What are Diffusion Models?

This short tutorial covers the basics of diffusion models, a simple yet expressive approach to generative modeling. They've been behind a recent string of impressive results, including OpenAI's DALL-E 2, Google's Imagen, and Stable Diffusion.

Errata:
At 12:39, parentheses are missing around the difference: \epsilon(x, t, y) - \epsilon(x, t, \empty). See https://i.imgur.com/PhUxugm.png for corrected version.

Timestamps:
0:00 - Intro
1:07 - Forward process
3:07 - Posterior of forward process
4:16 - Reverse process
5:34 - Variational lower bound
9:26 - Reduced variance objective
10:27 - Reverse step implementation
11:38 - Conditional generation
13:45 - Comparison with other deep generative models
14:34 - Connection to score matching models

Special thanks to Jonathan Ho and Elmira Amirloo for feedback on this video.

Papers:
Feller, 1949: On the Theory of Stochastic Processes, with Particular Reference to Applications (https://digitalassets.lib.berkeley.edu/math/ucb/text/math_s1_article-21.pdf)
Sohl-Dickstein et al., 2015: Deep Unsupervised Learning using Nonequilibrium Thermodynamics (https://arxiv.org/abs/1503.03585)
Ho et al., 2020: Denoising Diffusion Probabilistic Models (https://arxiv.org/abs/2006.11239)
Song u0026 Ermon, 2019: Generative Modeling by Estimating Gradients of the Data Distribution (https://arxiv.org/abs/1907.05600)
Dhariwal u0026 Nichol, 2021: Diffusion Models Beat GANs on Image Synthesis (https://arxiv.org/abs/2105.05233)
Nichol et al., 2021: GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models (https://arxiv.org/abs/2112.10741)
Saharia et al., 2021: Palette: Image-to-Image Diffusion Models (https://arxiv.org/abs/2111.05826)
Ramesh et al, 2022: Hierarchical Text-Conditional Image Generation with CLIP Latents (https://arxiv.org/abs/2204.06125)
Saharia et al., 2022: Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding (https://arxiv.org/abs/2205.11487)
Song et al., 2021: Denoising Diffusion Implicit Models (https://arxiv.org/abs/2010.02502)
Nichol u0026 Dhariwal, 2021: Improved Denoising Diffusion Probabilistic Models (https://arxiv.org/abs/2102.09672)
Kingma et al., 2021: Variational Diffusion Models (https://arxiv.org/abs/2107.00630)
Song et al., 2021: Score-Based Generative Modeling through Stochastic Differential Equations (https://arxiv.org/abs/2011.13456)

Links:
YouTube: https://www.youtube.com/ariseffai
Twitter: https://twitter.com/ari_seff
Homepage: https://www.ariseff.com

If you'd like to help support the channel (completely optional), you can donate a cup of coffee via the following:
Venmo: https://venmo.com/ariseff
PayPal: https://www.paypal.me/ariseff