Related papers: Singularly Perturbed Profiles
Reaction-Diffusion (RD) systems provide a computational framework that governs many pattern formation processes in nature. Current RD system design practices boil down to trial-and-error parameter search. We propose a differentiable…
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or…
Accurate dose distribution prediction is crucial in the radiotherapy planning. Although previous methods based on convolutional neural network have shown promising performance, they have the problem of over-smoothing, leading to prediction…
The Method of Invariant Grid (MIG) is a model reduction technique based on the concept of slow invariant manifold (SIM), which approximates the SIM by a set of nodes in the concentration space (invariant grid). In the present work, the MIG…
Discrete diffusion models form a powerful class of generative models across diverse domains, including text and graphs. However, existing approaches face fundamental limitations. Masked diffusion models suffer from irreversible errors due…
Recent advancements in diffusion models have demonstrated significant success in unsupervised anomaly segmentation. For anomaly segmentation, these models are first trained on normal data; then, an anomalous image is noised to an…
Diffusion models (DMs) have exhibited remarkable efficacy in various image restoration tasks. However, existing approaches typically operate within the high-dimensional pixel space, resulting in high computational overhead. While methods…
Detail features of magnetic resonance images play a cru-cial role in accurate medical diagnosis and treatment, as they capture subtle changes that pose challenges for doc-tors when performing precise judgments. However, the widely utilized…
We propose a unified diffusion model-based correction and super-resolution method to enhance the fidelity and resolution of diverse low-quality data through a two-step pipeline. First, the correction step employs a novel enhanced stochastic…
This article concerns two methods for reducing large systems of chemical kinetics equations, namely, the method of intrinsic low-dimensional manifolds (ILDMs) due to Maas and Pope and an iterative method due to Fraser and further developed…
Discrete diffusion models have emerged as a promising direction for vision-language tasks, offering bidirectional context modeling and theoretical parallelization. However, their practical application is severely hindered by a…
Social recommendation has emerged as a powerful approach to enhance personalized recommendations by leveraging the social connections among users, such as following and friend relations observed in online social platforms. The fundamental…
Morphogenesis is central to biology but remains largely unexplored in chemistry. Reaction-diffusion (RD) mechanisms are, however, essential to understand how shape emerges in the living world. While numerical methods confirm the incredible…
Diffusion models have achieved impressive performance on multi-focus image fusion (MFIF). However, a key challenge in applying diffusion models to the ill-posed MFIF problem is that defocus blur can make common symmetric geometric…
We introduce regularised diffusion--shock (RDS) inpainting as a modification of diffusion--shock inpainting from our SSVM 2023 conference paper. RDS inpainting combines two carefully chosen components: homogeneous diffusion and…
Denoising Diffusion Probabilistic Models (DDPMs) can generate high-quality samples such as image and audio samples. However, DDPMs require hundreds to thousands of iterations to produce final samples. Several prior works have successfully…
Minimization of energy in gradient systems leads to formation of oscillatory and Turing patterns in reaction-diffusion systems. These patterns should be accurately computed using fine space and time meshes over long time horizons to reach…
Diffusion models (DMs) are capable of generating remarkably high-quality samples by iteratively denoising a random vector, a process that corresponds to moving along the probability flow ordinary differential equation (PF ODE).…
Slow-fast dynamical systems, i.e., singularly or non-singularly perturbed dynamical systems possess slow invariant manifolds on which trajectories evolve slowly. Since the last century various methods have been developed for approximating…
Human motion generation is a challenging task due to its high dimensionality and the difficulty of generating fine-grained motions. Diffusion methods have been proposed due to their high sample quality and expressiveness. Early approaches…