{"ID":2856928,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.10854","arxiv_id":"2510.10854","title":"Discrete State Diffusion Models: A Sample Complexity Perspective","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 $\\widetilde{\\mathcal{O}}(ε^{-2})$. 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.","short_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 applicat...","url_abs":"https://arxiv.org/abs/2510.10854","url_pdf":"https://arxiv.org/pdf/2510.10854v2","authors":"[\"Aadithya Srikanth\",\"Mudit Gaur\",\"Vaneet Aggarwal\"]","published":"2025-10-12T23:33:46Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\",\"stat.ML\"]","methods":"[\"Diffusion Model\"]","has_code":false}