Discrete State Diffusion Models: A Sample Complexity Perspective

Aadithya Srikanth, Mudit Gaur, Vaneet Aggarwal
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:3547-3555, 2026.

Abstract

Diffusion models have demonstrated remarkable performance in generating high-dimensional samples across domains such as vision, language, and the sciences. Although continuous-state diffusion models have been extensively studied both empirically and theoretically, discrete-state diffusion models, essential for applications involving text, sequences, and combinatorial structures, remain significantly less understood from a theoretical standpoint. In particular, all existing analyses of discrete-state models assume score estimation error bounds without studying sample complexity results. In this work, we present a principled theoretical framework for discrete-state diffusion, providing the first sample complexity bound of $\widetilde{\mathcal{O}}(\epsilon^{-2})$. Our structured decomposition of the score estimation error into statistical, approximation, optimization, and clipping components offers critical insights into how discrete-state models can be trained efficiently. This analysis addresses a fundamental gap in the literature and establishes the theoretical tractability and practical relevance of discrete-state diffusion models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-srikanth26a, title = { Discrete State Diffusion Models: A Sample Complexity Perspective }, author = {Srikanth, Aadithya and Gaur, Mudit and Aggarwal, Vaneet}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {3547--3555}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/srikanth26a/srikanth26a.pdf}, url = {https://proceedings.mlr.press/v300/srikanth26a.html}, abstract = { Diffusion models have demonstrated remarkable performance in generating high-dimensional samples across domains such as vision, language, and the sciences. Although continuous-state diffusion models have been extensively studied both empirically and theoretically, discrete-state diffusion models, essential for applications involving text, sequences, and combinatorial structures, remain significantly less understood from a theoretical standpoint. In particular, all existing analyses of discrete-state models assume score estimation error bounds without studying sample complexity results. In this work, we present a principled theoretical framework for discrete-state diffusion, providing the first sample complexity bound of $\widetilde{\mathcal{O}}(\epsilon^{-2})$. Our structured decomposition of the score estimation error into statistical, approximation, optimization, and clipping components offers critical insights into how discrete-state models can be trained efficiently. This analysis addresses a fundamental gap in the literature and establishes the theoretical tractability and practical relevance of discrete-state diffusion models. } }
Endnote
%0 Conference Paper %T Discrete State Diffusion Models: A Sample Complexity Perspective %A Aadithya Srikanth %A Mudit Gaur %A Vaneet Aggarwal %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-srikanth26a %I PMLR %P 3547--3555 %U https://proceedings.mlr.press/v300/srikanth26a.html %V 300 %X Diffusion models have demonstrated remarkable performance in generating high-dimensional samples across domains such as vision, language, and the sciences. Although continuous-state diffusion models have been extensively studied both empirically and theoretically, discrete-state diffusion models, essential for applications involving text, sequences, and combinatorial structures, remain significantly less understood from a theoretical standpoint. In particular, all existing analyses of discrete-state models assume score estimation error bounds without studying sample complexity results. In this work, we present a principled theoretical framework for discrete-state diffusion, providing the first sample complexity bound of $\widetilde{\mathcal{O}}(\epsilon^{-2})$. Our structured decomposition of the score estimation error into statistical, approximation, optimization, and clipping components offers critical insights into how discrete-state models can be trained efficiently. This analysis addresses a fundamental gap in the literature and establishes the theoretical tractability and practical relevance of discrete-state diffusion models.
APA
Srikanth, A., Gaur, M. & Aggarwal, V.. (2026). Discrete State Diffusion Models: A Sample Complexity Perspective . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:3547-3555 Available from https://proceedings.mlr.press/v300/srikanth26a.html.

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