Diffusion models are a family of state-of-the-art probabilistic generative models that have achieved ground breaking results in a number of fields ranging from image generation to protein structure design. In Part 1 of this two-part series, I will walk through the denoising diffusion probabilistic model (DDPM) as presented by Ho, Jain, and Abbeel (2020). Specifically, we will walk through the model definition, the derivation of the objective function, and the training and sampling algorithms....| Matthew N. Bernstein
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Variational autoencoders (VAEs) are a family of deep generative models with use cases that span many applications, from image processing to bioinformatics. There are two complimentary ways of viewing the VAE: as a probabilistic model that is fit using variational Bayesian inference, or as a type of autoencoding neural network. In this post, we present the mathematical theory behind VAEs, which is rooted in Bayesian inference, and how this theory leads to an emergent autoencoding algorithm. We...| Matthew N. Bernstein