Simple and Critical Iterative Denoising: A Recasting of Discrete Diffusion in Graph Generation

Yoann Boget
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:4713-4736, 2025.

Abstract

Discrete Diffusion and Flow Matching models have significantly advanced generative modeling for discrete structures, including graphs. However, the dependencies of the noisy distributions across time of these models lead to error accumulation and propagation during the reverse denoising process—a phenomenon known as compounding denoising errors. To address this problem, we propose a novel framework called Simple Iterative Denoising, which simplifies discrete diffusion and circumvents the issue by removing dependencies on previous intermediate states in the noising process. Additionally, we enhance our model by incorporating a Critic, which during generation selectively retains or corrupts elements in an instance based on their likelihood under the data distribution. Our empirical evaluations demonstrate that the proposed method significantly outperforms existing discrete diffusion baselines in graph generation tasks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-boget25a, title = {Simple and Critical Iterative Denoising: A Recasting of Discrete Diffusion in Graph Generation}, author = {Boget, Yoann}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {4713--4736}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/boget25a/boget25a.pdf}, url = {https://proceedings.mlr.press/v267/boget25a.html}, abstract = {Discrete Diffusion and Flow Matching models have significantly advanced generative modeling for discrete structures, including graphs. However, the dependencies of the noisy distributions across time of these models lead to error accumulation and propagation during the reverse denoising process—a phenomenon known as compounding denoising errors. To address this problem, we propose a novel framework called Simple Iterative Denoising, which simplifies discrete diffusion and circumvents the issue by removing dependencies on previous intermediate states in the noising process. Additionally, we enhance our model by incorporating a Critic, which during generation selectively retains or corrupts elements in an instance based on their likelihood under the data distribution. Our empirical evaluations demonstrate that the proposed method significantly outperforms existing discrete diffusion baselines in graph generation tasks.} }
Endnote
%0 Conference Paper %T Simple and Critical Iterative Denoising: A Recasting of Discrete Diffusion in Graph Generation %A Yoann Boget %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-boget25a %I PMLR %P 4713--4736 %U https://proceedings.mlr.press/v267/boget25a.html %V 267 %X Discrete Diffusion and Flow Matching models have significantly advanced generative modeling for discrete structures, including graphs. However, the dependencies of the noisy distributions across time of these models lead to error accumulation and propagation during the reverse denoising process—a phenomenon known as compounding denoising errors. To address this problem, we propose a novel framework called Simple Iterative Denoising, which simplifies discrete diffusion and circumvents the issue by removing dependencies on previous intermediate states in the noising process. Additionally, we enhance our model by incorporating a Critic, which during generation selectively retains or corrupts elements in an instance based on their likelihood under the data distribution. Our empirical evaluations demonstrate that the proposed method significantly outperforms existing discrete diffusion baselines in graph generation tasks.
APA
Boget, Y.. (2025). Simple and Critical Iterative Denoising: A Recasting of Discrete Diffusion in Graph Generation. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:4713-4736 Available from https://proceedings.mlr.press/v267/boget25a.html.

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