\textbf{Naresh Kumar Devulapally}
\text{CSE 4/555: Intro to Pattern Recognition}
Article link for the math derivation discussed in class with live code!!
\text{Lecture 3}
\text{Denoising Diffusion Probabilistic Models}
\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
- Recap of the Generative AI model architectures.
- The bigger picture in all generative models.
- The bottleneck in Variational AutoEncoders.
- Diffusion Models (Recent Models).
- Forward Diffusion Process
- Reverse Diffusion Process
- Training Architecture
- Coding Example
\( \text{Agenda of this Lecture:}\)
\text{July 10, 2025}
\text{Diffusion Models}
\text{Apr. 3, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{July 10, 2025}
\text{VAEs - Recap}
P(x \mid z)
P(z \mid x)
Posterior
Generative Model
\text{Apr. 3, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{July 10, 2025}
\text{Conditional Variational AutoEncoders}
P(x \mid z)
P(z \mid x)
Posterior
Generative Model
\text{Apr. 3, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{July 10, 2025}
\text{Conditional Variational AutoEncoders}
\text{Apr. 3, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{July 10, 2025}
\text{Generative Adversarial Models}
\text{Apr. 3, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{July 10, 2025}
\text{VAEs to Diffusion Models}
Data reconstruction using VAEs
\text{Apr. 3, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{July 10, 2025}
\text{Diffusion Models}
- Forward Process
- Reverse Process
Diffusion Models
\text{Apr. 3, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{July 10, 2025}
\text{Diffusion Models}
\text{Apr. 3, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{July 10, 2025}
\text{Diffusion Models}
\text{Apr. 3, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{July 10, 2025}
\text{Diffusion Models}
\text{Apr. 3, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{July 10, 2025}
\text{Diffusion Models}
\text{Apr. 3, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{July 10, 2025}
\text{Diffusion Models - Part 2}
Expectation
\text{Apr. 3, 2026}
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\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{July 10, 2025}
\text{Diffusion Models - Part 2}
Jensen's Inequality
\text{Apr. 3, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{July 10, 2025}
\text{Diffusion Models - Part 2}
KL Divergence
\text{Apr. 3, 2026}
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\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{July 10, 2025}
\text{Diffusion Models - Part 2}
VAE Loss
\text{Apr. 3, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{July 10, 2025}
\text{Diffusion Models - Part 2}
Notation
- \( x_0 \) : Original data sample (image, audio, etc.)
- \( x_t \): Noised version of \( x_0 \) at timestep \( t \)
- \( x_T \): Final noise, ideally standard Gaussian
- \( \beta_t \): Variance schedule, determines noise magnitude at step \( t \)
- \( \alpha_t = 1 - \beta_t,\quad \bar{\alpha}_t = \prod_{s=1}^t \alpha_s \)
- Noise is added as:
x_t = \sqrt{\bar{\alpha}_t} x_0 + \sqrt{1 - \bar{\alpha}_t} \, \epsilon,\quad \epsilon \sim \mathcal{N}(0, I)
\text{Apr. 3, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{July 10, 2025}
\text{Diffusion Models}
\text{Apr. 3, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{July 10, 2025}
\text{Diffusion Models - Part 2}
What does \( \beta_t \) do?
\text{Apr. 3, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{July 10, 2025}
\text{Diffusion Models - Part 2}
Forward and Reverse Processes
\text{Apr. 3, 2026}
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\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{July 10, 2025}
\text{Diffusion Models - Part 2}
Forward Process
\text{Apr. 3, 2026}
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\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{July 10, 2025}
\text{Diffusion Models - Part 2}
Forward Process
\text{Apr. 3, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{July 10, 2025}
\text{Diffusion Models - Part 2}
Reverse Process
\text{Apr. 3, 2026}
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\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{July 10, 2025}
\text{Diffusion Models - Part 2}
Diffusion Loss
\text{Apr. 3, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{July 10, 2025}
\text{Diffusion Models - Part 2}
Diffusion Loss
Calvin Luo's
Diffusion Tutorial
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\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
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\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{July 10, 2025}
\text{Diffusion Models - Part 2}
Diffusion Loss
\text{Apr. 3, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{July 10, 2025}
\text{Diffusion Models - Part 2}
Diffusion Loss
\text{Apr. 3, 2026}
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\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
\text{CSE 4/555: Pattern Recognition, Sp. 26}
\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
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\text{July 10, 2025}
\text{Diffusion Models - Part 2}
Reverse Process Update
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\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
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\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
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\text{July 10, 2025}
\text{Diffusion Models - Part 2}
Summary
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\text{Naresh Kumar Devulapally}
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\text{Naresh Kumar Devulapally}
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\text{July 10, 2025}
\text{Diffusion Models - Part 2}
References
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\text{Naresh Kumar Devulapally}
\text{Apr. 7, 2026}
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\text{Naresh Kumar Devulapally}
\text{Apr. 2, 2026}
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Lecture 3: Denoising Diffusion Probabilistic Models
By Naresh Kumar Devulapally
