Geometric Interpretation of Diffusion Model

(DDPM, DDIM & Beyond)

Jun Ji, Dept. of AI Application

Diffusion Model Timeline

DDPM (Denoising Diffusion Probabilistic Models)

DDPM (Denoising Diffusion Probabilistic Models)

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DDPM (Denoising Diffusion Probabilistic Models)

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x0

x0

xT

xT

Diffusion Step : alpha

Sampling Step : beta

Diffusion Step : beta

Sampling Step : beta

DDIM (Denoising Diffusion Implicit Model)

Figure 2: Graphical model for accelerated generation, where τ = [1, 3].

Figure 1: Graphical models for diffusion (left) and non-Markovian (right) inference models.

DDIM (Denoising Diffusion Implicit Model)

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DDIM (Denoising Diffusion Implicit Model)

x0

xT

Diffusion Step : alpha

Sampling Step : alpha

Ref.

• Ho, J., Jain, A., & Abbeel, P. (2020). Denoising Diffusion Probabilistic Models.
• Song, J., Meng, C., & Ermon, S. (2021). Denoising Diffusion Implicit Models.
• Dhariwal, P., & Nichol, A. (2021). Diffusion Models Beat GANs on Image Synthesis.
• Keras DDIM Code Example : https://keras.io/examples/generative/ddim/
• Labml.ai code with equation : https://nn.labml.ai/diffusion/index.htm

X0

XT

X1

(0,...,0)

X0

XT

X1

(0,...,0)