Related papers: Exact simulation of diffusion first exit times: al…

Gem5, an open-source, flexible, and cost-effective simulator, is widely recognized and utilized in both academic and industry fields for hardware simulation. However, the typically time-consuming nature of simulating programs on Gem5…

In this note we propose an exact simulation algorithm for the solution of dX_t=dW_t+b(X_t)dt (1) where b is a smooth real function except at point 0 where b(0+)\neq b(0-). The main idea is to sample an exact skeleton of X using an algorithm…

Diffusion models have garnered significant attention since they can effectively learn complex multivariate Gaussian distributions, resulting in diverse, high-quality outcomes. They introduce Gaussian noise into training data and reconstruct…

Many physical, chemical, and biological systems depend on the first passage time (FPT) of a diffusive searcher to a target. Typically, this FPT is much slower than the characteristic diffusion timescale. For example, this is the case if the…

Motion prediction is a challenging problem in autonomous driving as it demands the system to comprehend stochastic dynamics and the multi-modal nature of real-world agent interactions. Diffusion models have recently risen to prominence, and…

In this paper, we study the diffusion approximation for singularly perturbed stochastic reaction-diffusion equation with a fast oscillating term. The asymptotic limit for the original system is obtained, where an extra Gaussian term…

Discrete optimization is a central problem in artificial intelligence. The optimization of the aggregated cost of a network of cost functions arises in a variety of problems including (W)CSP, DCOP, as well as optimization in stochastic…

With a view to statistical inference for discretely observed diffusion models, we propose simple methods of simulating diffusion bridges, approximately and exactly. Diffusion bridge simulation plays a fundamental role in likelihood and…

A sampling-based method is introduced to approximate the Gittins index for a general family of alternative bandit processes. The approximation consists of a truncation of the optimization horizon and support for the immediate rewards, an…

Many scientific questions can be framed as asking for a first passage time (FPT), which generically describes the time it takes a random "searcher" to find a "target." The important timescale in a variety of biophysical systems is the time…

This tutorial provides an in-depth guide on inference-time guidance and alignment methods for optimizing downstream reward functions in diffusion models. While diffusion models are renowned for their generative modeling capabilities,…

We systematically develop beneficial and practical velocity measures for accurate and efficient statistical simulations of the Langevin equation with direct applications to computational statistical mechanics and molecular dynamics…

Consider scene understanding problems such as predicting where a person is probably reaching, or inferring the pose of 3D objects from depth images, or inferring the probable street crossings of pedestrians at a busy intersection. This…

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…

An important thread in the study of data-stream algorithms focuses on settings where stream items are active only for a limited time. We introduce a new expiration model, where each item arrives with its own expiration time. The special…

In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm so-called Walk on Moving Spheres was already introduced in the Brownian context. The aim is…

Arbitrary style transfer (AST) and domain generalization (DG) are important yet challenging visual learning tasks, which can be cast as a feature distribution matching problem. With the assumption of Gaussian feature distribution,…

We present an acceleration method for sequences of large-scale linear systems, such as the ones arising from the numerical solution of time-dependent partial differential equations coupled with algebraic constraints. We discuss different…

The diffusion approximation of stochastic gradient descent (SGD) in current literature is only valid on a finite time interval. In this paper, we establish the uniform-in-time diffusion approximation of SGD, by only assuming that the…

We present an exact Bayesian inference method for discrete statistical models, which can find exact solutions to a large class of discrete inference problems, even with infinite support and continuous priors. To express such models, we…