Empirical Bayes (EB) estimators can match the first-order asymptotic risk of maximum likelihood (ML) while behaving very differently at second order: recent excess mean squared error (XMSE) analysis shows that kernel-based EB estimation may be worse than ML when the kernel is poorly aligned with the true parameter. This paper turns that diagnostic into a design principle. We propose an XMSE-aware mixed estimator that interpolates between ML and EB shrinkage. Its fixed-weight XMSE is a scalar quadratic, yielding a closed-form oracle mixing weight that is no worse than both ML and the base EB estimator at the XMSE scale. A plug-in implementation based on finite-sample XMSE approximations is proved consistent, with a second-order oracle regret rate for an interior oracle weight. We further establish a transfer of the regret bound to the fixed-weight risk curve evaluated at the selected weight, a thresholded boundary rule, and extensions to compact kernel families and to finite and growing kernel dictionaries with high-probability oracle bounds. Finite impulse response simulations with SURE-tuned, hard-selection, and trace-corrected baselines, together with the public Silverbox and Cascaded Tanks benchmarks, show that the proposed estimator retains most of the benefit of regularization when it is helpful and retreats toward ML under kernel misspecification, with an identified finite-de analyzed on the benchmarks.

Uncertainty quantification (UQ) in scientific machine learning is increasingly critical as neural networks are widely adopted to tackle complex problems across diverse scientific disciplines. For physics-informed neural networks (PINNs), a prominent model in scientific machine learning, uncertainty is typically quantified using Bayesian or dropout methods. However, both approaches suffer from a fundamental limitation: the prior distribution or dropout rate required to construct honest confidence sets cannot be determined without additional information. In this paper, we propose a novel method within the framework of extended fiducial inference (EFI) to provide rigorous uncertainty quantification for PINNs. The proposed method leverages a narrow-neck hyper-network to learn the parameters of the PINN and quantify their uncertainty based on imputed random errors in the observations. This approach overcomes the limitations of Bayesian and dropout methods, enabling the construction of honest confidence sets based solely on observed data. This advancement represents a significant breakthrough for PINNs, greatly enhancing their reliability, interpretability, and applicability to real-world scientific and engineering challenges. Moreover, it establishes a new theoretical framework for EFI, extending its application to large-scale models, eliminating the need for sparse hyper-networks, and significantly improving the automaticity and robustness of statistical inference.

The process of editing an image can be naturally modeled as evaluating a counterfactual query: "What would an image look like if a particular feature had changed?" While recent advances in text-guided image editing leverage powerful pre-trained models to produce visually appealing images, they often lack counterfactual consistency - ignoring how features are causally related and how changing one may affect others. In contrast, existing causal-based editing approaches offer solid theoretical foundations and perform well in specific settings, but remain limited in scalability and often rely on labeled data. In this work, we aim to bridge the gap between causal editing and large-scale text-to-image generation through two main contributions. First, we introduce Backdoor Disentangled Causal Latent Space (BD-CLS), a new class of latent spaces that allows for the encoding of causal inductive biases. One desirable property of this latent space is that, even under weak supervision, it can be shown to exhibit counterfactual consistency. Second, and building on this result, we develop BD-CLS-Edit, an algorithm capable of learning a BD-CLS from a (non-causal) pre-trained Stable Diffusion model. This enables counterfactual image editing without retraining. Our method ensures that edits respect the causal relationships among features, even when some features are unlabeled or unprompted and the original latent space is oblivious to the environment's underlying cause-and-effect relationships.

Guidance techniques are commonly used in diffusion and flow models to improve image quality and input consistency for conditional generative tasks such as classconditional and text-to-image generation. In particular, classifier-free guidance (CFG) is the most widely adopted guidance technique. It results, however, in trade-offs across quality, diversity and consistency: improving some at the expense of others. While recent work has shown that it is possible to disentangle thesefactors to some extent, such methods come with an overhead of requiring an additional (weaker) model, or require more forward passes per sampling step. In this paper, we propose Entropy Rectifying Guidance (ERG), a simple and effective guidance method based on inference-time changes in the attention mechanism of state-of-the-art diffusion transformer architectures, which allows for simultaneousimprovements over image quality, diversity and prompt consistency. ERG is more general than CFG and similar guidance techniques, as it extends to unconditional sampling. We show that ERG results in significant improvements in various tasks, including text-to-image, class-conditional and unconditional image generation. We also show that ERG can be seamlessly combined with other recent guidance methods such as CADS and APG, further improving generation results.

Video generation has emerged as a promising tool for world simulation, leveraging visual data to replicate real-world environments. Within this context, egocentric video generation, which centers on the human perspective, holds significant potential for enhancing applications in virtual reality, augmented reality, and gaming. However, the generation of egocentric videos presents substantial challenges due to the dynamic nature of egocentric viewpoints, the intricate diversity of actions, and the complex variety of scenes encountered. Existing datasets are inadequate for addressing these challenges effectively. To bridge this gap, we present EgoVid-5M, the first high-quality dataset specifically curated for egocentric video generation. EgoVid-5M encompasses 5 million egocentric video clips and is enriched with detailed action annotations, including 5M high-level textual descriptions and 65K fine-grained kinematic control annotations. To ensure the integrity and usability of the dataset, we implement a sophisticated data cleaning pipeline designed to maintain frame consistency, action coherence, and motion smoothness under egocentric conditions. Furthermore, we introduce EgoDreamer, which is capable of generating egocentric videos driven simultaneously by action descriptions and kinematic control signals. The EgoVid-5M dataset, associated action annotations, and all data cleansing metadata will be released for the advancement of research in egocentric video generation.

However, its capability for accurate surface reconstruction remains underexplored. Due to the discrete and unstructured nature of Gaussians, supervision based solely on image rendering loss often leads to inaccurate geometry and inconsistent multi-view alignment. In this work, we propose a novel method that enhances the geometric representation of 3DGaussians through view alignment (VA). Specifically, we incorporate edge-aware image cues into the rendering loss to improve surface boundary delineation. To enforce geometric consistency across views, we introduce a visibility-aware photometric alignment loss that models occlusions and encourages accurate spatial relationships among Gaussians. To further mitigate ambiguities caused by lighting variations, we incorporate normal-based constraints to refine the spatial orientation of Gaussians and improve local surface estimation. Additionally, we leverage deep image feature embeddings to enforce cross-view consistency, enhancing the robustness of the learned geometry under varying viewpoints and illumination. Extensive experiments on standard benchmarks demonstrate that our method achieves stateof-the-art performance in both surface reconstruction and novel view synthesis. The source code is available at https://github.com/LeoQLi/VA-GS.

It is a challenging problem to reproduce rich spatial details while maintaining temporal consistency in real-world video super-resolution (Real-VSR), especially when we leverage pre-trained generative models such as stable diffusion (SD) for realistic details synthesis.

We propose the first framework capable of computing a 4D spatio-temporal grid of video architecture.

Conventional video outpainting methods primarily focus on maintaining coherent textures and visual consistency across frames. However, they often fail at handling dynamic scenes due to the complex motion of objects or camera movement, leading to temporal incoherence and visible flickering artifacts across frames. This is primarily because they lack instance-aware modeling to accurately separate and track individual object motions throughout the video. In this paper, we propose a novel video outpainting framework that explicitly takes shadow-object pairs into consideration to enhance the temporal and spatial consistency of instances, even when they are temporarily invisible. Specifically, we first track the shadow-object pairs across frames and predict the instances in the scene to unveil the spatial regions of invisible instances. Then, these prediction results are fed to guide the instance-aware optical flow completion to unveil the temporal motion of invisible instances. Next, these spatiotemporal guidances of instances are used to guide the video outpainting process. Finally, a video-aware discriminator is implemented to enhance alignment among dynamic shadows and the extended semantics in the scene. Comprehensive experiments underscore the superiority of our approach, outperforming existing state-of-the-art methods in widely recognized benchmarks.

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