CLIMB-flow: Coupled Linear Inverse posterior sampling via Multiscale-Based flow

Zeqiu Yu; Ruizhi Yuan; Mathews Jacob

cs.CVSep 27, 2026

CLIMB-flow: Coupled Linear Inverse posterior sampling via Multiscale-Based flow

Authors: Zeqiu Yu, Ruizhi Yuan, Mathews Jacob

Organizations: Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA, USA · Department of Biostatistics and Health Data Science, University of Pittsburgh, Pittsburgh, PA, USA

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.

Figures & tables

Figure 1: Preview of CLIMB-Flow reconstructions. Inference proceeds from coarse to fine, with upsampling (U) linking successive scales. At scale $k$ , a coupled target connects the noisy interpolant $x_{\tau}^{k}$ and clean image $x_{1}^{k}$ : the velocity network supplies prior information through the former, while measurements constrain the latter. Each panel shows one step of the approximate Gibbs sweep, repeated $S_{\mathrm{it}}$ times before advancing to the next scale.

Type	Model	Inpaint (box)				Inpaint (random)				Super resolution 4 $\times$
Type	Model	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$
P;F	Ours (Mode)	22.21	0.834	0.188	86.80	28.96	0.856	0.110	35.70	25.97	0.712	0.351	97.00
P;F	Ours	22.17	0.779	0.179	77.80	28.18	0.795	0.105	32.40	25.31	0.681	0.266	79.49
P;D	DAPS [ 5 ]	21.43	0.725	0.214	109.85	28.44	0.775	0.135	54.25	25.89	0.694	0.276	83.57
P;D	DPS [ 3 ]	18.94	0.722	0.257	126.52	23.52	0.745	0.297	87.53	21.13	0.489	0.361	106.32
P;D	DDRM [ 2 ]	18.63	0.733	0.254	116.37	–	–	–	–	22.62	0.521	0.324	103.85

Table 1: Quantitative results. Left: ImageNet comparisons with pixel- and latent-domain diffusion baselines. Ours (Mode) achieves the highest SSIM on all three tasks, while Ours achieves the lowest LPIPS/FID on both inpainting tasks and super-resolution. Right: CelebA comparisons with pixel-domain flow solvers and DiffPIR. Ours (Mode) leads PSNR/SSIM on all four tasks, with PSNR gains of

1.37

–

7.66

dB over the best competing baseline per task; Ours improves LPIPS over Mode on three tasks. Bold / underline : best/second-best among all methods in each panel, including both CLIMB-Flow variants; ties are marked equally. P/L: pixel/latent domain; D/F: diffusion/flow.

Figure 2: Qualitative results. (a) $4\times$ super-resolution comparisons with LatentDAPS and ReSample illustrate richer textures and lower LPIPS from sampling versus higher PSNR/SSIM from Mode. (b) Reconstructions on AFHQ $512\times 512$ with box inpainting: the top row shows generation diversity on ImageNet samples and the bottom row shows the convergence trajectory.

Figure 3: fastMRI reconstruction. Comparing with 4 baselines under $8\times$ accelerated MRI reconstruction. The MMSE and reconstruction error maps take 16 reconstructions. CLIMB-Flow algorithms achieves the best PSNR and SSIM, while preserving anatomical structure and fine-grained details.

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A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors

Zhaoqiang Liu, Tongyao Pang, Ruibing Wang, Yang Zheng

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Diffusion Priors Bayesian Inverse Problems Residual Conditional Diffusion Model Posterior Inverse Dynamics

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Pretrained diffusion models represent image distributions through a continuum of progressively smoothed distributions. This multiscale structure organizes generation from global structure to fine detail and supports high-quality, diverse samples. We exploit the same multiscale diffusion prior for linear imaging inverse problems. Rather than using the pretrained model only as a denoiser in an outer iteration, we define a surrogate likelihood whose center is aligned with the clean-image coordinate and whose covariance accounts for residual diffusion uncertainty. This construction defines an explicit surrogate posterior path, from which we derive continuous posterior dynamics. A tunable Langevin component supports target tracking and allows the amount of posterior exploration to be adapted to the application. We prove endpoint consistency and a finite-horizon tracking bound and, in the exact-score setting, first-order weak accuracy. For computation, we derive the Posterior-Dynamics Implicit--Explicit sampler (PD-IMEX), a stable method using one score evaluation per diffusion scale and an implicit data-consistency update. Experiments on deblurring, super-resolution, and inpainting show strong reconstruction quality at 100 score evaluations, coarse-grid stability, and controllable fidelity--diversity behavior.

Abstract

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