  We introduce Score identity Distillation (SiD), an innovative data-free
method that distills the generative capabilities of pretrained diffusion models
into a single-step generator. SiD not only facilitates an exponentially fast
reduction in Fr\'echet inception distance (FID) during distillation but also
approaches or even exceeds the FID performance of the original teacher
diffusion models. By reformulating forward diffusion processes as semi-implicit
distributions, we leverage three score-related identities to create an
innovative loss mechanism. This mechanism achieves rapid FID reduction by
training the generator using its own synthesized images, eliminating the need
for real data or reverse-diffusion-based generation, all accomplished within
significantly shortened generation time. Upon evaluation across four benchmark
datasets, the SiD algorithm demonstrates high iteration efficiency during
distillation and surpasses competing distillation approaches, whether they are
one-step or few-step, data-free, or dependent on training data, in terms of
generation quality. This achievement not only redefines the benchmarks for
efficiency and effectiveness in diffusion distillation but also in the broader
field of diffusion-based generation. The PyTorch implementation is available at
https://github.com/mingyuanzhou/SiD
