Implicit Diffusion (DDIM)
Deterministic, few-step sampling from a diffusion model — without retraining.
Motivation
Standard diffusion sampling is slow — hundreds of stochastic steps. Denoising Diffusion Implicit Models keep the same training objective but replace the sampler with a non-Markovian, deterministic process, cutting the number of steps by an order of magnitude while preserving sample quality.
Method
DDIM defines a family of inference processes that share the marginals of the diffusion forward chain but need not be Markovian. Setting the injected noise to zero yields a deterministic map from latent to sample — effectively an ODE integrator over the same score field.
Mathematical core
Because sampling becomes deterministic, the latent code acquires a meaningful geometry: interpolating in latent space produces smooth semantic transitions, and the forward map is (approximately) invertible. This is the bridge from diffusion to the probability-flow ODE and to continuous normalizing flows.