Related papers: On the exact and $\varepsilon$-strong simulation o…
Diffusion models have recently achieved great success in the synthesis of high-quality images and videos. However, the existing denoising techniques in diffusion models are commonly based on step-by-step noise predictions, which suffers…
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…
An implicit Euler finite-volume scheme for general cross-diffusion systems with volume-filling constraints is proposed and analyzed. The diffusion matrix may be nonsymmetric and not positive semidefinite, but the diffusion system is assumed…
We present a novel method for the accurate numerical determination of the phase behavior of fluid mixtures having large particle size asymmetries. By incorporating the recently developed geometric cluster algorithm within a restricted Gibbs…
Variable selection for high-dimensional, highly correlated data has long been a challenging problem, often yielding unstable and unreliable models. We propose a resample-aggregate framework that exploits diffusion models' ability to…
Diffusion models deliver state-of-the-art generative performance across diverse modalities but remain computationally expensive due to their inherently iterative sampling process. Existing training-free acceleration methods typically…
Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…
We propose enforcing constraints on Model-Based Diffusion by introducing emerging barrier functions inspired by interior point methods. We demonstrate that the standard Model-Based Diffusion algorithm can lead to catastrophic performance…
Kinetic equations model the position-velocity distribution of particles subject to transport and collision effects. Under a diffusive scaling, these combined effects converge to a diffusion equation for the position density in the limit of…
Statistical inference for discretely observed jump-diffusion processes is a complex problem which motivates new methodological challenges. Thus existing approaches invariably resort to time-discretisations which inevitably lead to…
We provide a class of diffusion processes for continuous time-varying multivariate angular data with explicit transition probability densities, enabling exact likelihood inference. The presented diffusions are time-reversible and can be…
We present a novel parametric finite element approach for simulating the surface diffusion of curves and surfaces. Our core strategy incorporates a predictor-corrector time-stepping method, which enhances the classical first-order temporal…
The inverse design of metasurfaces faces inherent challenges due to the nonlinear and highly complex relationship between geometric configurations and their electromagnetic behavior. Traditional optimization approaches often suffer from…
Diffusion models have demonstrated superior performance across various generative tasks including images, videos, and audio. However, they encounter difficulties in directly generating high-resolution samples. Previously proposed solutions…
The increasing application of cardiorespiratory simulations for diagnosis and surgical planning necessitates the development of computational methods significantly faster than the current technology. To achieve this objective, we leverage…
Most end-to-end autonomous driving methods rely on imitation learning from single expert demonstrations, often leading to conservative and homogeneous behaviors that limit generalization in complex real-world scenarios. In this work, we…
The gradient discretisation method (GDM) is a generic framework for designing and analysing numerical schemes for diffusion models. In this paper, we study the GDM for the porous medium equation, including fast diffusion and slow diffusion…
We introduced and analyzed robust recovery-based a posteriori error estimators for various lower order finite element approximations to interface problems in [9, 10], where the recoveries of the flux and/or gradient are implicit (i.e.,…
Diffusion models have demonstrated state-of-the-art performance across vision, language, and scientific domains. Despite their empirical success, prior theoretical analyses of the sample complexity suffer from poor scaling with input data…
In this paper we construct numerical schemes to approximate linear transport equations with slab geometry by diffusion equations. We treat both the case of pure diffusive scaling and the case where kinetic and diffusive scalings coexist.…