We present an accessible first course on the mathematics of diffusion models and flow matching for machine learning. We aim to teach diffusion as simply as possible, with minimal mathematical and machine learning prerequisites, but enough technical detail to reason about its correctness. Unlike most tutorials on this subject, we take neither a Variational Auto Encoder (VAE) nor a Stochastic Differential Equations (SDE) approach. In fact, for the…
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An increasing number of the machine learning (ML) models we build at Apple each year are either partly or fully adopting the Transformer architecture. This architecture helps enable experiences such as panoptic segmentation in Camera with HyperDETR, on-device scene analysis in Photos, image captioning for accessibility, machine translation, and many others. This year at WWDC 2022, Apple is making available an open-source reference PyTorch implementation of the Transformer architecture, giving developers worldwide a way to seamlessly deploy their state-of-the-art Transformer models on Apple devices.

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