Multivariate time series in domains such as finance, climate science, and healthcare often exhibit long-term trends, seasonal patterns, and short-term fluctuations, complicating causal inference under non-stationarity and autocorrelation. Existing causal discovery methods typically operate on raw observations, making them vulnerable to spurious edges and misattributed temporal dependencies. We introduce a decomposition-based causal discovery framework that separates each time series into trend, seasonal, and residual components and performs component-specific causal analysis. Trend components are assessed using stationarity tests, seasonal components using kernel-based dependence measures, and residual components using constraint-based causal discovery. The resulting component-level graphs are integrated into a unified multi-scale causal structure. This approach isolates long- and short-range causal effects, reduces spurious associations, and improves interpretability. Across extensive synthetic benchmarks and real-world climate data, our framework more accurately recovers ground-truth causal structure than state-of-the-art baselines, particularly under strong non-stationarity and temporal autocorrelation.

Chamfer Distance (CD) and Earth Mover's Distance (EMD) are two broadly adopted metrics for measuring the similarity between two point sets. However, CD is usually insensitive to mismatched local density, and EMD is usually dominated by global distribution while overlooks the fidelity of detailed structures. Besides, their unbounded value range induces a heavy influence from the outliers. These defects prevent them from providing a consistent evaluation. To tackle these problems, we propose a new similarity measure named Density-aware Chamfer Distance (DCD). It is derived from CD and benefits from several desirable properties: 1) it can detect disparity of density distributions and is thus a more intensive measure of similarity compared to CD; 2) it is stricter with detailed structures and significantly more computationally efficient than EMD; 3) the bounded value range encourages a more stable and reasonable evaluation over the whole test set.

We use Eqn. 1 in training for the loss between the coarse shape with 1024 points and the ground truth CD and the uniform loss are not sensitive to it. DCD and EMD can reflect the increasingly mismatched density, while CD and uniform loss are not sensitive to it. We introduce two hyper-parameters in Sec. Visualization of the distance contributed by each point. We invite 15 volunteers to complete the study.

Chamfer Distance (CD) and Earth Mover's Distance (EMD) are two broadly

Accurate segmentation of anatomical structures in the apical four-chamber (A4C) view of fetal echocardiography is essential for early diagnosis and prenatal evaluation of congenital heart disease (CHD). However, precise segmentation remains challenging due to ultrasound artifacts, speckle noise, anatomical variability, and boundary ambiguity across different gestational stages. To reduce the workload of sonogra-phers and enhance segmentation accuracy, we propose DCD, an advanced deep learning-based model for automatic segmentation of key anatomical structures in the fetal A4C view. Our model incorporates a Dense Atrous Spatial Pyramid Pooling (Dense ASPP) module, enabling superior multi-scale feature extraction, and a Convolutional Block Attention Module (CBAM) to enhance adaptive feature representation. By effectively capturing both local and global contextual information, DCD achieves precise and robust segmentation, contributing to improved prenatal cardiac assessment.

Point cloud (PC) processing tasks-such as completion, upsampling, denoising, and colorization-are crucial in applications like autonomous driving and 3D reconstruction. Despite substantial advancements, prior approaches often address each of these tasks independently, with separate models focused on individual issues. However, this isolated approach fails to account for the fact that defects like incompleteness, low resolution, noise, and lack of color frequently coexist, with each defect influencing and correlating with the others. Simply applying these models sequentially can lead to error accumulation from each model, along with increased computational costs. To address these challenges, we introduce SuperPC, the first unified diffusion model capable of concurrently handling all four tasks. Our approach employs a three-level-conditioned diffusion framework, enhanced by a novel spatial-mix-fusion strategy, to leverage the correlations among these four defects for simultaneous, efficient processing. We show that SuperPC outperforms the state-of-the-art specialized models as well as their combination on all four individual tasks.

Chamfer Distance (CD) and Earth Mover's Distance (EMD) are two broadly adopted metrics for measuring the similarity between two point sets. However, CD is usually insensitive to mismatched local density, and EMD is usually dominated by global distribution while overlooks the fidelity of detailed structures. Besides, their unbounded value range induces a heavy influence from the outliers. These defects prevent them from providing a consistent evaluation. To tackle these problems, we propose a new similarity measure named Density-aware Chamfer Distance (DCD). It is derived from CD and benefits from several desirable properties: 1) it can detect disparity of density distributions and is thus a more intensive measure of similarity compared to CD; 2) it is stricter with detailed structures and significantly more computationally efficient than EMD; 3) the bounded value range encourages a more stable and reasonable evaluation over the whole test set.

Discrete diffusion models have recently shown significant progress in modeling complex data, such as natural languages and DNA sequences. However, unlike diffusion models for continuous data, which can generate high-quality samples in just a few denoising steps, modern discrete diffusion models still require hundreds or even thousands of denoising steps to perform well. In this paper, we identify a fundamental limitation that prevents discrete diffusion models from achieving strong performance with fewer steps -- they fail to capture dependencies between output variables at each denoising step. To address this issue, we provide a formal explanation and introduce a general approach to supplement the missing dependency information by incorporating another deep generative model, termed the copula model. Our method does not require fine-tuning either the diffusion model or the copula model, yet it enables high-quality sample generation with significantly fewer denoising steps. When we apply this approach to autoregressive copula models, the combined model outperforms both models individually in unconditional and conditional text generation. Specifically, the hybrid model achieves better (un)conditional text generation using 8 to 32 times fewer denoising steps than the diffusion model alone. In addition to presenting an effective discrete diffusion generation algorithm, this paper emphasizes the importance of modeling inter-variable dependencies in discrete diffusion.