Making Every Step Count: Spatio-Temporal Information Allocation for Imaging Inverse Problems

Flow-based generative models have emerged as powerful image priors for training-free inverse problem solving, capturing coherent semantics and fine-grained structure. Despite these strengths, existing flow-based inverse solvers primarily focus on the design of individual updates, largely overlooking spatio-temporal information allocation under a fixed number of function evaluations (NFEs). Temporally, insufficient early exploration can trap the flow trajectory in an incorrect semantic basin, whereas excessive allocation of NFEs to early stages leaves little budget for late-stage refinement. Spatially, data consistency provides direct constraints only within observed regions, whereas the recovery of missing regions relies mainly on the generative prior. To address these two issues, we introduce two complementary and training-free components, i.e., Spectrum-Adaptive Scheduling (SAS) and Measurement-Prioritized Attention (MPA). For temporal allocation, SAS distributes the available NFEs over flow time according to the degradation spectrum and logSNR geometry, thus better balancing semantic exploration and detail refinement. For spatial propagation, MPA exploits data-prior conflicts to guide information toward weakly constrained regions, thereby enhancing semantic and structural fidelity. Extensive experiments on standard image inverse problems, e.g., super-resolution, motion deblurring, and inpainting, demonstrate that the proposed components can be integrated into existing flow-based inverse solvers in a plug-and-play manner without retraining or additional flow-model evaluations, and can also significantly improve the restoration quality of existing solvers.

SC-Diff: Semantically Calibrated Diffusion for Visible-to-Infrared Image Translation

Visible-to-infrared image translation provides a practical way to expand infrared training data using abundant visible images. Diffusion models are promising for this task because of their strong generative performance. However, existing diffusion-based methods typically use semantic priors only as external conditions, without explicitly regulating token interactions within the denoising network. Consequently, they struggle to preserve object locations, shapes, and semantic layouts required for reliable annotation reuse. We propose SC-Diff, a semantically calibrated latent diffusion framework that uses semantic priors for both conditional guidance and internal self-attention calibration. A pretrained SAM3 model with predefined text prompts first extracts category-specific semantic masks from visible images. These masks are merged into a semantic map and fused with the visible image as the input condition. The same map is converted into token-level semantic labels to calibrate self-attention in the denoising network. Based on these labels, we introduce Semantic-Guided Self-Attention Calibration (SGSC), which adaptively applies positive biases to query-key pairs of the same category. The query-wise calibration strength depends on the dispersion of attention across semantic categories and the attention assigned to the query's own category. The original attention scores further modulate the bias, giving greater calibration to same-category keys with stronger responses. This soft calibration reduces cross-category interference while retaining global contextual interactions, thereby improving semantic consistency in generated infrared images. Extensive experiments show that SC-Diff improves perceptual quality and produces more effective synthetic training data for downstream infrared object detection.

Harnessing the Potential of Optimizing Data Mixtures via Bayesian Domain Reweighting

The performance of Large Language Models (LLMs) is fundamentally influenced by the distributional composition of multi-domain pre-training data. While manual heuristics were prevalent in early models, they increasingly fail to capture the intricate synergies between domains as data complexity grows. To overcome the issue, a dominant approach seeks to fit a proxy function mapping between domain weights and their corresponding validation losses, and then find the optimal domain weights to minimize validation losses. These methods rely on strong structural assumptions, such as rank invariance or scaling laws, which are often violated, resulting in non-negligible estimation bias. A promising approach is to directly optimize the weighting scheme from data. However, it suffers from unstable optimization trajectory and prohibitive computational overhead, limiting its potential to search better domain weights configurations. This paper presents a Bayesian domain weighting method to infer the weights from a Dirichlet distribution via introducing Gamma prior information learned from observations. Experimental results demonstrate that proposed method could achieve stable and efficient domain weights learning, and identifies optimal mixtures while consuming substantially less data than search-based function-fitting methods, revitalizing optimization-based domain weighting for large-scale applications.

Registration-Grounded Spectral Fusion for Unregistered WLI/NBI Endoscopic Lesion Segmentation

White-light imaging (WLI) and narrow-band imaging (NBI) provide complementary views of endoscopic lesions, but their paired observations are often spatially misaligned due to viewpoint changes, tissue deformation, and sequential handheld acquisition. This makes direct WLI/NBI fusion prone to mixing non-corresponding regions and may even degrade segmentation around lesion boundaries. To address this problem, we propose a reliability-aware complex-domain fusion framework for paired-but-unregistered WLI/NBI lesion segmentation. The framework first establishes topology-regularized feature correspondence and further estimates where the cross-modal correspondence is reliable. Guided by this reliability, the model selectively fuses WLI and NBI features in a learnable complex representation. In this representation, WLI-derived cues mainly provide appearance-related magnitude responses, while NBI-derived cues provide structure-sensitive phase responses. Unlike conventional real-valued or symmetric multimodal fusion, the proposed method explicitly models the different roles of WLI and NBI and suppresses unreliable cross-modal interaction in locally mismatched regions. Experiments on paired WLI/NBI endoscopic datasets show that the proposed reliability-aware registration grounding and complex-domain fusion consistently improve lesion segmentation performance. Role-reversal and module ablation studies further validate the necessity of both the modality-role design and reliability-guided cross-modal interaction.

Flash EQ-Linear: Accelerating Equivariant Linear Layers via Group-wise Discrete Fourier Transform

Equivariant networks embed geometric symmetries as structural priors through weight sharing, achieving remarkable parameter efficiency across vision tasks. However, this parameter efficiency does not translate into compute efficiency: existing implementations unroll the structured weights into dense matrices and dispatch them to generic dense kernels, so the FLOPs of an equivariant layer are no smaller than those of a non-equivariant counterpart. In this paper, we observe that the equivariant linear (EQ-Linear) layer---the most fundamental and frequently used module in modern equivariant architectures---is essentially a circular convolution along the group dimension composed with a linear transform along the channel dimension. Building on this observation, we propose Flash EQ-Linear, an exact acceleration algorithm that reduces the complexity from $\mathcal{O}(NDC)$ to $\mathcal{O}(NDC/T)$ by combining the Fourier convolution theorem along the group dimension with the conjugate symmetry of the real DFT. We further provide dedicated CUDA kernels for Flash EQ-Linear, covering both forward and backward passes and both FP32 and FP16 precision. At the operator level, Flash EQ-Linear achieves up to ${2\times}$ forward speedup over PyTorch's F.linear; at the network level, Flash EQ-ViT and Flash EQ-Swin achieve up to ${1.7\times}$ end-to-end speedup over both equivariant and non-equivariant baselines. To our knowledge, this is the first time equivariant networks strictly dominate their non-equivariant counterparts along all three axes simultaneously: accuracy, parameter efficiency, and inference speed.Code is available at https://github.com/zhongchenzhao/FlashEQLinear.

Sharper Analysis of Single-Loop Methods for Bilevel Optimization

Bilevel optimization underpins many machine learning applications, including hyperparameter optimization, meta-learning, neural architecture search, and reinforcement learning. While hypergradient-based methods have advanced significantly, a gap persists between theoretical guarantees and practical single-loop implementations required for efficiency. We bridge this gap by establishing sharper convergence results for single-loop approximate implicit differentiation (AID) and iterative differentiation (ITD) methods, leveraging our proposed analytical framework, decoupled norm analysis (DNA). For AID, we improve the convergence rate from $\mathcal{O}(κ^6/K)$ to $\mathcal{O}(κ^5/K)$, where $κ$ is the condition number of the inner-level problem. For ITD, we prove that the asymptotic error is $\mathcal{O}(κ^2)$, exactly matching the known lower bound and improving upon the previous $\mathcal{O}(κ^3)$ guarantee. Numerical experiments on synthetic and real tasks corroborate our theoretical findings.

Randomized neural operator for parametric PDEs with fast training and conformal uncertainty quantification

Repeatedly solving parametric PDEs is essential for uncertainty quantification, design optimization and inverse problems, but conventional neural operators require expensive non-convex training. We introduce PCA--RaNN, a randomized latent neural operator that combines PCA-based dimensionality reduction with fixed random features and a closed-form least-squares readout. It recasts latent operator learning as fixed-feature linear regression, reducing training time by one to three orders of magnitude across benchmarks while maintaining competitive accuracy. We introduce an energy-matched scaling rule and a lightweight two-parameter BFGS refinement to correct suboptimal feature scales. Ensemble averaging reduces predictive variance. On Burgers, Darcy, Navier--Stokes and backward heat equation benchmarks, PCA--RaNN provides a favorable speed--accuracy trade-off against operator-learning baselines. The ensemble supports split-conformal prediction intervals, and the linear readout enables rapid online adaptation via recursive least squares without retraining hidden features. This provides an efficient, uncertainty-aware surrogate for many-query scientific workflows.

Deciphering Neural Reparameterized Full-Waveform Inversion with Neural Sensitivity Kernel and Wave Tangent Kernel

Full-waveform inversion (FWI) estimates unknown parameters in the wave equation from limited boundary measurements. Recent advances in neural reparameterized FWI (NeurFWI) demonstrate that representing the parameters using a neural network can reduce the reliance on the high-quality initial model and wavefield data, at the cost of slow high-resolution convergence. However, its underlying theoretical mechanism remains unclear. In this study, we establish the neural sensitivity kernel (NSK) and the wave tangent kernel (WTK) to analyze their convergence behavior from both model and data domains. These theoretical frameworks show that the neural tangent kernel (NTK) induced by neural representation adaptively modulates the original sensitivity and wave tangent kernels. This modulation leads to several key outcomes, i.e., the spectral filtering effect, the gradient wavenumber modulation, and the wave frequency bias, connecting the convergence behavior of NeurFWI with the eigen-structures of NSK and WTK. Building on these insights, we propose several enhanced NeurFWI methods with tailored eigen-structures in NSK and WTK to improve inversion performances and efficiency. We numerically validate these theoretical claims and the proposed methods in seismic exploration, and firstly extend their application to medical imaging.

HIR-ALIGN: Enhancing Hyperspectral Image Restoration via Diffusion-Based Data Generation

Hyperspectral image (HSI) restoration is crucial for reliable analysis, as real HSIs suffer from degradations like noise, blur, and resolution loss. However, existing models trained on source data often fail on target domains lacking clean references, a common occurrence in practice. To address this issue, we present HIR-ALIGN, a plug-and-play target-adaptive augmentation framework that enhances hyperspectral image restoration by augmenting limited training images with synthetic data that closely matches the target distribution using no extra data. It consists of three stages: (i) proxy generation, where off-the-shelf restoration models restore degraded target observations to produce semantics-preserving proxy HSIs that approximate target-domain clean images; (ii) distribution-adaptive synthesis, where a blur-robust unCLIP diffusion model generates target-aligned RGBs from proxy RGBs, with prompt conditioning and embedding-space noise initialization. Then, a warp-based spectral transfer module synthesizes HSIs by aligning each generated RGB with the proxy RGB, estimating soft patch-wise transport weights, and applying these weights and learnable local interpolation kernels to the proxy HSI; and (iii) aligned supervised finetuning, where restoration networks pretrained on the source distribution are finetuned using both the proxy HSIs and synthesized target-aligned HSIs, and are then deployed on degraded target images. We further provide theoretical analysis showing that augmentation-based finetuning can achieve lower target-domain restoration risk by jointly improving target distribution coverage and controlling spectral bias. Extensive experiments on simulated and real datasets across denoising and super-resolution tasks demonstrate that HIR-ALIGN consistently improves source-only supervised baselines, outperforming both source-only counterparts and representative unsupervised methods.

Aligning Network Equivariance with Data Symmetry: A Theoretical Framework and Adaptive Approach for Image Restoration

Image restoration is an inherently ill posed inverse problem. Equivariant networks that embed geometric symmetry priors can mitigate this ill posedness and improve performance. However, current understanding of the relationship between network equivariance and data symmetry remains largely heuristic. Particularly for real world data with imperfect symmetry, existing research lacks a systematic theoretical framework to quantify symmetry, select transformation groups, or evaluate model data alignment. To bridge this gap, we conduct an analysis from an optimization perspective and formalize the intrinsic relationship among data symmetry priors, model equivariance, and generalization capability. Specifically, we propose for the first time a quantifiable definition of non strict symmetry at the dataset level (rather than sample level) and use it as a constraint to formulate the restoration inverse problem. We then show that the equivariance for restoration models can be naturally derived from this inverse problems incorporated the proposed symmetry constraints, and that the equivariance error of the optimal restoration operator is strictly bounded by the data symmetry error and the discretization mesh size. Furthermore, by analyzing the network's empirical risk, we demonstrate that aligning equivariance with data symmetry optimizes the bias variance trade off, minimizing the total expected risk. Guided by these insights, we propose a Sample Adaptive Equivariant Network that uses a hypernetwork and transformation learnable equivariant convolutions to dynamically align with each sample's inherent symmetry. Extensive experiments on super resolution, denoising, and deraining validate our theoretical findings and show significant superiority over standard baselines and traditional equivariant models. Our code and supplementary material are available at https://github.com/tanfy929/SA-Conv.