“Understanding Diffusion Models: A Unified Perspective”, 2022-08-25 ():
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 3 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 3 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.