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This arXiv paper proposes a generative method for discrete data such as graphs, using a non-Markovian noising scheme on the probability simplex in place of direct discrete-state diffusion. The authors report gains over discrete diffusion and flow-matching baselines on synthetic and real graph benchmarks, but these are academic results, so readers should check how well they hold up on larger, more varied tasks. The main point for ML practitioners is the design choice: avoiding abrupt discrete state jumps may be a simpler route to strong graph generation.
Unrestrained Simplex Denoising for Discrete Data. A Non-Markovian Approach Applied to Graph Generation
arXiv:2603.28572v2 Announce Type: replace Abstract: Denoising models such as Diffusion or Flow Matching have recently advanced generative modeling for discrete structures, yet most approaches operate directly in the discrete state space, leading to 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.
Title: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 operate directly in the discrete state space, leading to 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.
Simplex Denoising. Updated after reviewing. NeurIPS 2026 accepted paper
Machine Learning (cs.LG)
arXiv:2603.28572 [cs.LG]
(or arXiv:2603.28572v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2603.28572 Focus to learn more arXiv-issued DOI via DataCite
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