Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing
arxiv(2024)
Abstract
Diffusion models have recently achieved success in solving Bayesian inverse
problems with learned data priors. Current methods build on top of the
diffusion sampling process, where each denoising step makes small modifications
to samples from the previous step. However, this process struggles to correct
errors from earlier sampling steps, leading to worse performance in complicated
nonlinear inverse problems, such as phase retrieval. To address this challenge,
we propose a new method called Decoupled Annealing Posterior Sampling (DAPS)
that relies on a novel noise annealing process. Specifically, we decouple
consecutive steps in a diffusion sampling trajectory, allowing them to vary
considerably from one another while ensuring their time-marginals anneal to the
true posterior as we reduce noise levels. This approach enables the exploration
of a larger solution space, improving the success rate for accurate
reconstructions. We demonstrate that DAPS significantly improves sample quality
and stability across multiple image restoration tasks, particularly in
complicated nonlinear inverse problems. For example, we achieve a PSNR of
30.72dB on the FFHQ 256 dataset for phase retrieval, which is an improvement of
9.12dB compared to existing methods.
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