[Paper Review] Stabilizing Diffusion Posterior Sampling by Noise--Frequency Continuation

Feng Tian, Yixuan Li+4 more|arXiv (Cornell University)|Jan 30, 2026

Advanced Neuroimaging Techniques and Applications0 citations

TL;DR

Introduces a noise–frequency continuation framework for diffusion posterior sampling that enforces measurement consistency within a noise-dependent frequency band, improving stability and detail recovery in ill-posed inverse problems.

ABSTRACT

Diffusion posterior sampling solves inverse problems by combining a pretrained diffusion prior with measurement-consistency guidance, but it often fails to recover fine details because measurement terms are applied in a manner that is weakly coupled to the diffusion noise level. At high noise, data-consistency gradients computed from inaccurate estimates can be geometrically incongruent with the posterior geometry, inducing early-step drift, spurious high-frequency artifacts, plus sensitivity to schedules and ill-conditioned operators. To address these concerns, we propose a noise--frequency Continuation framework that constructs a continuous family of intermediate posteriors whose likelihood enforces measurement consistency only within a noise-dependent frequency band. This principle is instantiated with a stabilized posterior sampler that combines a diffusion predictor, band-limited likelihood guidance, and a multi-resolution consistency strategy that aggressively commits reliable coarse corrections while conservatively adopting high-frequency details only when they become identifiable. Across super-resolution, inpainting, and deblurring, our method achieves state-of-the-art performance and improves motion deblurring PSNR by up to 5 dB over strong baselines.

Motivation & Objective

• Address instability and loss of fine details in diffusion posterior sampling under severe degradations.
• Couple diffusion noise level with frequency-banded measurement guidance to avoid gradient misalignment at high noise.
• Develop a practical sampler that uses band-limited likelihood guidance and a multi-resolution Haar-based consistency strategy.
• Demonstrate improvements on super-resolution, inpainting, and deblurring over strong baselines under training-free settings.

Proposed method

• Construct a continuous family of intermediate posteriors where the likelihood is bandwidth-limited according to the current diffusion noise level.
• Use a frequency-guided measurement objective that blends full-band loss and band-limited loss with a noise-dependent schedule.
• Refine the PF-ODE estimate of x0 at each noise level via Langevin dynamics within the intermediate posterior.
• Introduce Haar-based multi-resolution fusion to commit coarse corrections aggressively and regulate high-frequency detail adoption.
• Employ a two-stage process: band-limited refinement of x0, then reintroduction of higher frequencies as identifiability improves, followed by re-noising and iteration.

Figure 1 : Results of Different Sampling Steps. The first and third rows show the estimated image $\boldsymbol{\hat{x}}_{0}$ , while the second and fourth rows show the corresponding noised image $\boldsymbol{x}_{T}$ at different timesteps. Across timesteps, the evaluated outputs preserve a similar

Experimental results

Research questions

• RQ1 Can coupling noise level with frequency bandwidth improve stability of diffusion posterior sampling under ill-conditioned degradations?
• RQ2 Does band-limited likelihood guidance combined with Haar fusion reduce high-frequency artifacts while preserving global structure?
• RQ3 How much PSNR/SSIM/LPIPS gains are achievable in super-resolution, inpainting, and deblurring without training-specific adjustments?
• RQ4 What is the role of multi-resolution (Haar) consistency in mitigating semantic information gaps introduced by band-limited likelihoods?

Key findings

• The proposed noise–frequency continuation framework yields improved stability and detail recovery across tasks including super-resolution, inpainting, and deblurring.
• Band-limited likelihood guidance with a gradual expansion of usable frequency content reduces early drift and sensitivity to schedules and operator conditioning.
• Haar-domain fusion provides a principled way to commit coarse corrections while cautiously incorporating high-frequency details, reducing artifacts.
• Empirical results show state-of-the-art performance in several settings, including up to ~5 dB PSNR gains on motion deblurring over strong baselines.
• The method maintains strong SSIM and LPIPS while improving PSNR across FFHQ and ImageNet datasets.

Figure 2 : Method Overview. First of all, a pre-trained diffusion model is applied to acquire the estimated $\boldsymbol{\hat{x}}_{0}$ . Second, we optimize $\boldsymbol{\hat{x}}_{0}$ in frequency domain and apply Haar fusion. Afterwards, target features are generated after iteratively sampling, and