Related papers: Tuned Finite-Difference Diffusion Operators
Diffusion models are widely used for generative tasks across domains. Given a pre-trained diffusion model, it is often desirable to fine-tune it further either to correct for errors in learning or to align with downstream applications.…
Stably placing an object in a multi-object scene is a fundamental challenge in robotic manipulation, as placements must be penetration-free, establish precise surface contact, and result in a force equilibrium. To assess stability, existing…
In a recent paper (see [7]), a quasi-nonlocal coupling method was introduced to seamlessly bridge a nonlocal diffusion model with the classical local diffusion counterpart in a one-dimensional space. The proposed coupling framework removes…
We consider large deviations of empirical measures of diffusion processes. In a first part, we present conditions to obtain a large deviations principle (LDP) for a precise class of unbounded functions. This provides an analogue to the…
We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be…
Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible…
The increased model capacity of Diffusion Transformers (DiTs) and the demand for generating higher resolutions of images and videos have led to a significant rise in inference latency, impacting real-time performance adversely. While prior…
When applying the finite-differences method to numerically solve the one-dimensional diffusion equation, one must choose discretization steps $\Delta x$, $\Delta t$ in space and time, respectively. By applying large-deviation theory on the…
A low diffusive flux difference splitting based kinetic scheme is developed based on a discrete velocity Boltzmann equation, with a novel three velocity model. While two discrete velocities are used for upwinding, the third discrete…
Diffusion models have revolutionized generative tasks through high-fidelity outputs, yet flow matching (FM) offers faster inference and empirical performance gains. However, current foundation FM models are computationally prohibitive for…
There is a class of physical filtration processes where the input is adequately modeled by a continuous periodic function f (x) of bounded variation over its period, and the output depends only on certain harmonics of the Fourier expansion…
Machine learning models are gaining increasing popularity in the domain of fluid dynamics for their potential to accelerate the production of high-fidelity computational fluid dynamics data. However, many recently proposed machine learning…
When modeling propagation and scattering phenomena using integral equations discretized by the boundary element method, it is common practice to approximate the boundary of the scatterer with a mesh comprising elements of size approximately…
Score-based diffusion models achieve state-of-the-art performance for inverse problems, but their practical deployment is hindered by long inference times and cumbersome hyperparameter tuning. While pretrained diffusion models can be reused…
Scaling by training on large datasets has been shown to enhance the quality and fidelity of image generation and manipulation with diffusion models; however, such large datasets are not always accessible in medical imaging due to cost and…
This paper presents a spatial two-grid (STG) compact difference scheme for a two-dimensional (2D) nonlinear diffusion-wave equation with variable exponent, which describes, e.g., the propagation of mechanical diffusive waves in viscoelastic…
This paper is concerned with the distributed control and stabilization problems for linear discrete-time large scale systems with imposed constraints. The main contributions of this paper are: Firstly, by using the maximum principle…
Discrete diffusion models excel at visual synthesis but rely on slow, iterative decoding. Existing single-step distillation methods attempt to bypass this bottleneck, either by training auxiliary score networks that effectively double…
Image retouching aims to enhance the visual quality of photos. Considering the different aesthetic preferences of users, the target of retouching is subjective. However, current retouching methods mostly adopt deterministic models, which…
Recent studies demonstrate that diffusion planners benefit from sparse-step planning over single-step planning. Training models to skip steps in their trajectories helps capture long-term dependencies without additional memory or…