Recent advances in *inverse problem* solving have increasingly adopted flow *priors* over diffusion models due to their ability to construct straight probability paths from noise to data, thereby enhancing efficiency in both training and inference. However, current flow-based inverse solvers face two primary limitations: (i) they operate directly in pixel space, which demands heavy computational resources for training and restricts scalability to high-resolution images, and (ii) they employ guidance strategies with *prior*-agnostic posterior covariances, which can weaken alignment with the generative trajectory and degrade posterior coverage. In this paper, we propose **LFlow** (**L**atent Refinement via **Flow**s), a *training-free* framework for solving linear inverse problems via pretrained latent flow priors. LFlow leverages the efficiency of flow matching to perform ODE sampling in latent space along an optimal path. This latent formulation further allows us to introduce a theoretically grounded posterior covariance, derived from the optimal vector field, enabling effective flow guidance. Experimental results demonstrate that our proposed method outperforms state-of-the-art latent diffusion solvers in reconstruction quality across most tasks.

In medical imaging, inverse problems aim to infer highfidelity images from incomplete, noisy measurements, minimizing expenses and risks to patients in clinical settings. Diffusion models have recently emerged as a promising solution to such practical challenges, proving particularly useful for the training-free inference of images from partially acquired measurements in Magnetic Resonance Imaging (MRI) and Computed Tomography (CT). A central challenge, however, is how to guide an unconditional denoised estimate to conform to the measurement information. Existing methods often employ either deficient projection or inefficient posterior approximation, leading to suboptimal performance. In this paper, we propose Bi-level Guided Diffusion Models (BGDM), a zero-shot imaging framework that efficiently steers the image generation process through a bi-level guidance strategy. Specifically, BGDM first approximates an inner-level conditional posterior mean to establish an initial measurement-consistent prediction and then solves an outer-level proximal optimization objective to reinforce the measurement consistency. Our experimental findings, leveraging publicly available MRI and CT datasets, indicate that BGDM is more effective and efficient compared to baseline methods, consistently generating high-fidelity medical images and significantly reducing hallucinatory artifacts in cases of sparse measurements. Code https://github.com/hosseinaskari-cs/BGDM.

Abstract Unsupervised domain adaptation (UDA) aims at enhancing the generalizability of the classification model learned from the labeled source domain to an unlabeled target domain. An established approach to UDA is to constrain the classifier on an intermediate representation that is distributionally invariant across domains. However, recent theoretical and empirical research has revealed that relying only on invariance fails to guarantee a small target error, thus making equality in the distribution of representations unnecessary. In this paper, we propose to relax invariant representation learning by finding a general relationship between the source and target representations, which allows an interchange of the more discriminative domain information. To this end, we formalize the MapFlow framework, which explicitly constructs an invertible mapping between the target encoded distribution and variationally induced source representation. Empirical results on public benchmark datasets show the desirable performance of our proposed algorithm compared to state-of-the-art methods.