Random Walks with Tweedie: A Unified View of Score-Based Diffusion Models
This work simplifies the theoretical justification of diffusion models for the signal processing community, offering a more accessible framework, though it is incremental as it builds on existing models.
The authors tackled the complex theory behind score-based diffusion models by providing a simple, unified derivation using textbook results, leading to generic algorithmic templates for training and sampling, and showed that alternative choices can yield comparable results.
We present a concise derivation for several influential score-based diffusion models that relies on only a few textbook results. Diffusion models have recently emerged as powerful tools for generating realistic, synthetic signals -- particularly natural images -- and often play a 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 multiple complex theoretical justifications exist in the literature. Here, we provide a simple and largely self-contained theoretical justification for score-based diffusion models that is targeted towards the signal processing community. This approach leads to generic algorithmic templates for training and generating samples with diffusion models. We show that several influential diffusion models correspond to particular choices within these templates and demonstrate that alternative, more straightforward algorithmic choices can provide comparable results. This approach has the added benefit of enabling conditional sampling without any likelihood approximation.