Related papers: Another Approximation of the First-Passage Time De…

The problem of a spatially discontinuous diffusion coefficient ($D(\boldsymbol x)$) is one that may be encountered in hydrogeologic systems due to natural geological features or as a consequence of numerical discretization of flow…

Diffusion Language Models (DLMs) offer a promising parallel generation paradigm but suffer from slow inference due to numerous refinement steps and the inability to use standard KV caching. We introduce CDLM (Consistency Diffusion Language…

The estimation of probability density functions (PDF) using approximate maps is a fundamental building block in computational probability. We consider forward problems in uncertainty quantification: the inputs or the parameters of a…

A variety of researchers have successfully obtained the parameters of low dimensional diffusion models using the data that comes out of atomistic simulations. This naturally raises a variety of questions about efficient estimation,…

In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability for a finite time step $\Delta t$, and a…

Transition probability density functions (TPDFs) are fundamental to computational finance, including option pricing and hedging. Advancing recent work in deep learning, we develop novel neural TPDF generators through solving backward…

We propose a new molecular simulation framework that combines the transferability, robustness and chemical flexibility of an ab initio method with the accuracy and efficiency of a machine learned force field. The key to achieve this mix is…

Autoregressive language models (ARMs) deliver strong likelihoods, but are inherently serial: they generate one token per forward pass, which limits throughput and inflates latency for long sequences. Diffusion Language Models (DLMs)…

This chapter presents controlled approximations of Kohn-Sham density functional theory (DFT) that enable very large scale simulations. The work is motivated by the study of defects in crystalline solids, though the ideas can be used in…

Uncertainty propagation in nonlinear dynamic systems remains an outstanding problem in scientific computing and control. Numerous approaches have been developed, but are limited in their capability to tackle problems with more than a few…

Motivated by the dynamics of resonant neurons we discuss the properties of the first passage time (FPT) densities for nonmarkovian differentiable random processes. We start from an exact expression for the FPT density in terms of an…

Piecewise Diffusion Markov Processes (PDifMPs) are valuable for modelling systems where continuous dynamics are interrupted by sudden shifts and/or changes in drift and diffusion. The first-passage time (FPT) in such models plays a central…

This paper introduces Discrete Markov Probabilistic Models (DMPMs), a novel discrete diffusion algorithm for discrete data generation. The algorithm operates in discrete bit space, where the noising process is a continuous-time Markov chain…

Diffusion models have achieved remarkable success in generating high-fidelity content but suffer from slow, iterative sampling, resulting in high latency that limits their use in interactive applications. We introduce DRiffusion, a parallel…

Denoising Diffusion Models (DDMs) have become a popular tool for generating high-quality samples from complex data distributions. These models are able to capture sophisticated patterns and structures in the data, and can generate samples…

In this article, we consider diffusion approximations for a general class of stochastic recursions. Such recursions arise as models for population growth, genetics, financial securities, multiplicative time series, numerical schemes and…

Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus…

We study and develop the stochastic Markov reward model (sMRM), which extends the Markov chain where transition time/reward as modelled as random variables. Techniques are presented to enable computing first-passage time distributions (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…

Probability density function (PDF) methods are a promising alternative to predicting the transport of solutes in groundwater under uncertainty. They make it possible to derive the evolution equations of the mean concentration and the…