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

TL;DR

This paper introduces a non-Markovian simplex denoising framework for discrete data that improves generative modeling by operating on the probability simplex, simplifying the process and outperforming existing methods.

Contribution

The authors propose unrestrained simplex denoising, a novel non-Markovian approach that enhances performance and simplifies discrete generative modeling on the probability simplex.

Findings

Outperforms strong discrete diffusion and flow-matching baselines

Works effectively on synthetic and real-world graph benchmarks

Highlights the probability simplex as a powerful framework for discrete data 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.