[论文解读] Stabilizing Diffusion Posterior Sampling by Noise--Frequency Continuation

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

Advanced Neuroimaging Techniques and Applications被引用 0

一句话总结

引入一种噪声-频率连续框架用于扩散后验采样，在噪声相关频带内强制测量一致性，从而在病态逆问题中提升稳定性与细节恢复。

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.

研究动机与目标

• 在严重退化下解决扩散后验采样的不稳定性与细节丢失问题。
• 将扩散噪声水平与带频测量引导耦合，避免高噪声下的梯度错位。
• 开发一个实际可用的采样器，使用带限似然引导与多分辨率 Haar 基于的一致性策略。
• 在训练自由设定下，在超分辨率、修复和去模糊方面相对于强基线显示改进。

提出的方法

• 构建一个连续的中间后验族，其中在当前扩散噪声水平下对似然进行带宽限制。
• 使用带频引导的测量目标，结合全带损失与带限损失的噪声依赖性调度。
• 在中间后验中通过 Langevin 动力学在每个噪声水平上细化 x0 的 PF-ODE 估计。
• 引入基于 Haar 的多分辨率融合，在积极地提交粗略修正的同时，调控高频细节的采纳。
• 采用两阶段流程：对 x0 进行带限细化，然后在识别性提高后重新引入更高频率，随后再去噪并迭代。

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

实验结果

研究问题

• RQ1 将噪声水平与频带带宽耦合是否能在病态降解下改善扩散后验采样的稳定性？
• RQ2 带限似然引导结合 Haar 融合是否在保留全局结构的同时减少高频伪影？
• RQ3 在不进行训练特定调整的情况下，超分、修复和去模糊可获得多少 PSNR/SSIM/LPIPS 增益？
• RQ4 多分辨率（Haar）一致性的作用在于减小带限似然引入的语义信息缺口吗？

主要发现

• 所提出的噪声-频率连续框架在超分辨率、修复和去模糊等任务中展现出更好的稳定性与细节恢复。
• 带限似然引导与可用频率内容逐步扩展，降低早期漂移以及对调度与算子条件的敏感性。
• Haar 域融合提供了一种以原理性方式提交粗略修正、谨慎引入高频细节的方法，降低伪影。
• 经验结果在若干设置中达到行业领先水平，在运动去模糊等任务上对强基线的 PSNR 提升约 ~5 dB。
• 该方法在 FFHQ 与 ImageNet 数据集上保持了强的 SSIM 与 LPIPS，同时提升了 PSNR。

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