  Diffusion models have emerged as powerful generative techniques for solving
inverse problems. Despite their success in a variety of inverse problems in
imaging, these models require many steps to converge, leading to slow inference
time. Recently, there has been a trend in diffusion models for employing
sophisticated noise schedules that involve more frequent iterations of
timesteps at lower noise levels, thereby improving image generation and
convergence speed. However, application of these ideas for solving inverse
problems with diffusion models remain challenging, as these noise schedules do
not perform well when using empirical tuning for the forward model
log-likelihood term weights. To tackle these challenges, we propose zero-shot
approximate posterior sampling (ZAPS) that leverages connections to zero-shot
physics-driven deep learning. ZAPS fixes the number of sampling steps, and uses
zero-shot training with a physics-guided loss function to learn log-likelihood
weights at each irregular timestep. We apply ZAPS to the recently proposed
diffusion posterior sampling method as baseline, though ZAPS can also be used
with other posterior sampling diffusion models. We further approximate the
Hessian of the logarithm of the prior using a diagonalization approach with
learnable diagonal entries for computational efficiency. These parameters are
optimized over a fixed number of epochs with a given computational budget. Our
results for various noisy inverse problems, including Gaussian and motion
deblurring, inpainting, and super-resolution show that ZAPS reduces inference
time, provides robustness to irregular noise schedules and improves
reconstruction quality. Code is available at https://github.com/ualcalar17/ZAPS
