Discrete State Diffusion Models: A Sample Complexity Perspective
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912904034385920 |
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| author | Srikanth, Aadithya Gaur, Mudit Aggarwal, Vaneet |
| author_facet | Srikanth, Aadithya Gaur, Mudit Aggarwal, Vaneet |
| contents | 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 $\widetilde{\mathcal{O}}(ε^{-2})$. 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_10854 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Discrete State Diffusion Models: A Sample Complexity Perspective Srikanth, Aadithya Gaur, Mudit Aggarwal, Vaneet Machine Learning Artificial Intelligence 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 $\widetilde{\mathcal{O}}(ε^{-2})$. 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. |
| title | Discrete State Diffusion Models: A Sample Complexity Perspective |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2510.10854 |