Improved Sample Complexity For Diffusion Model Training Without Empirical Risk Minimizer Access

• URL: http://arxiv.org/abs/2505.18344v5
• Date: Sat, 04 Oct 2025 02:28:12 GMT
• Title: Improved Sample Complexity For Diffusion Model Training Without Empirical Risk Minimizer Access
• Authors: Mudit Gaur, Prashant Trivedi, Sasidhar Kunapuli, Amrit Singh Bedi, Vaneet Aggarwal,
• Abstract summary: We present a principled theoretical framework analyzing diffusion models, providing a state-of-the-art sample complexity bound to $widetildemathcalO(epsilon-4)$.<n>Our structured decomposition of the score estimation error into statistical and optimization components offers critical insights into how diffusion models can be trained efficiently.
• Score: 47.96419637803502
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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, they remain significantly less understood from a theoretical standpoint. In particular, all existing analyses of discrete-state models assume access to an empirical risk minimizer. In this work, we present a principled theoretical framework analyzing diffusion models, providing a state-of-the-art sample complexity bound of $\widetilde{\mathcal{O}}(\epsilon^{-4})$. Our structured decomposition of the score estimation error into statistical and optimization components offers critical insights into how diffusion models can be trained efficiently. This analysis addresses a fundamental gap in the literature and establishes the theoretical tractability and practical relevance of diffusion models.

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