New scale-consistent diffusion method sharpens image reconstruction in 100 steps

Diffusion models excel at generating images, but solving inverse problems—like super-resolution, deblurring, or inpainting—requires posterior sampling with a pretrained diffusion prior. That conditional score is usually intractable, forcing prior methods to rely on approximations that drift from the true posterior. In a new arXiv paper, Zhaoqiang Liu, Tongyao Pang, Ruibing Wang, and Yang Zheng propose scale-consistent posterior dynamics, an ideal one-parameter posterior SDE family where a stochasticity parameter controls transport vs. exploration without altering the posterior marginals.

To make it practical, they re-express the likelihood in rescaled clean-image coordinates and use log-SNR to organize posterior proxies. Projecting diffusion uncertainty through the forward operator yields a noise-conditioned covariance path, and they interleave transport with a frozen-target Langevin corrector to ensure the surrogate SDE actually follows the posterior. Discrete implementation uses a Lie–Trotter splitter with a variance-matched split-step IMEX predictor. On FFHQ and ImageNet, 100 score evaluations deliver competitive super-resolution and deblurring fidelity, and a box-inpainting study confirms the importance of injecting matched innovation after the stiff likelihood solve. The method also comes with convergence guarantees and a first-order weak error bound.