• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.28 no.1
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• pp.1-21
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• 2024

This review comprehensively explores the evolution, theoretical underpinnings, variations, and applications of diffusion models. Originating as a generative framework, diffusion models have rapidly ascended to the forefront of machine learning research, owing to their exceptional capability, stability, and versatility. We dissect the core principles driving diffusion processes, elucidating their mathematical foundations and the mechanisms by which they iteratively refine noise into structured data. We highlight pivotal advancements and the integration of auxiliary techniques that have significantly enhanced their efficiency and stability. Variants such as bridges that broaden the applicability of diffusion models to wider domains are introduced. We put special emphasis on the ability of diffusion models as a crucial foundation model, with modalities ranging from image, 3D assets, and video. The role of diffusion models as a general foundation model leads to its versatility in many of the downstream tasks such as solving inverse problems and image editing. Through this review, we aim to provide a thorough and accessible compendium for both newcomers and seasoned researchers in the field.

• Journal of the Korean Ceramic Society
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• v.47 no.1
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• pp.26-38
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• 2010

Degradation in Solid Oxide Fuel Cell performance can be ascribed to the following fundamental processes from the materials chemical point of view; that is, diffusion in solids and reaction with gaseous impurities. For SOFC materials, diffusion in solids is usually slow in operation temperatures $800\sim1000^{\circ}C$. Even at $800^{\circ}C$, however, a few processes are rapid enough to lead to some degradations; namely, Sr diffusion in doped ceria, cation diffusion in cathode materials, diffusion related with metal corrosion, and sintering of nickel anodes. For gaseous impurities, chromium containing vapors are important to know how the chemical stability of cathode materials is related with degradation of performance. For LSM as the most stable cathode among the perovskite-type cathodes, electrochemical reduction reaction of $CrO_3$(g) at the electrochemically active sites is crucial, whereas the rest of the cathodes have the $SrCrO_4$ formation at the point where cathodes meet with the gases, leading to rather complicated processes to the degradations, depending on the amount and distribution of reacted Cr component. These features can be easily generalized to other impurities in air or to the reaction of nickel anodes with gaseous impurities in anode atmosphere.

• Journal of the Korea Institute of Military Science and Technology
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• v.11 no.1
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• pp.57-65
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• 2008

Superplastic forming/diffusion bonding(SPF/DB) processes with inner contact were analyzed using a 3-D rigid visco-plastic finite element method. A constant-triangular element based on membrane approximation and an incremental theory of plasticity are employed for the formulation. The hierarchical search algorithm for the contact searching has been applied. The algorithms for contact force processing were designed to handle equally well contact between deformable bodies, as well as rigid bodies. The plate of three and four sheets for 3-D SPF/DB model are analyzed using the developed program. The validity for the analysis is verified by comparison between analysis, experiment and results in the literature.

• Journal of the Korean Wood Science and Technology
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• v.19 no.4
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• pp.7-17
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• 1991

The feasibility of treating three softwood(Japanese larch pitch pine, and Korean pine) thinned logs by double-diffusion treatment processes was investigated. Some posts were incised before immersion, and others were imersed in hot copper sulfate solution. Comparison among species indicated that. in general, pitch pine was most treatable and Japanese larch least treatable. For all three species, almost all treatment schedules gave consistently good penetration and high net retention, but very steep gradient of preservative distribution. As expected, the treatability was increased by the extension of immersion time, increased concentration of treating solution, incising. and heating of the first solution. Of the variables tested, it appears that heating of the first solution is the most important. From the data in this paper, it may be concluded that, if the first solution is not heated, the best schedule is #3. If the first solution is healed. it appears the best schedules are #10 or #11. Since heating of the first solution improves the treatability. schedules # 10 or :#11 are recommended if the cost of heating might be justified. The data presented in this paper indicate that double-diffusion treatment processes seem to offer a promise as a comparatively effective and easy-operating method of treating thinned logs for the small-scale production of treated stock.

• Journal of Mechanical Science and Technology
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• v.16 no.1
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• pp.116-124
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• 2002

In order to investigate the soot formation and oxidation processes, we employed the two variable approach and its source terms representing soot nucleation, coagulation, surface growth and oxidation. For the simulation of the taxi-symmetric turbulent reacting flows, the pressure-velocity coupling is handled by the pressure based finite volume method. We also employed laminar flamelet model to calculate the thermo-chemical properties and the proper soot source terms from the information of detailed chemical kinetic model. The numerical and physical models used in this study successfully predict the essential features of the combustion processes and soot formation characteristics in the reacting flow field.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.677-683
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• 2012

W.Choi([1]) obtains a complete description of ergodic property and several property by making use of the semigroup method. In this note, we shall consider separately the martingale problems for two operators A and B as a detail decomposition of operator L. A key point is that the (K, L, $p$)-martingale problem in population genetics model is related to diffusion processes, so we begin with some a priori estimates and we shall show existence of contraction semigroup {$T_t$} associated with decomposition operator A.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.813-837
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• 2022

In this paper we consider inverse problem for a general class of nonlinear stochastic differential equations on Hilbert spaces whose generating operators (drift, diffusion and jump kernels) are unknown. We introduce a class of function spaces and put a suitable topology on such spaces and prove existence of optimal generating operators from these spaces. We present also necessary conditions of optimality including an algorithm and its convergence whereby one can construct the optimal generators (drift, diffusion and jump kernel).

• Proceedings of the Membrane Society of Korea Conference
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• 1997.10a
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• pp.27-30
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• 1997

1. Introduction : Molecular diffusion of small molecules in polymers plays an important role in many areas where polymers are acting as barriers, and in separation processes, such as selective diffusion. Different applications of polymers have different requirements on their transport properties. Therefore, reliable predictions of diffusion coefficients for small molecules in polymeric materials could be a useful tool to design appropriate materials. For many years, the theories based on free-volume concepts have been widely used to correlate and predict diffusion behavior in polymer/solvent systems. In the theory derived by Vrentas and Duda, the empty space between molecules that is available for molecular transport, referred to as hole free-volume, is being redistributed. Molecular transport will occur only when a free-volume of sufficient size appears adjacent to a molecule and the molecule has enough energy to jump into this void. The diffusive jump is considered complete when the void left behind is closed before the molecule returns to its original position. In this paper, the Vrentas-Duda free-volume theory is presented and the methods to estimate free-volume parameters for predicting polymer/ solvent diffusion coefficients are described in detail.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.7
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• pp.1036-1044
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• 1995

In this paper, a band-pass filter is implemented with the diffusion and difference processes by using the diffusion neural network model. The center frequency of this band-pass filter can be varied by iterations of the diffusion and difference operations, and the selectivity can be determined by iterations of the difference operation. We propose an efficient algorithm that can generate various band-pass filters using arbitrary diffusion and difference iterations. This algorithm needs only simple operations of diffusion and difference.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.33B no.7
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• pp.163-172
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• 1996

Recently, it was reported that gaussian distribution and difference of two gaussians (DOG) to have band pass characteristics can be generated by simple iterative processes of the diffusion networks. In this paper, we propose method of improved implementation of a diffusion filter which can reduce total runing time, and operate by simple algorithm in contrast to the latest diffusion filter. We rebuild the diffusion network to a difference network which can generate DOG independently. Different filter characteristics are obtained just by each diffusion process and difference process. Quantitative analysis shows that the center frequency and the selectivity of each filter channel can be varied independently. Also, it would requires smaller amount of hardwares than conventioanl method to build a filter bank.