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

2026-03-30

AI Summary

Existing methods for discrete data generation operate directly in discrete spaces, often leading to abrupt state transitions that compromise generation quality and stability. This work proposes a non-Markovian denoising framework based on probability simplices, modeling the discrete data generation process within a continuous simplex space. By introducing a conditionally independent noise mechanism, the approach circumvents the redundant constraints inherent in conventional discrete diffusion models, thereby simplifying the model architecture while preserving theoretical rigor. Extensive experiments on multiple synthetic and real-world graph datasets demonstrate that the proposed method significantly outperforms current discrete diffusion and flow-matching approaches, confirming its effectiveness and superiority in discrete generative tasks.

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.

Problem

• discrete data
• denoising models
• generative modeling
• graph generation
• probability simplex

Innovation

• simplex denoising
• non-Markovian
• discrete generative modeling
• graph generation
• probability simplex