  We introduce the Fixed Point Diffusion Model (FPDM), a novel approach to
image generation that integrates the concept of fixed point solving into the
framework of diffusion-based generative modeling. Our approach embeds an
implicit fixed point solving layer into the denoising network of a diffusion
model, transforming the diffusion process into a sequence of closely-related
fixed point problems. Combined with a new stochastic training method, this
approach significantly reduces model size, reduces memory usage, and
accelerates training. Moreover, it enables the development of two new
techniques to improve sampling efficiency: reallocating computation across
timesteps and reusing fixed point solutions between timesteps. We conduct
extensive experiments with state-of-the-art models on ImageNet, FFHQ,
CelebA-HQ, and LSUN-Church, demonstrating substantial improvements in
performance and efficiency. Compared to the state-of-the-art DiT model, FPDM
contains 87% fewer parameters, consumes 60% less memory during training, and
improves image generation quality in situations where sampling computation or
time is limited. Our code and pretrained models are available at
https://lukemelas.github.io/fixed-point-diffusion-models.
