Perturb-and-Solve: Efficient Learned-Operator Conditioning for Latent Diffusion Inverse Problems

Latent diffusion models serve as powerful priors for solving inverse problems in image restoration, such as deblurring, inpainting, and super-resolution. **Current methods have a trade-off between generality and efficiency.** Solvers that are restricted to a fixed set of degradation operators are fast and efficient. Methods that support arbitrary degradation operators are slow and require gradients through the diffusion network. To break this bottleneck, we introduce PASEO (**P**erturb-**A**nd-**S**olve for **E**fficient **O**perator conditioning), a method that uses a small ($\sim$1M parameters) learned network to degrade diffusion model predictions in latent space. **PASEO supports learned degradation operators without back-propagating through the diffusion network.** We efficiently sample reconstructions from an approximate posterior by combining the diffusion model's prediction with the observed image. We do this by adding noise and solving linear equations based on a local linear approximation of the learned network, without building or inverting large covariance matrices. Across super-resolution, deblurring, and inpainting on FFHQ and COCO, PASEO achieves strong perceptual quality while running up to $19\times$ faster and using up to 34% less peak memory than the tested baselines, with the same or fewer model evaluations.