Understanding Diffusion Models: A Unified Perspective

• URL: http://arxiv.org/abs/2208.11970v1
• Date: Thu, 25 Aug 2022 09:55:25 GMT
• Title: Understanding Diffusion Models: A Unified Perspective
• Authors: Calvin Luo
• Abstract summary: Diffusion models have shown incredible capabilities as generative models. We review, demystify, and unify the understanding of diffusion models across both variational and score-based perspectives.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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