Understanding Diffusion Models: A Unified Perspective

TL;DR

This paper provides a comprehensive, unified theoretical framework for diffusion models, clarifying their variational and score-based perspectives, and discusses methods for learning and guiding these models for generative tasks.

Contribution

It unifies variational and score-based views of diffusion models, deriving key assumptions and objectives, and explains how to learn and guide these models effectively.

Findings

Diffusion models can be understood through a unified variational and score-based framework.

Key assumptions enable scalable optimization of diffusion models.

Guidance techniques improve conditional generation with diffusion models.

Abstract

Diffusion models have shown incredible capabilities as generative models; indeed, they power the current state-of-the-art models on text-conditioned image generation such as Imagen and DALL-E 2. In this work we review, demystify, and unify the understanding of diffusion models across both variational and score-based perspectives. We first derive Variational Diffusion Models (VDM) as a special case of a Markovian Hierarchical Variational Autoencoder, where three key assumptions enable tractable computation and scalable optimization of the ELBO. We then prove that optimizing a VDM boils down to learning a neural network to predict one of three potential objectives: the original source input from any arbitrary noisification of it, the original source noise from any arbitrarily noisified input, or the score function of a noisified input at any arbitrary noise level. We then dive deeper into what it means to learn the score function, and connect the variational perspective of a diffusion model explicitly with the Score-based Generative Modeling perspective through Tweedie's Formula. Lastly, we cover how to learn a conditional distribution using diffusion models via guidance.