Problem
Research questions and friction points this paper is trying to address.
Bayesian inverse problems
latent diffusion models
spatial detail loss
non-linear optimization
posterior sampling
CLIMB-flow: Coupled Linear Inverse posterior sampling via Multiscale-Based flow
🤖 AI Summary
This study addresses the limitations of latent diffusion models in solving Bayesian inverse problems, where spatial compression causes detail loss and nonlinear optimization bottlenecks. To overcome these challenges, this work proposes a multi-scale coupled linear posterior sampling algorithm tailored for pyramid architectures. The method employs a coarse-to-fine hierarchical strategy to generate images directly in the pixel domain. By alternately executing endpoint estimation, data consistency updates, and re-noising steps combined with approximate Gibbs sampling, it achieves high-fidelity reconstruction. This approach effectively mitigates the deficiencies of latent variable compression, yielding PSNR improvements of 1.37–7.66 dB on tasks such as CelebA, while supporting high-resolution 512×512 pixel-domain reconstruction.
📝 Abstract
Diffusion models are now widely used in Bayesian inverse problems in imaging as priors, where latent diffusion models are often used for larger scale problems to keep the computational complexity and model-size manageable. Unfortunately, the auto-encoder based compression results in loss of spatial detail. In addition, the optimization is converted to a non-linear problem. In this paper, we introduce a posterior sampling algorithm customized for the pyramidal/cascaded architecture, which relies on a coarse to fine hierarchical strategy to generate images in the pixel domain. We present CLIMB-Flow which alternates between three steps: an end-point estimation from the current coarse and noisy image, data-consistent update of the clean image, and re-noising it back to the level the network expects. Together these steps sample the posterior at that scale using an approximate Gibbs sampling from two conditional distributions. Experiments on ImageNet, CelebA, AFHQ and fastMRI span inpainting, deblurring, super-resolution and accelerated MRI, with PSNR gains of 1.37-7.66 dB over the strongest competing method on CelebA and pixel-domain reconstruction up to 512x512.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Diffusion models
Bayesian inverse problems
Posterior sampling
Multiscale-based flow
Pixel-domain reconstruction
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