DDIM

DDIM, short for Denoising Diffusion Implicit Models, is a sampling framework for diffusion-based generative models that yields deterministic, non-Markovian trajectories and can reduce the number of sampling steps required to generate high-quality samples. It builds on the denoising diffusion probabilistic model (DDPM) by reinterpreting the diffusion process in a way that permits an explicit, largely deterministic reverse path.

In practice, a neural network trained to predict x0 (the original image) or equivalently the noise at each step is used. DDIM derives a reverse-time update that computes x_{t−1} from x_t using the predicted x0, enabling skipping steps and producing a deterministic sample when a stochasticity parameter is set to zero. This yields a family of samplers parameterized by the number of steps and by the amount of stochasticity allowed in the reverse process.

Applications and impact: The approach enables faster sampling compared to the standard DDPM, often reducing steps from 1000 to tens or hundreds with modest quality loss, and has been incorporated into many diffusion-model implementations for image, video, and general generative tasks.

Relationship to likelihood: DDIM does not in general maximize or provide exact likelihood estimates; it instead offers a reparameterization of the diffusion model’s reverse process with deterministic or semi-deterministic sampling, while preserving the same data distribution under certain conditions.

History: Introduced in 2020 by Jiaming Song, Chenlin Meng, and Stefano Ermon as Denoising Diffusion Implicit Models. The method has influenced subsequent research on efficient diffusion sampling and driven practical applications in generative modeling.