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Recently, diffusion models have shown remarkable results in image synthesis by gradually removing noise and amplifying signals. Although the simple generative process surprisingly works well, is this the best way to generate image data? For…
The theory of degenerate parabolic equations of the forms \[ u_t=(\Phi(u_x))_{x} \quad {\rm and} \quad v_{t}=(\Phi(v))_{xx} \] is used to analyze the process of contour enhancement in image processing, based on the evolution model of…
Diffusion models have recently gained traction as a powerful class of deep generative priors, excelling in a wide range of image restoration tasks due to their exceptional ability to model data distributions. To solve image restoration…
Image enhancement holds extensive applications in real-world scenarios due to complex environments and limitations of imaging devices. Conventional methods are often constrained by their tailored models, resulting in diminished robustness…
Based on a recent novel formulation of parametric anisotropic curve shortening flow, we analyse a fully discrete numerical method of this geometric evolution equation. The method uses piecewise linear finite elements in space and a backward…
Diffusion models represent the state-of-the-art for solving inverse problems such as image restoration tasks. Diffusion-based inverse solvers incorporate a likelihood term to guide prior sampling, generating data consistent with the…
We propose self-diffusion, a novel framework for solving inverse problems without relying on pretrained generative models. Traditional diffusion-based approaches require training a model on a clean dataset to learn to reverse the forward…
While learned image compression (LIC) focuses on efficient data transmission, generative image compression (GIC) extends this framework by integrating generative modeling to produce photo-realistic reconstructed images. In this paper, we…
The presence of noise is an intrinsic problem in acquisition processes for digital images. One way to enhance images is to combine the forward and backward diffusion equations. However, the latter problem is well known to be exponentially…
We proposed a structure-preserving stabilized parametric finite element method (SPFEM) for the evolution of closed curves under anisotropic surface diffusion with an arbitrary surface energy $\hat{\gamma}(\theta)$. By introducing a…
Due to the high potential for abuse of GenAI systems, the task of detecting synthetic images has recently become of great interest to the research community. Unfortunately, existing image-space detectors quickly become obsolete as new…
A method is developed within an adaptive framework to solve quasilinear diffusion problems with internal and possibly boundary layers starting from a coarse mesh. The solution process is assumed to start on a mesh where the problem is badly…
Diffusion models have been demonstrated as strong priors for solving general inverse problems. Most existing Diffusion model-based Inverse Problem Solvers (DIS) employ a plug-and-play approach to guide the sampling trajectory with either…
In recent times, diffusion models have achieved remarkable performance in image restoration tasks. Their core mechanism relies on the restricted presumption of degradation prior to the additive noise operation. However, the blur model, one…
We propose and analyse numerical schemes for a system of quasilinear, degenerate evolution equations modelling biofilm growth as well as other processes such as flow through porous media and the spreading of wildfires. The first equation in…
Recent advances in Artificial Intelligence Generated Content (AIGC) have garnered significant interest, accompanied by an increasing need to transmit and compress the vast number of AI-generated images (AIGIs). However, there is a…
Diffusion models are powerful tools for sampling from high-dimensional distributions by progressively transforming pure noise into structured data through a denoising process. When equipped with a guidance mechanism, these models can also…
Recent inversion-free, flow-based image editing methods such as FlowEdit leverages a pre-trained noise-to-image flow model such as Stable Diffusion 3, enabling text-driven manipulation by solving an ordinary differential equation (ODE).…
The inverse of an invertible convolution is an important operation that comes up in Normalizing Flows, Image Deblurring, etc. The naive algorithm for backpropagation of this operation using Gaussian elimination has running time $O(n^3)$…
Standard diffusion models involve an image transform -- adding Gaussian noise -- and an image restoration operator that inverts this degradation. We observe that the generative behavior of diffusion models is not strongly dependent on the…