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[2510.10854] Discrete State Diffusion Models: A Sample Complexity Perspective
Summary
This article presents a theoretical framework for discrete-state diffusion models, offering the first sample complexity bounds and insights into efficient training methods.
Why It Matters
Understanding discrete-state diffusion models is crucial for applications in text and combinatorial structures. This research fills a significant gap in theoretical knowledge, providing a foundation for future advancements in machine learning and AI.
Key Takeaways
- Introduces the first sample complexity bound for discrete-state diffusion models.
- Decomposes score estimation error into distinct components for better understanding.
- Addresses a critical gap in the literature on discrete-state models.
- Highlights the practical relevance of discrete-state diffusion in various applications.
- Provides insights that can lead to more efficient training methodologies.
Computer Science > Machine Learning arXiv:2510.10854 (cs) [Submitted on 12 Oct 2025 (v1), last revised 14 Feb 2026 (this version, v2)] Title:Discrete State Diffusion Models: A Sample Complexity Perspective Authors:Aadithya Srikanth, Mudit Gaur, Vaneet Aggarwal View a PDF of the paper titled Discrete State Diffusion Models: A Sample Complexity Perspective, by Aadithya Srikanth and 2 other authors View PDF HTML (experimental) 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 establishe...
