Diffusion Model Research Articles

U and Th zonation in apatite observed by synchrotron X-ray fluorescence tomography and implications for the (U–Th) ∕ He system

Abstract. Synchrotron X-ray fluorescence microtomography can non-destructively image the three-dimensional distribution of several trace elements in whole apatite crystals at the resolution of 1 µm3. This allows for precise determination of the physical geometry of a crystal and the quantification of the relative abundance of the radioactive parent nuclides uranium and thorium with high fidelity. We use these data to develop a more precise alpha ejection correction for (U–Th) / He thermochronology and high-resolution models of apatite crystals that are the foundation for a new generation of three-dimensional diffusion modeling. The application of synchrotron radiation to non-destructive imaging of minerals used for geochronology sheds light on causes of long-standing unresolved problems in the field that are rooted in previously unmeasurable parent nuclide zonation, especially the pervasive overdispersion of single-crystal ages.

IDEEA: information diffusion model for integrating gene expression and EEG data in identifying Alzheimer’s disease markers

Abstract Understanding the genetic components of Alzheimer’s disease (AD) via transcriptome analysis often necessitates the use of invasive methods. This work focuses on overcoming the difficulties associated with the invasive process of collecting brain tissue samples in order to measure and investigate the transcriptome behavior of AD. Our approach called IDEEA (Information Diffusion model for integrating gene Expression and EEG data in identifying Alzheimer’s disease markers) involves systematically linking two different but complementary modalities: transcriptomics and EEG data. We preprocess these two data types by calculating the spectral and transcriptional sample distances, over 11 brain regions encompassing 6 distinct frequency bands. Subsequently, we employ a genetic algorithm approach to integrate the distinct features of the preprocessed data. Our experimental results show that
IDEEA converges rapidly to local optima gene subsets, in fewer than 250 iterations. Our algorithm identifies novel genes along with genes that have previously been linked to AD. It is also capable of detecting genes with transcription patterns specific to individual EEG bands as well as those with common patterns among bands. In particular, the alpha2 (10-13 Hz) frequency band yielded 8 AD associated genes out of the top 100 most frequently selected genes by our algorithm, with a p-value of
0.05. Our method not only identifies AD-related genes but also genes that interact with AD genes in terms of transcription regulation. We evaluated various aspects of our approach, including the genetic algorithm performance, band-pair association and gene interaction topology. Our approach reveals AD-relevant genes with transcription patterns inferred from EEG alone, across various frequency bands, avoiding the risky brain tissue collection process. This is a significant advancement toward the early identification of AD using non-invasive EEG recordings.

Addressing high-performance data sparsity in metasurface inverse design using multi-objective optimization and diffusion probabilistic models

Recent advancements in deep learning, particularly generative networks capable of producing high-freedom structures, have significantly enhanced the precise generation of meta-atoms. However, these methodologies typically rely on an abundance of high-performance data, which remains scarce in many practical design scenarios. To bridge this gap, our study introduces what we believe to be a novel approach that synergistically combines multi-objective optimization algorithms with an enhanced diffusion model featuring an attention mechanism, termed MetaDiffusion-Att. Using the complex design task of dual-polarized, wide-angle incidence, and broadband low-emissivity electromagnetic glass as an application example, we demonstrate the effectiveness of our method through qualitative and quantitative experiments. The introduced multi-objective optimization method significantly captures more high-performance samples while ensuring high degrees of freedom, compared to currently widely used generic dataset construction methods. The MetaDiffusion-Att model, improved by the introduced attention mechanism, significantly outperforms conventional WGAN-GP and conditional VAE methods in generation accuracy and quality under small datasets. Furthermore, the proposed method exhibits extrapolation capabilities, generating new structures with performance surpassing that of the dataset, further enriching the design space. This framework provides a promising solution for the inverse design of metasurfaces in challenging scenarios with sparse high-performance samples.

Neural differentiable modeling with diffusion-based super-resolution for two-dimensional spatiotemporal turbulence

Simulating spatiotemporal turbulence with high fidelity remains a cornerstone challenge in computational fluid dynamics (CFD) due to its intricate multiscale nature and prohibitive computational demands. Traditional approaches typically employ closure models, which attempt to represent small-scale features in an unresolved manner. However, these methods often sacrifice accuracy and lose high-frequency/wavenumber information, especially in scenarios involving complex flow physics. In this paper, we introduce an innovative neural differentiable modeling framework designed to enhance the predictability and efficiency of spatiotemporal turbulence simulations. Our approach features differentiable hybrid modeling techniques that seamlessly integrate deep neural networks with numerical PDE solvers within a differentiable programming framework, synergizing deep learning with physics-based CFD modeling. Specifically, a hybrid differentiable neural solver is constructed on a coarser grid to capture large-scale turbulent phenomena, followed by the application of a Bayesian conditional diffusion model that generates small-scale turbulence conditioned on large-scale flow predictions. Two innovative hybrid architecture designs are studied, and their performance is evaluated through comparative analysis against conventional large eddy simulation techniques with physics-based subgrid-scale closures and purely data-driven neural solvers. The findings underscore the potential of the neural differentiable modeling framework to significantly enhance the accuracy and computational efficiency of turbulence simulations. This study not only demonstrates the efficacy of merging deep learning with physics-based numerical solvers but also sets a new precedent for advanced CFD modeling techniques, highlighting the transformative impact of differentiable programming in scientific computing.

A highly naturalistic facial expression generation method with embedded vein features based on diffusion model

Abstract Facial expression generation technology has achieved notable progress in computer vision and artificial intelligence. However, challenges persist regarding background consistency, expression clarity, and detailed representation. Additionally, the instability of generative adversarial networks (GANs) during training affects both image quality and diversity. While diffusion models have demonstrated potential advantages over GANs, research on controllable expression generation remains limited. To address these challenges, this paper proposes a highly natural facial expression generation method based on denoising diffusion implicit models (DDIM) with embedded vein features. This approach avoids adversarial training by employing gradual diffusion to generate specific expressions, thereby enhancing both the diversity and authenticity of the images. Vein features are introduced and embedded within the generated expression images to protect the intellectual property of algorithm-generated digital resources. Firstly, image and expression text guide words are combined as conditional inputs to improve the authenticity and diversity of the generated images. Secondly, a classification coding network is introduced to guide expression generation, thus enhancing the accuracy and consistency of the produced expressions. Furthermore, this paper proposes a vein feature fusion method based on multi-directional local dynamic feature coding operator (MLDFO) and integrates DDIM with frequency-domain watermarking technology to achieve image intellectual property protection. Experimental results demonstrate the effectiveness of this method across several public datasets, including FFHQ, CelebA, FV-USM, and SDUMLA-HMT. Notably, in the CelebA dataset, the average expression recognition rate increased by 11.41%, with a 100.00% recognition rate for happy expressions. The generated expression images exhibit a high degree of authenticity and consistency, and the video conversion tests reveal a natural and smooth effect. These results confirm that this method not only advances facial expression generation technology but also significantly enhances the steganographic protection of images.

Controllable Anime Image Editing via Probability of Attribute Tags

AbstractEditing anime images via probabilities of attribute tags allows controlling the degree of the manipulation in an intuitive and convenient manner. Existing methods fall short in the progressive modification and preservation of unintended regions in the input image. We propose a controllable anime image editing framework based on adjusting the tag probabilities, in which a probability encoding network (PEN) is developed to encode the probabilities into features that capture continuous characteristic of the probabilities. Thus, the encoded features are able to direct the generative process of a pre‐trained diffusion model and facilitate the linear manipulation. We also introduce a local editing module that automatically identifies the intended regions and constrains the edits to be applied to those regions only, which preserves the others unchanged. Comprehensive comparisons with existing methods indicate the effectiveness of our framework in both one‐shot and linear editing modes. Results in additional applications further demonstrate the generalization ability of our approach.

Artificial intelligence reveals past climate extremes by reconstructing historical records

The understanding of recent climate extremes and the characterization of climate risk require examining these extremes within a historical context. However, the existing datasets of observed extremes generally exhibit spatial gaps and inaccuracies due to inadequate spatial extrapolation. This problem arises from traditional statistical methods used to account for the lack of measurements, particularly prevalent before the mid-20th century. In this work, we use artificial intelligence to reconstruct observations of European climate extremes (warm and cold days and nights) by leveraging Earth system model data from CMIP6 through transfer learning. Our method surpasses conventional statistical techniques and diffusion models, showcasing its ability to reconstruct past extreme events and reveal spatial trends across an extensive time span (1901-2018) that is not covered by most reanalysis datasets. Providing our dataset to the climate community will improve the characterization of climate extremes, resulting in better risk management and policies.

Density‐Aware Diffusion Model for Efficient Image Dehazing

AbstractExisting image dehazing methods have made remarkable progress. However, they generally perform poorly on images with dense haze, and often suffer from unsatisfactory results with detail degradation or color distortion. In this paper, we propose a density‐aware diffusion model (DADM) for image dehazing. Guided by the haze density, our DADM can handle images with dense haze and complex environments. Specifically, we introduce a density‐aware dehazing network (DADNet) in the reverse diffusion process, which can help DADM gradually recover a clear haze‐free image from a haze image. To improve the performance of the network, we design a cross‐feature density extraction module (CDEModule) to extract the haze density for the image and a density‐guided feature fusion block (DFFBlock) to learn the effective contextual features. Furthermore, we introduce an indirect sampling strategy in the test sampling process, which not only suppresses the accumulation of errors but also ensures the stability of the results. Extensive experiments on popular benchmarks validate the superior performance of the proposed method. The code is released in https://github.com/benchacha/DADM.

Investigation of heat generation and radiation effects on boundary layer flow of Prandtl liquid with Cattaneo–Christov double diffusion models

In this analysis, a bidirectional stretched sheet is used to produce a 3D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{D}$$\\end{document} flow of Prandtl liquid with improve mass diffusion and heat conduction models. This study advances knowledge of magnetohydrodynamics, radiation impacts, and heat production in fluid dynamics and transport processes. The Prandtl fluid model is critical for modeling non-Newtonian fluids, capturing its viscoelastic features, and allowing for precise simulation in industrial applications. It gives a mathematical foundation for analyzing complex fluid behaviors, which is necessary for optimizing operations utilizing such fluids. It uses the boundary layer method to simplify the fundamental equations and Cattaneo–Christov double diffusion models. The optimal homotopy analysis method is used to solve nonlinear ODEs caused by non-dimensional similarity variables. This investigation undertakes the calculation of drag coefficient for surfaces mass transfer rates and heat transfer rates proximate to the solid boundary. Furthermore, it conducts a comprehensive analysis of the influences exerted by various parameters on concentration and temperature profiles employing graphical representations for a rigorous examination. The Prandtl fluid model describes the viscoelastic characteristics of non-Newtonian fluids through constitutive equations, dimensional evaluation, and numerical simulations, which are frequently validated by experiments. The results show that changes in thermal and concentration relaxation parameters are accompanied by a decline in temperature. Temperature field rises as the thermal radiation parameter and heat generation increases. The work's novelty consists in its advanced modeling of Prandtl non-Newtonian fluids via Cattaneo–Christov double diffusion models, which incorporate magnetohydrodynamics and radiation effects and use optimal homotopy analysis for accurate parametric analyses of heat and mass transfer.

Highlighted Diffusion Model as Plug-in Priors for Polyp Segmentation.

Automated polyp segmentation from colonoscopy images is crucial for colorectal cancer diagnosis. The accuracy of such segmentation, however, is challenged by two main factors. First, the variability in polyps' size, shape, and color, coupled with the scarcity of well-annotated data due to the need for specialized manual annotation, hampers the efficacy of existing deep learning methods. Second, concealed polyps often blend with adjacent intestinal tissues, leading to poor contrast that challenges segmentation models. Recently, diffusion models have been explored and adapted for polyp segmentation tasks. However, the significant domain gap between RGB-colonoscopy images and grayscale segmentation masks, along with the low efficiency of the diffusion generation process, hinders the practical implementation of these models. To mitigate these challenges, we introduce the Highlighted Diffusion Model Plus (HDM+), a two-stage polyp segmentation framework. This framework incorporates the Highlighted Diffusion Model (HDM) to provide explicit semantic guidance, thereby enhancing segmentation accuracy. In the initial stage, the HDM is trained using highlighted ground-truth data, which emphasizes polyp regions while suppressing the background in the images. This approach reduces the domain gap by focusing on the image itself rather than on the segmentation mask. In the subsequent second stage, we employ the highlighted features from the trained HDM's U-Net model as plug-in priors for polyp segmentation, rather than generating highlighted images, thereby increasing efficiency. Extensive experiments conducted on six polyp segmentation benchmarks demonstrate the effectiveness of our approach.

Universal Fingerprint Generation: Controllable Diffusion Model with Multimodal Conditions.

The utilization of synthetic data for fingerprint recognition has garnered increased attention due to its potential to alleviate privacy concerns surrounding sensitive biometric data. However, current methods for generating fingerprints have limitations in creating impressions of the same finger with useful intra-class variations. To tackle this challenge, we present GenPrint, a framework to produce fingerprint images of various types while maintaining identity and offering humanly understandable control over different appearance factors such as fingerprint class, acquisition type, sensor device, and quality level. Unlike previous fingerprint generation approaches, GenPrint is not confined to replicating style characteristics from the training dataset alone: it enables the generation of novel styles from unseen devices without requiring additional fine-tuning. To accomplish these objectives, we developed GenPrint using latent diffusion models with multimodal conditions (text and image) for consistent generation of style and identity. Our experiments leverage a variety of publicly available datasets for training and evaluation. Results demonstrate the benefits of GenPrint in terms of identity preservation, explainable control, and universality of generated images. Importantly, the GenPrint-generated images yield comparable or even superior accuracy to models trained solely on real data and further enhances performance when augmenting the diversity of existing real fingerprint datasets.

Mathematical model for nanofibers' diffusion in a nanofluid and numerical simulation

Mathematical model for nanofibers' diffusion in a nanofluid and numerical simulation

Pore-scale binary diffusion behavior of Hydrogen-Cushion gas in saline aquifers for underground hydrogen Storage: Optimization of cushion gas type

Cushion gas is required to prevent hydrogen (H2) trapping and interactions between H2 and brine for underground hydrogen storage (UHS) in saline aquifers. However, selecting an appropriate type of cushion gas is not a straightforward task, as it affects the H2 diffusion characteristic in subsurface porous media, thereby impacting purity, recoverability, etc. In this paper, we developed a modified pore network model (PNM) for binary diffusion that incorporates multi-scale diffusion mechanisms to forecast the H2 effective diffusion coefficient (DH2e) and evaluate the impacts of the cushion gas on DH2e. Additionally, the model accounts for the water-lock effects of residual brine, focusing exclusively on the connected pore-throats occupied by the gas phase, which are identified using the invasion percolation algorithm with trapping. Our key findings are as follows: 1) CO2 and N2 demonstrate superior containment effects on H2 compared to CH4 under the specific conditions of the target aquifer, reducing the H2 contamination caused by binary diffusion; 2) The size and topology of porous media exert minimal impacts on the selection of cushion gas, yet they markedly affect the DH2e; 3) The pressure and temperature conditions of the saline aquifer are critical factors in cushion gas selection, with temperature being the more influential parameter. This study provides valuable insights for the implementation of industry-scale UHS in saline aquifers.

Report on the AAPM grand challenge on deep generative modeling for learning medical image statistics.

The findings of the 2023 AAPM Grand Challenge on Deep Generative Modeling for Learning Medical Image Statistics are reported in this SpecialReport. The goal of this challenge was to promote the development of deep generative models for medical imaging and to emphasize the need for their domain-relevant assessments via the analysis of relevant imagestatistics. As part of this Grand Challenge, a common training dataset and an evaluation procedure was developed for benchmarking deep generative models for medical image synthesis. To create the training dataset, an established 3D virtual breast phantom was adapted. The resulting dataset comprised about 108000 images of size 512 512. For the evaluation of submissions to the Challenge, an ensemble of 10000 DGM-generated images from each submission was employed. The evaluation procedure consisted of two stages. In the first stage, a preliminary check for memorization and image quality (via the Fréchet Inception Distance [FID]) was performed. Submissions that passed the first stage were then evaluated for the reproducibility of image statistics corresponding to several feature families including texture, morphology, image moments, fractal statistics, and skeleton statistics. A summary measure in this feature space was employed to rank the submissions. Additional analyses of submissions was performed to assess DGM performance specific to individual feature families, the four classes in the training data, and also to identify various artifacts. Fifty-eight submissions from 12 unique users were received for this Challenge. Out of these 12 submissions, 9 submissions passed the first stage of evaluation and were eligible for ranking. The top-ranked submission employed a conditional latent diffusion model, whereas the joint runners-up employed a generative adversarial network, followed by another network for image superresolution. In general, we observed that the overall ranking of the top 9 submissions according to our evaluation method (i) did not match the FID-based ranking, and (ii) differed with respect to individual feature families. Another important finding from our additional analyses was that different DGMs demonstrated similar kinds ofartifacts. This Grand Challenge highlighted the need for domain-specific evaluation to further DGM design as well as deployment. It also demonstrated that the specification of a DGM may differ depending on its intendeduse.

A comment on the Revised Diffusion Model for Conflict tasks (RDMC).

In conflict tasks, such as the Simon, Eriksen flanker, or Stroop task, a relevant and an irrelevant feature indicate the same or different responses in congruent and incongruent trials, respectively. The congruency effect refers to faster and less error-prone responses in congruent relative to incongruent trials. Distributional analyses reveal that the congruency effect in the Simon task becomes smaller with increasing RTs, reflected by a negative-going delta function. In contrast, for other tasks, the delta function is typically positive-going, meaning that congruency effects become larger with increasing RTs. The Diffusion Model for Conflict tasks (DMC; Ulrich et al., Cognitive Psychology, 78, 148-174, 2015) accounts for this by explicitly modeling the information accumulated from the relevant and the irrelevant features and attributes negatively- versus positively-sloped delta functions to different peak times of a pulse-like activation resulting from the task-irrelevant feature. Because the underlying function implies negative drift rates, Lee and Sewell (Psychonomic Bulletin & Review, 31(5), 1-31, 2024) recently questioned this assumption and suggested their Revised Diffusion Model for Conflict tasks (RDMC). We address three issues regarding RDMC compared to DMC: (1) The pulse-like function is not as implausible as Lee and Sewell suggest. (2) RDMC itself comes with a questionable assumption that different parameters are required for congruent and incongruent trials. (3) Moreover, we present data from a new parameter recovery study, suggesting that RDMC lacks acceptable recovery of several parameters (in particular compared to DMC). In this light, we discuss RDMC as not (yet) a revised version of DMC.

A least-squares Fourier frame method for nonlocal diffusion models on arbitrary domains

We introduce a least-squares Fourier frame method for solving nonlocal diffusion models with Dirichlet volume constraint on arbitrary domains. The mathematical structure of a frame rather than a basis allows using a discrete least-squares approximation on irregular domains and imposing non-periodic boundary conditions. The method has inherited the one-dimensional integral expression of Fourier symbols of the nonlocal diffusion operator from Fourier spectral methods for any d spatial dimensions. High precision of its solution can be achieved via a direct solver such as pivoted QR decomposition even though the corresponding system is extremely ill-conditioned, due to the redundancy in the frame. The extension of AZ algorithm improves the complexity of solving the rectangular linear system to O(Nlog2⁡N) for 1d problems and O(N2log2⁡N) for 2d problems, compared with O(N3) of the direct solvers, where N is the number of degrees of freedom. We present ample numerical experiments to show the flexibility, fast convergence and asymptotical compatibility of the proposed method.

Impulsive adolescents exhibit inefficient processing and a low decision threshold when decoding facial expressions of emotions.

Borderline personality disorder (BPD) is a debilitating psychiatric illness whose symptoms frequently emerge during adolescence. Initial studies in adults suggest that the interpersonal difficulties common in BPD may emerge from disrupted processing of social and emotional stimuli. Less is known about these processes in adolescents with BPD symptoms, despite substantial changes in socioemotional processing during this developmental period. 86 adolescents and young adults with and without BPD symptoms completed an emotional interference task involving the identification of a facial emotion expression in the presence of a conflicting or congruent emotion word. We used hierarchical drift diffusion modeling to index speed of processing and decision boundary. Using Bayesian multilevel regression, we characterized age-related differences in facial emotion processing. We then examined whether BPD symptom dimensions were associated with facial emotion processing on this task. To determine the specificity of our effects, we analyzed behavioral data from a corresponding nonemotional interference task. Impulsivity, but not negative affectivity or interpersonal dysfunction, predicted inefficient processing when presented with conflicting negative emotional stimuli. Across both tasks, impulsivity in adolescents was further associated with a lower decision boundary. Impulsive adolescents were especially likely to make fast, but inaccurate decisions about another person's emotional state. Impulsive adolescents with BPD symptoms are prone to making errors when appraising facial expressions of emotions, which may potentiate or worsen interpersonal conflicts. Our findings highlight the role of lower-level social cognitive processes in interpersonal difficulties among vulnerable youth during a sensitive developmental window.

Comparison Between Gans and Diffusion Models in the Generation of Synthetic Images for Enhancing Tree Species Recognition

Objective: This study investigates the application of Generative Adversarial Networks (GANs) and Diffusion Models in data augmentation to improve the classification of tree species images, which is essential for sustainable forest management. Theoretical Framework: Fundamental concepts of machine learning, generative and classifier networks, as well as data augmentation techniques through synthetic image generation, are presented, establishing a solid foundation for the research. Method: The research utilized 2,178 images of cross-sections of wood from 18 species, applying Deep Convolutional GAN (DCGAN) and U-Net with diffusion on a rare species, evaluated using FID and IS metrics. The generated images were used to train and validate classification models, assessed by F1-score. Results and Discussion: The results revealed that Diffusion Models generated more realistic images and performed better in the classification of the rare species. The discussion contextualizes these results in light of the theoretical framework, exploring their implications for environmental management. Limitations, such as the impact of indiscriminate addition of synthetic data, are also addressed. Research Implications: The practical and theoretical implications of this research are discussed, providing insights into how the results can be applied or influence practices in the field of forest management and environmental management. These implications may cover areas such as sustainable innovation and biodiversity conservation. Originality/Value: This study contributes to the literature by demonstrating the potential of Diffusion Models to outperform GANs in generating synthetic images for sustainable forest management purposes. The relevance and value of this research are evidenced by its practical application in promoting innovative and sustainable practices in environmental management.

Findings from the 'Ask Me About PrEP' HIV Pre-Exposure Prophylaxis Awareness Programme in England.

HIV incidence has decreased in England by over a third since 2019. Despite the early success of HIV Pre-Exposure Prophylaxis (PrEP) in reducing HIV transmission in the United Kingdom, many people who could benefit from HIV PrEP do not yet know about it, or know how to access it. This paper presents the findings of the first England-wide national peer-to-peer based diffusion model to disseminate information about PrEP. Ask Me About PrEP (AMAP) was a 5-month pilot programme which commenced in November 2021. Volunteer mobilisers were encouraged to use their existing knowledge of their communities and geographical areas to assist them in discussing PrEP with their peers. 12 enrolled mobilisers took part in three project evaluation focus groups between November 2021 and March 2022, and five AMAP project staff took part in one focus group in March 2022. Additionally, descriptive statistical analysis explored volunteer mobiliser recruitment to the AMAP project, demographical data of project staff and volunteer mobilisers, volunteer mobiliser attrition rates, and the project's impact. 96 volunteers enrolled, completed training and volunteered as mobilisers. Thoroughout the project, mobilisers engaged their peers in 11,889 conversations about PrEP through individual conversations, online group conversations, online workplace educational events, and social media. The focus groups enabled key stakeholders to reflect on their experiences of the pilot programme. Four key themes were identified during the focus groups: motivations to mobilise and recruitment experiences; training, learning, and materials; mobilisation activity; and support and social networking. Our evaluation demonstrates that peer-to-peer diffusion models used to increase awareness of HIV PrEP in key unreached groups, offer an acceptable public health intervention model for volunteers and project staff.

Reconstructing Molecular Networks by Causal Diffusion Do-Calculus Analysis with Deep Learning.

Quantifying molecular regulations between genes/molecules causally from observed data is crucial for elucidating the molecular mechanisms underlying biological processes at the network level. Presently, most methods for inferring gene regulatory and biological networks rely on association studies or observational causal-analysis approaches. This study introduces a novel approach that combines intervention operations and diffusion models within a do-calculus framework by deep learning, i.e., Causal Diffusion Do-calculus (CDD) analysis, to infer causal networks between molecules. CDD can extract causal relations from observed data owing to its intervention operations, thereby significantly enhancing the accuracy and generalizability of causal network inference. Computationally, CDD has been applied to both simulated data and real omics data, which demonstrates that CDD outperforms existing methods in accurately inferring gene regulatory networks and identifying causal links from genes to disease phenotypes. Especially, compared with the Mendelian randomization algorithm and other existing methods, the CDD can reliably identify the disease genes or molecules for complex diseases with better performances. In addition, the causal analysis between various diseases and the potential factors in different populations from the UK Biobank database is also conducted, which further validated the effectiveness of CDD.