Classical Diffusion Model Research Articles

Combination of edge enhancement and cold diffusion model for low dose CT image denoising.

Since the quality of low dose CT (LDCT) images is often severely affected by noise and artifacts, it is very important to maintain high quality CT images while effectively reducing the radiation dose. In recent years, the representation of diffusion models to produce high quality images and stable trainability has attracted wide attention. With the extension of the cold diffusion model to the classical diffusion model, its application has greater flexibility. Inspired by the cold diffusion model, we proposes a low dose CT image denoising method, called CECDM, based on the combination of edge enhancement and cold diffusion model. The LDCT image is taken as the end point (forward) of the diffusion process and the starting point (reverse) of the sampling process. Improved sobel operator and Convolution Block Attention Module are added to the network, and compound loss function is adopted. The experimental results show that CECDM can effectively remove noise and artifacts from LDCT images while the inference time of a single image is reduced to 0.41 s. Compared with the existing LDCT image post-processing methods, CECDM has a significant improvement in all indexes.

Faedo-Galerkin method for the time-fractional reaction-diffusion model

This paper investigates a time-fractional reaction-diffusion equation characterized by a Caputo derivative of fractional order , incorporates non-local and memory effects that are essential for accurately modeling complex diffusion processes in such environments. These effects arise from the fractal nature of the media, which leads to anomalous diffusion behavior that cannot be adequately described by classical diffusion models. We start by giving a definition of a weak solution for this problem, ensuring that the solution satisfies the equation in a generalized sense. Subsequently, the Faedo-Galerkin method combined with compactness arguments is employed to establish the existence and uniqueness of the weak solution. This approach involves approximating the solution using a sequence of finite-dimensional functions and then passing to the limit to obtain the desired solution . Moreover, we establish the stability of these solutions, which is fundamental for understanding their behavior under varying conditions and ensuring the reliability of the model . Our findings contribute to a deeper understanding of anomalous diffusion phenomena in fractal media and provide a solid foundation for further research in this area.

ICDDPM: Image-conditioned denoising diffusion probabilistic model for real-world complex point cloud single view reconstruction

Point cloud single-view reconstruction (PC-SVR) generates high-quality point clouds from low-cost 2D images, offering a cost-effective solution to the expensive and inefficient acquisition of point cloud for real-world scene typically achieved through expensive LiDAR systems. However, current models that generate point clouds from real-world 2D images (e.g. maritime vessels) still have shortcomings in terms of quality and model generalization. In this paper, we proposed a image-conditioned denoising diffusion probabilistic model (ICDDPM) for real-world complex point cloud single view reconstruction to address these issues. We re-designed the structure of classic diffusion model, use latent shape vectors to seamlessly integrate 2D image encoder, point cloud encoder, and conditional diffusion model, to cater PC-SVR task. By guiding the diffusion process with the 2D images, which serve as crucial conditional information, ICDDPM achieves end-to-end point cloud generation with superior quality. 2D images are also employed as input in the reverse diffusion process to further achieve point cloud generation. We conducted qualitative and quantitative experiments on synthetic dataset ShapeNet and real-world dataset PASCAL3D+ (focused on experiments of vessel point cloud data specifically). The results indicate that the ICDDPM model demonstrates superior performance compared to state-of-the-art models. It is capable of generating point clouds with a greater level of global and local details from various 2D image data. Additionally, the model exhibits strong generalization abilities and requires fewer computational resources.

A theoretical perspective on solid-state ionic interfaces.

Solid-state ionic conductors find application across various domains in materials science, particularly showcasing their significance in energy storage and conversion technologies. To effectively utilize these materials in high-performance electrochemical devices, a comprehensive understanding and precise control of charge carriers' distribution and ionic mobility at interfaces are paramount. A major challenge lies in unravelling the atomic-level processes governing ion dynamics within intricate solid and interfacial structures, such as grain boundaries and heterophases. From a theoretical viewpoint, in this Perspective article, my focus is to offer an overview of the current comprehension of key aspects related to solid-state ionic interfaces, with a particular emphasis on solid electrolytes for batteries, while providing a personal critical assessment of recent research advancements. I begin by introducing fundamental concepts for understanding solid-state conductors, such as the classical diffusion model and chemical potential. Subsequently, I delve into the modelling of space-charge regions, which are pivotal for understanding the physicochemical origins of charge redistribution at electrified interfaces. Finally, I discuss modern computational methods, such as density functional theory and machine-learned potentials, which offer invaluable tools for gaining insights into the atomic-scale behaviour of solid-state ionic interfaces, including both ionic mobility and interfacial reactivity aspects. This article is part of the theme issue 'Celebrating the 15th anniversary of the Royal Society Newton International Fellowship'.

Differential games in the supply chain of innovative products with consumer purchase regret induced returns.

Innovative products entering the market will cause dynamic changes in market demand, and consumers' purchase regret and their return behavior make the market environment more and more complex, which in turn affects the dynamic decision-making in the supply chain. In this paper, under the situation of discrete decision time, combining with the objective reality, we make discrete modification to the classical Bass diffusion model (Bass model), construct a manufacturer-led, retailer-followed supply chain differential game model, analyze the optimal decision-making of the manufacturer and the retailer by combining with the theory of discrete optimal control, and then verify the conclusions by numerical simulation. The results show that: when retailers purchase directly from the manufacturer and sell in the market, the optimal pricing of the innovative product can make the supply chain as a whole, realizing Pareto optimality; consumer's purchase regret will increase the amount of returns, which will lead to the decrease of product sales and the profits of the manufacturer and the retailer; when the innovative product accounts for a different share of the market, the impact of purchase regret on the wholesale price and the retail price are also different. Therefore, manufacturers need to have an extensive comprehension of the market to minimize the negative effects of consumer regret and returns, and to formulate a reasonable pricing strategy for their products to gain as much profit as possible.

Quantum‐Noise‐Driven Generative Diffusion Models

AbstractGenerative models realized with Machine Learning (ML) techniques are powerful tools to infer complex and unknown data distributions from a finite number of training samples in order to produce new synthetic data. Diffusion Models (DMs) are an emerging framework that have recently overcome Generative Adversarial Networks (GANs) in creating high‐quality images. Here, is proposed and discussed the quantum generalization of DMs, i.e., three Quantum‐Noise‐Driven Generative Diffusion Models (QNDGDMs) that could be experimentally tested on real quantum systems. The idea is to harness unique quantum features, in particular the non‐trivial interplay among coherence, entanglement, and noise that the currently available noisy quantum processors do unavoidably suffer from, in order to overcome the main computational burdens of classical diffusion models during inference. Hence, the suggestion is to exploit quantum noise not as an issue to be detected and solved but instead as a beneficial key ingredient to generate complex probability distributions from which a quantum processor might sample more efficiently than a classical one. Three examples of the numerical simulations are also included for the proposed approaches. The results are expected to pave the way for new quantum‐inspired or quantum‐based generative diffusion algorithms addressing tasks as data generation with widespread real‐world applications.

SeisResoDiff: Seismic resolution enhancement based on a diffusion model

High resolution of post-stack seismic data assists in better interpretation of subsurface structures as well as high accuracy of impedance inversion. Therefore, geophysicists consistently strive to acquire higher resolution seismic images in petroleum exploration. Although there have been successful applications of conventional signal processing and machine learning for post-stack seismic resolution enhancement, there is limited reference to the seismic applications of the recent emergence and rapid development of generative artificial intelligence. Hence, we propose to apply diffusion models, among the most popular generative models, to enhance seismic resolution. Specifically, we apply the classic diffusion model—denoising diffusion probabilistic model (DDPM), conditioned on the seismic data in low resolution, to reconstruct corresponding high-resolution images. Herein the entire scheme is referred to as SeisResoDiff. To provide a comprehensive and clear understanding of SeisResoDiff, we introduce the basic theories of diffusion models and detail the optimization objective's derivation with the aid of diagrams and algorithms. For implementation, we first propose a practical workflow to acquire abundant training data based on the generated pseudo-wells. Subsequently, we apply the trained model to both synthetic and field datasets, evaluating the results in three aspects: the appearance of seismic sections and slices in the time domain, frequency spectra, and comparisons with the synthetic data using real well-logging data at the well locations. The results demonstrate not only effective seismic resolution enhancement, but also additional denoising by the diffusion model. Experimental comparisons indicate that training the model on noisy data, which are more realistic, outperforms training on clean data. The proposed scheme demonstrates superiority over some conventional methods in high-resolution reconstruction and denoising ability, yielding more competitive results compared to our previous research.

Pore-scale simulation of diffusion characteristics inside the bi-dispersed pore structure

The classical diffusion models fail to predict the diffusivity of bi-dispersed porous materials, particularly at low macro-porosity. In this work, a pore-scale simulation is carried out to investigate the diffusion process inside ordered and random bi-dispersed pore structures under different growth phases and shapes. The applicability of existing models is evaluated. The results reveal that Maxwell and Nield models are inadequate to predict the diffusivity of the ordered macropore structure under different growth phase types and shapes. Meanwhile, the ordered distribution of microporous spherical particles is superior to that of macropores. For random pore structure, the macropore-macropore diffusion path contributes to the error of the random pore model, which depends on the ratio of the micropore-macropore diffusivity.

Study on size effect and model optimization of methane desorption-diffusion in high rank coal

ABSTRACT Methane diffusion models are numerous, but their application, pros, and cons need to be summarized urgently, the link between particle size and methane desorption-diffusion is uncertain. Therefore, this paper carries out the methane desorption-diffusion experiments under multi-scale pressure and particle size conditions to study the effect of coal sample particle size on methane desorption-diffusion. Based on MATLAB, different diffusion models were fitted and comparatively analyzed, and the models were improved in view of their deficiencies. The results showed that the cumulative methane desorption amount and rate are inversely related to the particle size of coal. Comparative analysis of the models revealed that diffusion model under the third type of boundary conditions has a low fitting accuracy for full process of methane desorption, whereas it has a high fitting accuracy of 0.9831 for the first 1000 s of desorption data. Unipore diffusion model, bidisperse diffusion model and new model of dynamic diffusion coefficient have high fitting accuracy for the desorption data of high homogeneous coal, reaching above 0.97, but unipore diffusion model has only 0.5434 fitting accuracy for non-homogeneous coal samples. The fitting accuracy of improved classical unipore diffusion model for both homogeneous and non-homogeneous coals reaches 0.99, which is more extensive than that of unipore diffusion model, only take the first term can satisfy the accuracy requirement, so it is more convenient in the practical engineering application, and has certain reference significance for engineering calculations of gas content and prediction of gas protrusion.

Transcending classical diffusion models: nonlinear dynamics and solitary waves in the fractional Chaffee–Infante equation

Transcending classical diffusion models: nonlinear dynamics and solitary waves in the fractional Chaffee–Infante equation

Influence of salinity gradients on the diffusion of water and ionic species in dual porosity clay samples

Most of the available data on diffusion in natural clayey rocks consider tracer diffusion in the absence of a salinity gradient despite the fact that such gradients are frequently found in natural and engineered subsurface environments. To assess the role of such gradients on the diffusion properties of clayey materials, through-diffusion experiments were carried out in the presence and absence of a salinity gradient using salt-diffusion and radioisotope tracer techniques. The experiments were carried out with vermiculite samples that contained equal proportions of interparticle and interlayer porosities so as to assess also the role played by the two types of porosities on the diffusion of water and ions. Data were interpreted using both a classical Fickian diffusion model and with a reactive transport code, CrunchClay that can handle multi-porosity diffusion processes in the presence of charged surfaces. By combining experimental and simulated data, we demonstrated that (i) the flux of water diffusing through vermiculite interlayer porosity was minor compared to that diffusing through the interparticle porosity, and (ii) a model considering at least three types of porous volumes (interlayer, interparticle diffuse layer, and bulk interparticle) was necessary to reproduce consistently the variations of neutral and charged species diffusion as a function of salinity gradient conditions.

Modeling Sales of Multigeneration Technology Products in the Presence of Frequent Repeat Purchases: A Fractional Calculus-Based Approach

Frequently releasing a new product generation has become a common practice to sustain sales over time, thus accurately forecasting the sales trajectory of each product generation plays a vital role in the short-, medium-, and long-term planning of a firm. Classic multigeneration diffusion models do not incorporate within-generation repeat purchases, making them unusable for product lines with high rates of such purchases. Concentrating on technology products, we develop a multigeneration sales model to fill this void. We demonstrate that the new model can be used for predictive and prescriptive analytics. Our empirical results show that the new model estimates and forecasts sales more accurately than a state-of-the-art benchmark model that does not account for within-generation repeat purchases, underscoring the importance of incorporating repeat purchases. Furthermore, we use two different versions of our model to examine market entry timing under two main strategies, that is, (i) a phase-out transition strategy in which firms continue to sell the old generation after the release of the new generation, and (ii) a total transition strategy in which firms discontinue the old generation after the introduction of the new generation. Our results indicate that the repeat purchases rate determines whether it is optimal to expedite or delay the new product launch, underscoring the importance of incorporating repeat purchases in market entry strategies.

CoreDiff: Contextual Error-Modulated Generalized Diffusion Model for Low-Dose CT Denoising and Generalization.

Low-dose computed tomography (CT) images suffer from noise and artifacts due to photon starvation and electronic noise. Recently, some works have attempted to use diffusion models to address the over-smoothness and training instability encountered by previous deep-learning-based denoising models. However, diffusion models suffer from long inference time due to a large number of sampling steps involved. Very recently, cold diffusion model generalizes classical diffusion models and has greater flexibility. Inspired by cold diffusion, this paper presents a novel COntextual eRror-modulated gEneralized Diffusion model for low-dose CT (LDCT) denoising, termed CoreDiff. First, CoreDiff utilizes LDCT images to displace the random Gaussian noise and employs a novel mean-preserving degradation operator to mimic the physical process of CT degradation, significantly reducing sampling steps thanks to the informative LDCT images as the starting point of the sampling process. Second, to alleviate the error accumulation problem caused by the imperfect restoration operator in the sampling process, we propose a novel ContextuaL Error-modulAted Restoration Network (CLEAR-Net), which can leverage contextual information to constrain the sampling process from structural distortion and modulate time step embedding features for better alignment with the input at the next time step. Third, to rapidly generalize the trained model to a new, unseen dose level with as few resources as possible, we devise a one-shot learning framework to make CoreDiff generalize faster and better using only one single LDCT image (un)paired with normal-dose CT (NDCT). Extensive experimental results on four datasets demonstrate that our CoreDiff outperforms competing methods in denoising and generalization performance, with clinically acceptable inference time. Source code is made available at https://github.com/qgao21/CoreDiff.

Thermal diffusion, exhaust gas recirculation and blending effects on lean premixed hydrogen flames

Thermodiffusively-unstable lean premixed hydrogen flames are investigated using two-dimensional direct numerical simulation employing finite-rate chemical kinetics. Three databases are generated focussing on the inclusion of the Soret effect, the recirculation of exhaust gas, and blending with methane. A simple rescaling of a classic thermal diffusion model is presented and shown to mimic multicomponent diffusion with very low computational cost and little-to-no loss in accuracy. It is also shown that a previously developed model for mean local flame speeds in lean premixed hydrogen flames [1] can still be used provided Soret effects are taken into account in one-dimensional calculations. The addition of exhaust gas to the unburned mixture is found to enhance thermodiffusive instability; the primary mechanism for this was shown to be the highly-efficient third-body nature of water, with the reduction of adiabatic flame temperature a second-order effect. Again, the existing mean local flame speed model proved sufficient. Finally, blending with methane was found to reduce the thermodiffusive response of the flame, more so than the existing model suggests, despite adjustment of the fuel Lewis number; an adapted model is presented to account for this.

A priori tests of turbulence models for compressible flows

PurposeThe purpose of the paper is to analyse the performances of closures and compressibility corrections classically used in turbulence models when applied to highly-compressible turbulent boundary layers (TBLs) over flat plates.Design/methodology/approachA direct numerical simulation (DNS) database of TBLs, covering a wide range of thermodynamic conditions, is presented and exploited to perform a priori analyses of classical and recent closures for turbulent models. The results are systematically compared to the “exact” terms computed from DNS.FindingsThe few compressibility corrections available in the literature are not found to capture DNS data much better than the uncorrected original models, especially at the highest Mach numbers. Turbulent mass and heat fluxes are shown not to follow the classical gradient diffusion model, which was shown instead to provide acceptable results for modelling the vibrational turbulent heat flux.Originality/valueThe main originality of the present paper resides in the DNS database on which the a priori tests are conducted. The database contains some high-enthalpy simulations at large Mach numbers, allowing to test the performances of the turbulence models in the presence of both chemical dissociation and vibrational relaxation processes.

A New Fractional-order Derivative-based Nonlinear Anisotropic Diffusion Model for Biomedical Imaging

Medical imaging, the process of visual representation of different organs and tissues of the human body, is employed for monitoring the normal as well as abnormal anatomy and physiology of the body. Imaging which can provide healthcare solutions ensuring a regular measurement of various complex diseases plays a critical role in the diagnosis and management of many complex diseases and medical conditions, and the quality of a medical image, which is not a single factor but a composite of contrast, artifacts, distortion, noise, blur, and so forth, depends on several factors such as the characteristics of the equipment, the imaging method in question as well as the imaging variables chosen by the operator. The medical images (ultrasound image, X-rays, CT scans, MRIs, etc.) may lose significant features and become degraded due to the emergence of noise as a result of which the process of improvement pertaining to medical images has become a thought-provoking area of inquiry with challenges related to detecting the speckle noise in the images and finding the applicable solution in a timely manner. The partial differential equations (PDEs), in this sense, can be used extensively in different aspects with regard to image processing ranging from filtering to restoration, segmentation to edge enhancement and detection, denoising in particular, among the other ones. In this research paper, we present a conformable fractional derivative-based anisotropic diffusion model for removing speckle noise in ultrasound images. The proposed model providing to be efficient in reducing noise by preserving the essential image features like edges, corners and other sharp structures for ultrasound images in comparison to the classical anisotropic diffusion model. Furthermore, we aim at proving the viscosity solution of the fractional diffusion model. The finite difference method is used to discretize the fractional diffusion model and classical diffusion models. The peak signal-to-noise ratio (PSNR) is used for the quality of the smooth images. The comparative experimental results corroborate that the proposed, developed and extended mathematical model is capable of denoising and preserving the significant features in ultrasound towards better accuracy, precision and examination within the framework of biomedical imaging and other related medical, clinical, and image-signal related applied as well as computational processes.

An Overview of Image Generation of Industrial Surface Defects.

Intelligent defect detection technology combined with deep learning has gained widespread attention in recent years. However, the small number, and diverse and random nature, of defects on industrial surfaces pose a significant challenge to deep learning-based methods. Generating defect images can effectively solve this problem. This paper investigates and summarises traditional defect generation and deep learning-based methods. It analyses the various advantages and disadvantages of these methods and establishes a benchmark through classical adversarial networks and diffusion models. The performance of these methods in generating defect images is analysed through various indices. This paper discusses the existing methods, highlights the shortcomings and challenges in the field of defect image generation, and proposes future research directions. Finally, the paper concludes with a summary.

Internal oxidation of austenitic Fe-Ni-Cr alloys at high temperatures: Deduction of oxygen permeability and the influence of carbon-bearing gases

Internal oxidation was employed to determine oxygen permeability in the Fe-Ni system between 1000 ºC and 1150 ºC at the oxygen partial pressures of Fe/FeO equilibrium. Fe-Ni-Cr alloys were exposed to environments with and without carbon to assess the influence of dissolved carbon on oxygen permeability. A detailed examination of the classical diffusion model for internal oxidation allowed increased accuracy of the permeability measurement. Oxygen permeability decreased nonlinearly with Ni content in the alloy, driven by a decrease in oxygen solubility. No carbon effect was detected in Ni-containing alloys.

Beyond diffusion: a generalized mean-field theory of turbulent dust transport in protoplanetary discs

ABSTRACT Turbulence in protoplanetary discs, when present, plays a critical role in transporting dust particles embedded in the gaseous disc component. When using a field description of dust dynamics, a diffusion approach is traditionally used to model this turbulent dust transport. However, it has been shown that classical turbulent diffusion models are not fully self-consistent. Several shortcomings exist, including the ambiguous nature of the diffused quantity and the non-conservation of angular momentum. Orbital effects are also neglected without an explicit prescription. In response to these inconsistencies, we present a novel Eulerian turbulent dust transport model for isotropic and homogeneous turbulence on the basis of a mean-field theory. Our model is based on density-weighted averaging applied to the pressureless fluid equations and uses appropriate turbulence closures. Our model yields novel dynamic equations for the turbulent dust mass flux and recovers existing turbulent transport models in special limiting cases, thus providing a more general and self-consistent description of turbulent particle transport. Importantly, our model ensures the conservation of global angular and linear momentum unconditionally and implicitly accounts for the effects of orbital dynamics in protoplanetary discs. Furthermore, our model correctly describes the vertical settling–diffusion equilibrium solutions for both small and large particles. Hence, this work presents a generalized Eulerian turbulent dust transport model, establishing a comprehensive framework for more detailed studies of turbulent dust transport in protoplanetary discs.

Electron kinetics in a positive column of AC discharges in a dynamic regime

We have performed hybrid kinetic-fluid simulations of a positive column in alternating current (AC) argon discharges over a range of driving frequencies f and gas pressure p for the conditions when the spatial nonlocality of the electron energy distribution function (EEDF) is substantial. Our simulations confirmed that the most efficient conditions of plasma maintenance are observed in the dynamic regime when time modulations of mean electron energy (temperature) are substantial. The minimal values of the root mean square electric field and the electron temperature have been observed at f/p values of about 3 kHz Torr−1 in a tube of radius R = 1 cm. The ionization rate and plasma density reached maximal values under these conditions. The numerical solution of a kinetic equation allowed accounting for the kinetic effects associated with spatial and temporal nonlocality of the EEDF. Using the kinetic energy of electrons as an independent variable, we solved an anisotropic tensor diffusion equation in phase space. We clarified the role of different flux components during electron diffusion in phase space over surfaces of constant total energy. We have shown that the kinetic theory uncovers a more exciting and rich physics than the classical ambipolar diffusion (Schottky) model. Non-monotonic radial distributions of excitation rates, metastable densities, and plasma density have been observed in our simulations at pR > 6 Torr cm. The predicted off-axis plasma density peak in the dynamic regime has never been observed in experiments so far. We hope our results stimulate further experimental studies of the AC positive column. The kinetic analysis could help uncover new physics even for such a well-known plasma object as a positive column in noble gases.