  Diffusion models have emerged as state-of-the-art generative models for image
generation. However, sampling from diffusion models is usually time-consuming
due to the inherent autoregressive nature of their sampling process. In this
work, we propose a novel approach that accelerates the sampling of diffusion
models by parallelizing the autoregressive process. Specifically, we
reformulate the sampling process as solving a system of triangular nonlinear
equations through fixed-point iteration. With this innovative formulation, we
explore several systematic techniques to further reduce the iteration steps
required by the solving process. Applying these techniques, we introduce
ParaTAA, a universal and training-free parallel sampling algorithm that can
leverage extra computational and memory resources to increase the sampling
speed. Our experiments demonstrate that ParaTAA can decrease the inference
steps required by common sequential sampling algorithms such as DDIM and DDPM
by a factor of 4$\sim$14 times. Notably, when applying ParaTAA with 100 steps
DDIM for Stable Diffusion, a widely-used text-to-image diffusion model, it can
produce the same images as the sequential sampling in only 7 inference steps.
The code is available at https://github.com/TZW1998/ParaTAA-Diffusion.
