Improving Denoising Diffusion Models via Simultaneous Estimation of
  Image and Noise
Zhenkai Zhang Krista A. Ehinger Tom Drummond
This paper introduces two key contributions aimed at improving the speed and
quality of images generated through inverse diffusion processes. The first
contribution involves reparameterizing the diffusion process in terms of the
angle on a quarter-circular arc between the image and noise, specifically
setting the conventional $\displaystyle \sqrt{\bar{\alpha}}=\cos(\eta)$. This
reparameterization eliminates two singularities and allows for the expression
of diffusion evolution as a well-behaved ordinary differential equation (ODE).
In turn, this allows higher order ODE solvers such as Runge-Kutta methods to be
used effectively. The second contribution is to directly estimate both the
image ($\mathbf{x}_0$) and noise ($\mathbf{\epsilon}$) using our network, which
enables more stable calculations of the update step in the inverse diffusion
steps, as accurate estimation of both the image and noise are crucial at
different stages of the process. Together with these changes, our model
achieves faster generation, with the ability to converge on high-quality images
more quickly, and higher quality of the generated images, as measured by
metrics such as Frechet Inception Distance (FID), spatial Frechet Inception
Distance (sFID), precision, and recall.