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[2410.18784] Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionality
Summary
This paper explores the efficiency of denoising diffusion probabilistic models (DDPM) in adapting to unknown low dimensionality, proving that their iteration complexity scales nearly linearly with intrinsic data dimensions.
Why It Matters
Understanding the adaptive capabilities of DDPMs is crucial for improving generative models in AI. This research addresses the practical limitations of existing theories and enhances the efficiency of sampling processes, which is vital for applications in machine learning and data science.
Key Takeaways
- DDPMs can achieve optimal adaptivity to unknown low dimensionality.
- The iteration complexity of DDPMs scales nearly linearly with intrinsic data dimensions.
- This research aligns with concurrent work, enhancing the understanding of DDPM efficiency.
Computer Science > Machine Learning arXiv:2410.18784 (cs) [Submitted on 24 Oct 2024 (v1), last revised 15 Feb 2026 (this version, v3)] Title:Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionality Authors:Zhihan Huang, Yuting Wei, Yuxin Chen View a PDF of the paper titled Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionality, by Zhihan Huang and 2 other authors View PDF HTML (experimental) Abstract:The denoising diffusion probabilistic model (DDPM) has emerged as a mainstream generative model in generative AI. While sharp convergence guarantees have been established for the DDPM, the iteration complexity is, in general, proportional to the ambient data dimension, resulting in overly conservative theory that fails to explain its practical efficiency. This has motivated the recent work Li and Yan (2024a) to investigate how the DDPM can achieve sampling speed-ups through automatic exploitation of intrinsic low dimensionality of data. We strengthen this line of work by demonstrating, in some sense, optimal adaptivity to unknown low dimensionality. For a broad class of data distributions with intrinsic dimension $k$, we prove that the iteration complexity of the DDPM scales nearly linearly with $k$, which is optimal when using KL divergence to measure distributional discrepancy. Notably, our work is closely aligned with the independent concurrent work Potaptchik et al. (2024) -- posted two weeks prior...
