Asymptotic Learning Curves for Diffusion Models with Random Features Score and Manifold Data
arXiv:2603.22962v3 Announce Type: replace Abstract: We study the theoretical behavior of denoising score matching--the learning task associated to diffusion models--when the data distribution is supported on a low-dimensional manifold and the score is parameterized using a random feature neural network. We derive asymptotically exact expressions for the test, train, and score errors in the high-dimensional limit. Our analysis reveals that, for linear manifolds the sample complexity required to learn the score function scales linearly with the intrinsic dimension of the manifold, rather than wi
This research provides theoretical underpinnings for the efficiency of diffusion models, coming at a time when these models are central to generative AI advancements.
Understanding the sample complexity and error behaviors of diffusion models is crucial for their reliable scaling and deployment in real-world applications, impacting efficiency and resource allocation.
This research clarifies the theoretical limits and scaling properties of diffusion models, guiding future development towards more efficient and robust generative AI systems.
- · AI researchers
- · Generative AI developers
- · Cloud computing providers
- · Data scientists
- · Inefficient AI architectures
- · Organizations with limited compute
Improved understanding and optimization of diffusion models for various applications including content generation and data synthesis.
Accelerated development of more economical and performant generative AI systems requiring less data or computational resources.
Enhanced accessibility and proliferation of sophisticated AI models as their training becomes more theoretically grounded and efficient.
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