Zero-Shot Adaptation for Approximate Posterior Sampling of Diffusion Models in Inverse Problems

TL;DR

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, which reduces inference time, provides robustness to irregular noise schedules and improves reconstruction quality.

Abstract

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

Figures (17)

• Figure 1: Representative results of our algorithm for four distinct noisy inverse problems ($\sigma=0.05$), showing the ground truth (GT), measurement and reconstruction.
• Figure 2: Our zero-shot approximate posterior sampling (ZAPS) approach unrolls the sampling process for a fixed number of $S$ steps for arbitrary/irregular noise schedules, alternating between score model sampling (SMS) and likelihood guidance (LG). Our zero-shot fine-tuning approach has two key components: 1) The Hessian of the log prior is approximated using a discrete wavelet transform diagonalization technique, 2) Both the diagonal matrices, $\{{\bf D}_t\}$ and the log-likelihood weights, $\{\zeta_t\}$ are updated during fine-tuning. The fine-tuning is done for a fixed number of epochs with a given NFE budget, yielding a faster and more robust adaptive inverse problem solver.
• Figure 3: Representative images using various methods for solving Gaussian deblurring, motion deblurring and super-resolution ($\times4$) tasks. Proposed method qualitatively improves upon each method, including the baseline state-of-the-art DPS.
• Figure 4: Illustrative images using state-of-the-art methods for random ($70\%$) and box ($128\times128$) inpainting. Proposed method improves upon DDRM, while achieving similar performance to $\mathrm{\Pi}$GDM and DPS, with subtle improvements shown in zoomed insets.
• Figure 5: Study on different epochs and sampling steps combinations with fixed NFE. Results show similar quality for combinations with lower timestep approaches staring from higher loss/lower PSNR but converging to similar values.