DDIM Sampler
Chapter 20: ODE, SDE, and Continuous Limits of Algorithms — DDIM and Fast Diffusion Samplers
From the book
Chapter 20: ODE, SDE, and Continuous Limits of Algorithms. In the chapter mind map this icon labels DDIM and Fast Diffusion Samplers. The discussion below is excerpted and lightly edited from § DDIM and Fast Diffusion Samplers in Mathematics for AI and Machine Learning.
The reverse-time SDE of the matrix chapter has drift $\mathbf{f} - \mathbf{G}\mathbf{G}^\top \nabla_{\mathbf{x}} \log p_t$ and noise $\mathbf{G}\,d\bar{\mathbf{W}}_t$. Dropping the noise and halving the score term gives the probability flow ODE @eq:probability-flow-ode: the half that is removed is exactly the spreading the noise would have provided. The reverse SDE samples stochastically, the ODE deterministically, with the same marginals.
What this drawing shows
What you see. Three deterministic DDIM denoising paths grow from noise to data; a faint dashed SDE path stays for contrast with non-Markovian sampling.
In the mind map. Chapter 20 — DDIM and Fast Diffusion Samplers. See From the book above for definitions, figures, and worked examples.
Where to read next
Read the full definitions, figures, and worked examples in Chapter 20: ODE, SDE, and Continuous Limits of Algorithms — see the mind-map node DDIM and Fast Diffusion Samplers.
