Consistency models map any point on a diffusion trajectory directly to the trajectory origin, enabling single-step generation

A consistency model (Song et al. 2023) learns a function f:(x_t,t)->x_0 that maps any noisy point on the diffusion sampling trajectory back to its clean origin. The self-consistency property requires f(x_t,t) = f(x_{t’},t’) for all t,t’ on the same trajectory (and f is the identity at t=epsilon). This enables single-step generation (sample noise x_T, apply f to get x_0 directly), while an optional multi-step procedure trades compute for quality. Consistency models can be trained by distilling a pretrained diffusion model (Consistency Distillation, CD) or from scratch (Consistency Training, CT); CD is more compute-efficient but needs a pretrained teacher. An EMA copy of the weights stabilises training, and the LPIPS perceptual metric works better than L1/L2 as the distance function.

Examples

Single-step generation: x_0 = f_theta(x_T, T). The best reported CD configuration uses LPIPS distance, a Heun ODE solver, and N=18 discretisation steps.

Assessment

Define the self-consistency property and explain why it enables single-step generation. Contrast Consistency Distillation and Consistency Training in terms of data and compute requirements.