Unrestrained Simplex Denoising for Discrete Data. A Non-Markovian Approach Applied to Graph Generation
This addresses a bottleneck in discrete generative modeling for domains like graph generation, though it appears incremental as an extension of existing denoising methods.
The paper tackled the problem of abrupt state changes in discrete generative models by introducing simplex denoising, a framework operating on the probability simplex with a non-Markovian noising scheme, and it surpassed strong baselines on graph benchmarks.
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.