoretical guarantees of denoising-based generative models, our method removes unnecessary constraints, thereby improving performance and simplifying the formulation. Empirically, \emph{unrestrained simplex denoising} surpasses strong discrete diffusion and flow-matching baselines across synthetic and real-world graph benchmarks. These results highlight the probability simplex as an effective framework for discrete generative modeling.