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Random Walks with Tweedie: A Unified View of Score-Based Diffusion Models

Created by
  • Haebom

Author

Chicago Y. Park, Michael T. McCann, Cristina Garcia-Cardona, Brendt Wohlberg, Ulugbek S. Kamilov

Outline

This paper presents a concise derivation of several influential score-based diffusion models, drawing on only a few textbook-level results. Diffusion models have recently emerged as a powerful tool for generating realistic synthetic signals (especially natural images), and play a prominent role in state-of-the-art algorithms for inverse problems in image processing. While these algorithms are often surprisingly simple, the theory behind them is not, and there are several complex theoretical justifications in the literature. In this paper, we provide a simple and largely self-explanatory theoretical justification for score-based diffusion models for signal processing. This approach leads to a general algorithmic template for training and generating samples using diffusion models. We show that several influential diffusion models correspond to specific choices within this template, and that simpler alternative algorithmic choices can provide similar results. This approach has the additional advantage of enabling conditional sampling without any probability approximation.

Takeaways, Limitations

Takeaways:
Provides a concise and easy-to-understand theoretical foundation for score-based diffusion models.
We've made it more accessible by using terms and concepts familiar to researchers in the signal processing field.
We present a general algorithmic template for training diffusion models and generating samples.
Enables conditional sampling without likelihood approximation.
Provides a framework for integrating understanding of various diffusion models.
Limitations:
Further research may be needed to determine whether the presented theoretical framework is applicable to all score-based diffusion models.
It cannot be said that the performance of the proposed algorithm is optimal in all situations. Additional comparative performance analysis based on actual applications is required.
It is possible that the simplified approach presented in this paper omits details of some complex diffusion models.
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