  Diffusion-based generative models are extremely effective in generating
high-quality images, with generated samples often surpassing the quality of
those produced by other models under several metrics. One distinguishing
feature of these models, however, is that they typically require long sampling
chains to produce high-fidelity images. This presents a challenge not only from
the lenses of sampling time, but also from the inherent difficulty in
backpropagating through these chains in order to accomplish tasks such as model
inversion, i.e. approximately finding latent states that generate known images.
In this paper, we look at diffusion models through a different perspective,
that of a (deep) equilibrium (DEQ) fixed point model. Specifically, we extend
the recent denoising diffusion implicit model (DDIM; Song et al. 2020), and
model the entire sampling chain as a joint, multivariate fixed point system.
This setup provides an elegant unification of diffusion and equilibrium models,
and shows benefits in 1) single image sampling, as it replaces the fully-serial
typical sampling process with a parallel one; and 2) model inversion, where we
can leverage fast gradients in the DEQ setting to much more quickly find the
noise that generates a given image. The approach is also orthogonal and thus
complementary to other methods used to reduce the sampling time, or improve
model inversion. We demonstrate our method's strong performance across several
datasets, including CIFAR10, CelebA, and LSUN Bedrooms and Churches.
