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Rethinking Diffusion Model in High Dimension

Created by
  • Haebom

Author

Zhenxin Zheng, Zhenjie Zheng

Outline

Despite the success of diffusion models in generating high-dimensional data, this paper argues that diffusion models do not overcome the curse of dimensionality. While diffusion models are assumed to learn statistical properties of the underlying probability distribution, the paper argues that in practice, due to the degradation of the target function in high-dimensional sparse environments, they fail to effectively learn such properties. Instead, the paper proposes that the inference process of diffusion models can be explained within a simple framework without statistical concepts.

Takeaways, Limitations

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Takeaways:
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A new perspective on how diffusion models work: suggesting that, contrary to conventional understanding, diffusion models may not work in a way that learns statistical quantities.
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A new interpretation of the success of diffusion models in generating high-dimensional data: We suggest that the performance of diffusion models can be explained by factors other than statistical learning.
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We present a simplified framework that explains the inference process of the diffusion model.
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Limitations:
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Lack of concrete experimental evidence: Direct experimental evidence may be lacking for the claim that diffusion models do not effectively learn statistical quantities.
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Performance validation of the proposed alternative framework is needed: Further validation is needed to determine how well the proposed simple framework describes the performance of real-world diffusion models and what advantages it offers over existing methodologies.
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Lack of depth in theoretical basis: While it provides a fundamental understanding of how diffusion models work, it may lack depth in specific mechanisms or mathematical proofs.
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