FB-GDM：通过无监督变分推断实现高维线性逆问题的全贝叶斯引导扩散模型
FB-GDM: Fully-Bayesian Guided Diffusion Models for High-Dimensional Linear Inverse Problems via Unsupervised Variational Inference
- SATIE Laboratory（SATIE实验室）
- ENS Paris-Saclay（巴黎萨克雷高等师范学院）
- CNRS（法国国家科学研究中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
FB-GDM提出全贝叶斯引导扩散模型，通过变分推断自动学习精度参数，无需噪声水平或真实值校准，在高维线性逆问题中性能优于DPS和$\Pi$GDM，并具备跨任务鲁棒性。
AI中文摘要：
扩散模型是线性逆问题的强大先验，但参考引导方法，即扩散后验采样（DPS）和伪逆引导扩散模型（$\Pi$GDM），依赖于按任务调整的标量超参数，通常需要针对真实值进行调优。我们提出了FB-GDM，一种全贝叶斯引导扩散方法，消除了这一校准步骤。从$\Pi$GDM的高斯近似出发，我们推导出一个闭式条件分数，该分数依赖于两个精度参数（逆方差），一个与去噪近似相关，另一个与观测似然相关，并将它们视为潜在变量，在每一步反向过程中通过变分推断进行推断。一种可分离的分解使得每次更新的计算量随像素数量线性增长，因此推断在全图像分辨率下保持可处理，其成本与一次$\Pi$GDM运行相当。FB-GDM既不需要噪声水平也不需要真实值：其唯一输入是观测值和前向算子。在CelebA-HQ逆问题上的实验确立了两个结果。（i）仅从观测值推断出的精度参数，使FB-GDM在其标称设置下优于$\Pi$GDM，即使后者被给予真实噪声水平，根据算子不同可提升高达14 dB，并且与基于真实值校准的$\Pi$GDM基准（oracle）在0.1 dB内匹配。（ii）当前向算子、噪声水平或图像分布发生变化时，FB-GDM具有鲁棒性：它始终接近每个问题的$\Pi$GDM基准，并且不会出现DPS观察到的幻觉现象，而DPS在固定尺度下会显著退化，$\Pi$GDM只有在针对每个新问题基于真实值重新调优时才能保持竞争力。当先验应用于其训练集之外的图像时，数据和先验之间的这种重新平衡使FB-GDM保持忠实，而固定的面部先验引导否则可能产生幻觉。
英文摘要：
Diffusion models are powerful priors for linear inverse problems, but the reference guidance methods, Diffusion Posterior Sampling (DPS) and Pseudoinverse-Guided Diffusion Models ($Π$GDM), rely on scalar hyperparameters tuned per task, usually against the ground truth. We introduce FB-GDM, a fully-Bayesian guided diffusion method that removes this calibration step. Starting from the Gaussian approximation of $Π$GDM, we derive a closed-form conditional score that depends on two precision parameters (inverse variances), one associated with the denoising approximation and one with the observation likelihood, and treat them as latent variables inferred by variational inference at each reverse step. A separable factorization makes each update scale linearly with the number of pixels, so the inference stays tractable at full image resolution, at a cost comparable to one $Π$GDM run. FB-GDM requires neither the noise level nor the ground truth: its only inputs are the observation and the forward operator. Experiments on CelebA-HQ inverse problems establish two results. (i) The precision parameters, inferred from the observation alone, allow FB-GDM to outperform $Π$GDM at its nominal setting, even when the latter is given the true noise level, by up to 14 dB depending on the operator, and to match the ground-truth-calibrated $Π$GDM oracle within 0.1 dB. (ii) FB-GDM is robust when the forward operator, the noise level, or the image distribution changes: it stays close to a per-problem $Π$GDM oracle throughout and does not exhibit the hallucinations observed with DPS, whereas DPS substantially degrades at a fixed scale and $Π$GDM stays competitive only if it is re-tuned against the ground truth for each new problem. When the prior is applied to images outside its training set, this re-balancing between data and prior keeps FB-GDM faithful where a fixed face-prior guidance can otherwise hallucinate.
