Generative Models: Variational Autoencoders and Diffusion Models

yzj5306@psu.edu (Yiyang Jiang) — Mon, 21 Sep 2026 16:30:00 -0400


Presenter	Mengyao Zhang (Prof. Binghai Yan’s group, Penn State)
Date	September 21, 2026 · 4:30–6:00 PM
Location	Davey 339
Topic	Stat Mech in Machine Learning — generative models: VAEs and denoising diffusion
Notes	Handwritten, 6 pages (viewer and download below)

How do you draw a fresh sample from the distribution of natural images, when the only distributions you can sample directly are the uniform and the Gaussian? Both answers in this session start the same way. Draw a latent variable $z$ from a simple distribution, then learn a map that sends it to data. Training by maximum likelihood then runs into one obstacle: the posterior over the latent variable is intractable. The variational autoencoder handles it with one learned Gaussian posterior and a single decoding step, trained on the evidence lower bound (ELBO) with the reparameterization trick. The denoising diffusion probabilistic model (DDPM) has $T$ latent layers, and it fixes the approximate posterior to be a known noising process, so no encoder is learned at all. Its ELBO then collapses to a remarkably simple objective: predict the noise that was added. The handwritten notes carry every derivation, from the Gaussian-mixture M-step, through the closed-form Gaussian KL, to the DDPM posterior mean and sampling loop.

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Generative Models: Variational Autoencoders and Diffusion Models