Despite substantial advances in all-in-one image restoration for addressing diverse degradations within a unified model, existing methods remain vulnerable to out-of-distribution degradations, thereby limiting their generalization in real-world scenarios. To tackle the challenge, this work is motivated by the intuition that multisource degraded feature distributions are induced by different degradation-specific shifts from an underlying degradation-agnostic distribution, and recovering such a shared distribution is thus crucial for achieving generalization across degradations. With this insight, we propose BaryIR, a representation learning framework that aligns multisource degraded features in the Wasserstein barycenter (WB) space, which models a degradation-agnostic distribution by minimizing the average of Wasserstein distances to multisource degraded distributions. We further introduce residual subspaces, whose embeddings are mutually contrasted while remaining orthogonal to the WB embeddings. Consequently, BaryIR explicitly decouples two orthogonal spaces: a WB space that encodes the degradation-agnostic invariant contents shared across degradations, and residual subspaces that adaptively preserve the degradation-specific knowledge. This disentanglement mitigates overfitting to in-distribution degradations and enables adaptive restoration grounded on the degradation-agnostic shared invariance. Extensive experiments demonstrate that BaryIR performs competitively against state-of-the-art all-in-one methods. Notably, BaryIR generalizes well to unseen degradations (e.g., types and levels) and shows remarkable robustness in learning generalized features, even when trained on limited degradation types and evaluated on real-world data with mixed degradations.

Medical image reconstruction from measurement data is a vital but challenging inverse problem. Deep learning approaches have achieved promising results, but often requires paired measurement and high-quality images, which is typically simulated through a forward model, i.e., retrospective reconstruction. However, training on simulated pairs commonly leads to performance degradation on real prospective data due to the retrospective-to-prospective gap caused by incomplete imaging knowledge in simulation. To address this challenge, this paper introduces imaging Knowledge-Informed Dynamic Optimal Transport (KIDOT), a novel dynamic optimal transport framework with optimality in the sense of preserving consistency with imaging physics in transport, that conceptualizes reconstruction as finding a dynamic transport path. KIDOT learns from unpaired data by modeling reconstruction as a continuous evolution path from measurements to images, guided by an imaging knowledge-informed cost function and transport equation. This dynamic and knowledge-aware approach enhances robustness and better leverages unpaired data while respecting acquisition physics. Theoretically, we demonstrate that KIDOT naturally generalizes dynamic optimal transport, ensuring its mathematical rationale and solution existence. Extensive experiments on MRI and CT reconstruction demonstrate KIDOT's superior performance. Code is available at https://github.com/TaoranZheng717/KIDOT.

Unified, or more formally, all-in-one image restoration has emerged as a practical and promising low-level vision task for real-world applications. In this context, the key issue lies in how to deal with different types of degraded images simultaneously. Existing methods fit joint regression models over multi-domain degraded-clean image pairs of different degradations. However, due to the severe ill-posedness of inverting heterogeneous degradations, they often struggle with thoroughly perceiving the degradation semantics and rely on paired data for supervised training, yielding suboptimal restoration maps with structurally compromised results and lacking practicality for real-world or unpaired data. To break the barriers, we present a Degradation-Aware Residual-Conditioned Optimal Transport (DA-RCOT) approach that models (all-in-one) image restoration as an optimal transport (OT) problem for unpaired and paired settings, introducing the transport residual as a degradation-specific cue for both the transport cost and the transport map. Specifically, we formalize image restoration with a residual-guided OT objective by exploiting the degradation-specific patterns of the Fourier residual in the transport cost. More crucially, we design the transport map for restoration as a two-pass DA-RCOT map, in which the transport residual is computed in the first pass and then encoded as multi-scale residual embeddings to condition the second-pass restoration. This conditioning process injects intrinsic degradation knowledge (e.g., degradation type and level) and structural information from the multi-scale residual embeddings into the OT map, which thereby can dynamically adjust its behaviors for all-in-one restoration. Extensive experiments across five degradations demonstrate the favorable performance of DA-RCOT as compared to state-of-the-art methods, in terms of distortion measures, perceptual quality, and image structure preservation. Notably, DA-RCOT delivers superior adaptability to real-world scenarios even with mixed degradations and shows distinctive robustness to both degradation levels and the number of degradations.

Deep networks for 3D point clouds have achieved remarkable success in classification task but remain vulnerable to geometric variations resulting from inconsistent data acquisition procedures. This leads to significant performance degradation when models trained on a source domain are tested on out-of-distribution target domains, highlighting the challenges of 3D domain generalization and adaptation. In this paper, we introduce a novel Multi-Scale Part-based feature Representation, dubbed MSPR, as a generalizable representation for point cloud domain generalization and adaptation. Rather than relying on global shape feature, we align the part-level features of shapes at different scales to a set of learnable part-template features that encode local geometric structures shared between the source and the target domains. Specifically, shapes from different domains are organized into part-level features at various scales and then aligned to the part-template features. To balance the generalization and discrimination abilities of parts at different scales, we further design a cross-scale feature fusion module to exchange information between aligned part-based features at different scales. The fused part-based representations are finally aggregated by a part-based feature aggregation module. To improve the robustness of the aligned part-based representations and global shape representation to geometry variations, we further propose a Contrastive Learning framework on Shape Representation (CLSR). Experiments are conducted on 3D domain generalization and adaptation benchmarks for point cloud classification. Extensive experiments on 3D domain generalization and adaptation benchmarks demonstrate that proposed approach outperforms previous state-of-the-art methods in both tasks. Ablation studies confirm the effectiveness of the components in our model.

Deep learning-based image restoration methods generally struggle with faithfully preserving the structures of the original image. In this work, we propose a novel Residual-Conditioned Optimal Transport (RCOT) approach, which models image restoration as an optimal transport (OT) problem for both unpaired and paired settings, introducing the transport residual as a unique degradation-specific cue for both the transport cost and the transport map. Specifically, we first formalize a Fourier residual-guided OT objective by incorporating the degradation-specific information of the residual into the transport cost. We further design the transport map as a two-pass RCOT map that comprises a base model and a refinement process, in which the transport residual is computed by the base model in the first pass and then encoded as a degradation-specific embedding to condition the second-pass restoration. By duality, the RCOT problem is transformed into a minimax optimization problem, which can be solved by adversarially training neural networks. Extensive experiments on multiple restoration tasks show that RCOT achieves competitive performance in terms of both distortion measures and perceptual quality, restoring images with more faithful structures as compared with state-of-the-art methods.

Adversarial domain adaptation has been an effective approach for learning domain-invariant features by adversarial training. In this paper, we propose a novel adversarial domain adaptation approach defined in the spherical feature space, in which we define spherical classifier for label prediction and spherical domain discriminator for discriminating domain labels. In the spherical feature space, we develop a spherical robust pseudo-label loss to utilize pseudo-labels robustly, which weights the importance of the estimated labels of target domain data by the posterior probability of correct labeling, modeled by the Gaussian-uniform mixture model in the spherical space. Our proposed approach can be generally applied to both unsupervised and semi-supervised domain adaptation settings. In particular, to tackle the semi-supervised domain adaptation setting where a few labeled target domain data are available for training, we propose a novel reweighted adversarial training strategy for effectively reducing the intra-domain discrepancy within the target domain. We also present theoretical analysis for the proposed method based on the domain adaptation theory. Extensive experiments are conducted on multiple benchmarks for object recognition, digit recognition, and face recognition. The results show that our method either surpasses or is competitive compared with the recent methods for both unsupervised and semi-supervised domain adaptation. Ablation studies also confirm the effectiveness of the spherical classifier, spherical discriminator, spherical robust pseudo-label loss, and reweighted adversarial training strategy.

Deep networks trained on the source domain show degraded performance when tested on unseen target domain data. To enhance the model's generalization ability, most existing domain generalization methods learn domain invariant features by suppressing domain sensitive features. Different from them, we propose a Domain Projection and Contrastive Learning (DPCL) approach for generalized semantic segmentation, which includes two modules: Self-supervised Source Domain Projection (SSDP) and Multi-Level Contrastive Learning (MLCL). SSDP aims to reduce domain gap by projecting data to the source domain, while MLCL is a learning scheme to learn discriminative and generalizable features on the projected data. During test time, we first project the target data by SSDP to mitigate domain shift, then generate the segmentation results by the learned segmentation network based on MLCL. At test time, we can update the projected data by minimizing our proposed pixel-to-pixel contrastive loss to obtain better results. Extensive experiments for semantic segmentation demonstrate the favorable generalization capability of our method on benchmark datasets.

Universal domain adaptation (UniDA) aims to transfer knowledge from a labeled source domain to an unlabeled target domain without requiring the same label sets of both domains. The existence of domain and category shift makes the task challenging and requires us to distinguish “known” samples (i.e., samples whose labels exist in both domains) and “unknown” samples (i.e., samples whose labels exist in only one domain) in both domains before reducing the domain gap. In this paper, we consider the problem from the point of view of distribution matching which we only need to align two distributions partially. A novel approach, dubbed mini-batch Prototypical Partial Optimal Transport (m-PPOT), is proposed to conduct partial distribution alignment for UniDA. In training phase, besides minimizing m-PPOT, we also leverage the transport plan of m-PPOT to reweight source prototypes and target samples, and design reweighted entropy loss and reweighted cross-entropy loss to distinguish “known” and “unknown” samples. Experiments on four benchmarks show that our method outperforms the previous state-of-the-art UniDA methods.

Conditional score-based diffusion model (SBDM) is for conditional generation of target data with paired data as condition, and has achieved great success in image translation. However, it requires the paired data as condition, and there would be insufficient paired data provided in real-world applications. To tackle the applications with partially paired or even unpaired dataset, we propose a novel Optimal Transport-guided Conditional Score-based diffusion model (OTCS) in this paper. We build the coupling relationship for the unpaired or partially paired dataset based on $L_2$-regularized unsupervised or semi-supervised optimal transport, respectively. Based on the coupling relationship, we develop the objective for training the conditional score-based model for unpaired or partially paired settings, which is based on a reformulation and generalization of the conditional SBDM for paired setting. With the estimated coupling relationship, we effectively train the conditional score-based model by designing a ``resampling-by-compatibility'' strategy to choose the sampled data with high compatibility as guidance. Extensive experiments on unpaired super-resolution and semi-paired image-to-image translation demonstrated the effectiveness of the proposed OTCS model. From the viewpoint of optimal transport, OTCS provides an approach to transport data across distributions, which is a challenge for OT on large-scale datasets. We theoretically prove that OTCS realizes the data transport in OT with a theoretical bound.

Score-based diffusion models (SBDMs) have achieved state-of-the-art results in image generation. In this paper, we propose a Non-isotropic Gaussian Diffusion Model (NGDM) for image editing, which requires editing the source image while preserving the image regions irrelevant to the editing task. We construct NGDM by adding independent Gaussian noises with different variances to different image pixels. Instead of specifically training the NGDM, we rectify the NGDM into an isotropic Gaussian diffusion model with different pixels having different total forward diffusion time. We propose to reverse the diffusion by designing a sampling method that starts at different time for different pixels for denoising to generate images using the pre-trained isotropic Gaussian diffusion model. Experimental results show that NGDM achieves state-of-the-art performance for image editing tasks, considering the trade-off between the fidelity to the source image and alignment with the desired editing target.

Existing Optimal Transport (OT) methods mainly derive the optimal transport plan/matching under the criterion of transport cost/distance minimization, which may cause incorrect matching in some cases. In many applications, annotating a few matched keypoints across domains is reasonable or even effortless in annotation burden. It is valuable to investigate how to leverage the annotated keypoints to guide the correct matching in OT. In this paper, we propose a novel KeyPoint-Guided model by ReLation preservation (KPG-RL) that searches for the matching guided by the keypoints in OT. To impose the keypoints in OT, first, we propose a mask-based constraint of the transport plan that preserves the matching of keypoint pairs. Second, we propose to preserve the relation of each data point to the keypoints to guide the matching. The proposed KPG-RL model can be solved by the Sinkhorn's algorithm and is applicable even when distributions are supported in different spaces. We further utilize the relation preservation constraint in the Kantorovich Problem and Gromov-Wasserstein model to impose the guidance of keypoints in them. Meanwhile, the proposed KPG-RL model is extended to partial OT setting. As an application, we apply the proposed KPG-RL model to the heterogeneous domain adaptation. Experiments verified the effectiveness of the KPG-RL model.

Deep networks on 3D point clouds have achieved remarkable success in 3D classification, while they are vulnerable to geometry variations caused by inconsistent data acquisition procedures. This results in a challenging 3D domain generalization (3DDG) problem, that is to generalize a model trained on source domain to an unseen target domain. Based on the observation that local geometric structures are more generalizable than the whole shape, we propose to reduce the geometry shift by a generalizable part-based feature representation and design a novel part-based domain generalization network (PDG) for 3D point cloud classification. Specifically, we build a part-template feature space shared by source and target domains. Shapes from distinct domains are first organized to part-level features and then represented by part-template features. The transformed part-level features, dubbed aligned part-based representations, are then aggregated by a part-based feature aggregation module. To improve the robustness of the part-based representations, we further propose a contrastive learning framework upon part-based shape representation. Experiments and ablation studies on 3DDA and 3DDG benchmarks justify the efficacy of the proposed approach for domain generalization, compared with the previous state-of-the-art methods. Our code will be available on http://github.com/weixmath/PDG.

Partial domain adaptation (PDA) has gained much attention due to its practical setting. The current PDA methods usually adapt the feature extractor by aligning the target and reweighted source domain distributions. In this paper, we experimentally find that the feature adaptation by the reweighted distribution alignment in some state-of-the-art PDA methods is not robust to the ``noisy'' weights of source domain data, leading to negative domain transfer on some challenging benchmarks. To tackle the challenge of negative domain transfer, we propose a novel Adversarial Reweighting (AR) approach that adversarially learns the weights of source domain data to align the source and target domain distributions, and the transferable deep recognition network is learned on the reweighted source domain data. Based on this idea, we propose a training algorithm that alternately updates the parameters of the network and optimizes the weights of source domain data. Extensive experiments show that our method achieves state-of-the-art results on the benchmarks of ImageNet-Caltech, Office-Home, VisDA-2017, and DomainNet. Ablation studies also confirm the effectiveness of our approach.

Adversarial domain adaptation (DA) has been an effective approach for learning domain-invariant features by adversarial training. In this paper, we propose a novel adversarial DA approach completely defined in spherical feature space, in which we define spherical classifier for label prediction and spherical domain discriminator for discriminating domain labels. To utilize pseudo-label robustly, we develop a robust pseudo-label loss in the spherical feature space, which weights the importance of estimated labels of target data by posterior probability of correct labeling, modeled by Gaussian-uniform mixture model in spherical feature space. Extensive experiments show that our method achieves state-of-the-art results, and also confirm effectiveness of spherical classifier, spherical discriminator and spherical robust pseudo-label loss.