Scale-Consistent Posterior Dynamics for Diffusion Inverse Problems

Posterior sampling with a pretrained diffusion prior is governed by a conditional score whose intermediate likelihood component is generally intractable. We begin from an ideal one-parameter posterior SDE family in which a stochasticity parameter controls probability-flow transport and stochastic exploration without changing the posterior marginals. To obtain a tractable model, we express the likelihood in a rescaled clean-image coordinate and use log-SNR to organize the resulting posterior proxies. Projecting the diffusion uncertainty through the forward operator then yields a noise-conditioned covariance path whose targets approach the clean posterior. Because endpoint consistency of these targets does not ensure that a surrogate transport follows them, we interleave the transport with a frozen-target Langevin corrector, producing a continuous surrogate SDE. We discretize this model with an outer Lie--Trotter splitting and a variance-matched split-step IMEX predictor that treats the learned prior explicitly, the linear likelihood implicitly, and the stochastic innovation after the implicit solve. We prove marginal invariance of the ideal family, posterior convergence of the continuous surrogate under mixing and transport-defect conditions, and a first-order weak error bound for the discrete algorithm. Experiments on FFHQ and ImageNet with 100 score evaluations demonstrate competitive reconstruction fidelity for super-resolution and deblurring. A controlled 100-image ablation separates scale consistency from the finite-step effects of stochastic-increment placement, continuation, and corrector allocation. A separate noiseless box-inpainting study shows that large exploration reaches a performance plateau only when the matched innovation is injected after the stiff likelihood solve.

Outlier-Robust Diffusion Solvers for Inverse Problems

Methods based on diffusion models (DMs) for solving inverse problems (IPs) have recently achieved remarkable performance. However, DM-based methods typically struggle against outliers, which are common in real-world measurements. In this work, to tackle IPs with outliers, we first refine the measurement via explicit noise estimation to mitigate the effect of noise. Subsequently, we formulate an iteratively reweighted least squares objective based on the Huber loss to address the outliers. We propose a method utilizing gradient descent to approximately solve the corresponding optimization problem for the robust objective. To avoid delicate tuning of the learning rate required by the gradient descent method, we further employ the conjugate gradient method with an efficient strategy for updating. Extensive experiments on multiple image datasets for linear and nonlinear tasks under various conditions demonstrate that our proposed methods exhibit robustness to outliers and outperform recent DM-based methods in most cases.

Enhancing Low-resolution Image Representation Through Normalizing Flows

Low-resolution image representation is a special form of sparse representation that retains only low-frequency information while discarding high-frequency components. This property reduces storage and transmission costs and benefits various image processing tasks. However, a key challenge is to preserve essential visual content while maintaining the ability to accurately reconstruct the original images. This work proposes LR2Flow, a nonlinear framework that learns low-resolution image representations by integrating wavelet tight frame blocks with normalizing flows. We conduct a reconstruction error analysis of the proposed network, which demonstrates the necessity of designing invertible neural networks in the wavelet tight frame domain. Experimental results on various tasks, including image rescaling, compression, and denoising, demonstrate the effectiveness of the learned representations and the robustness of the proposed framework.