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

TL;DR

This paper offers a simplified, unified theoretical framework for score-based diffusion models, making them more accessible for signal processing applications and enabling new conditional sampling methods.

Contribution

It provides a concise, self-contained derivation of diffusion models, unifies existing models under a common template, and introduces straightforward algorithms for training and sampling.

Findings

Multiple diffusion models are special cases of a unified template.

Alternative algorithms can achieve comparable results to existing models.

Conditional sampling can be performed without likelihood approximation.

Abstract

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.