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In this video you'll learn about the Unadjusted Langevin Algorithm, and how it can be used to sample new data. This method was a precursor to what we now call "Diffusion models", which are just an annealed version of this algorithm.
Here is all the code used to produce the video, including the code of the "Implementation" chapter:
https://github.com/ytdeepia/Unadjusted-Langevin-Algorithm
If you want to dive deeper you should read these papers:
- "A Connection Between Score Matching and Denoising Autoencoders" by Pascal Vincent https://www.iro.umontreal.ca/~vincentp/Publications/smdae_techreport.pdf
- "Generative Modeling by Estimating Gradients of the Data Distribution" by Yang Song Generative Modeling by Estimating Gradients of the Data Distribution
- "Estimation of Non-Normalized Statistical Models byScore Matching" by AapoHyv arinen https://jmlr.org/papers/volume6/hyvarinen05a/hyvarinen05a.pdf
- "Solving Linear Inverse Problems Using the Prior Implicit in a Denoiser" by Zahra Kadkhodaie https://arxiv.org/abs/2007.13640
00:00 Intro
00:35 Sponsor
01:34 The Denoiser approximates the Posterior Mean
05:43 Tweedie's formula
10:23 Score Matching
12:39 Langevin Algorithm
14:47 Implementation and Examples
17:50 Limitations
19:18 Outro
This video features animations created with Manim, inspired by Grant Sanderson's work at @3blue1brown. This video was sponsored by Brilliant.
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