Related papers: Residual-Bridge Constructs for Conditioned Diffusi…
In this paper we outline methodology to efficiently simulate (jump) diffusion bridge sample paths without discretisation error. We achieve this by considering the simulation of conditioned (jump) diffusion bridge sample paths in light of…
In this paper, we establish a relationship between the asymptotic form of conditional boundary crossing probabilities and first passage time densities for diffusion processes. Namely, we show that, under broad assumptions, the first…
Stochastic processes of bridge types having pinned initial and terminal conditions have been widely used in applied research areas, but they all have a common drawback in that the model at hand is possibly misspecified owing to its…
We present an extended version of an invited talk given on the International Conference "Turbulent Mixing and Beyond". The dynamical and statistical description of stably stratified turbulent boundary layers with the important example of…
A class of generative models that unifies flow-based and diffusion-based methods is introduced. These models extend the framework proposed in Albergo and Vanden-Eijnden (2023), enabling the use of a broad class of continuous-time stochastic…
We study the small-time asymptotics for hypoelliptic diffusion processes conditioned by their initial and final positions, in a model class of diffusions satisfying a weak H\"ormander condition where the diffusivity is constant and the…
Stochastic differential equations provide a powerful tool for modelling dynamic phenomena affected by random noise. In case of repeated observations of time series for several experimental units, it is often the case that some of the…
Flow matching and diffusion bridge models have emerged as leading paradigms in generative speech enhancement, modeling stochastic processes between paired noisy and clean speech signals based on principles such as flow matching, score…
Motivated by the polynuclear growth model, we consider a Brownian bridge b(t) with b(\pm T)=0 conditioned to stay above the semicircle c_T(t)=\sqrtT^2-t^2. In the limit of large T, the fluctuation scale of b(t)-c_T(t) is T^{1/3} and its…
Diffusions are a fundamental class of models in many fields, including finance, engineering, and biology. Simulating diffusions is challenging as their sample paths are infinite-dimensional and their transition functions are typically…
In this paper, using an algorithm based on the retrospective rejection sampling scheme, we propose an exact simulation of a Brownian diffusion whose drift admits several jumps. We treat explicitly and extensively the case of two jumps,…
This paper motivates the use of random-bridges -- stochastic processes conditioned to take target distributions at fixed timepoints -- in the realm of generative modelling. Herein, random-bridges can act as stochastic transports between two…
This study makes the first attempt to use the 2/3-order fractional Laplacian modeling of enhanced diffusing movements of random turbulent particle resulting from nonlinear inertial interactions. A combined effect of the inertial…
In this paper, we simulate diffusion bridges by using an approximation of the Wiener-chaos expansion (WCE), or a Fourier-Hermite expansion, for a related diffusion process. Indeed, we consider the solution of stochastic differential…
While Macroscopic Fluctuation Theory (MFT) has been highly successful in analyzing non-equilibrium steady states, its application to non-steady-state processes remains limited. In this study, we apply MFT to the relaxation process of…
Denoising diffusion models (DDM) have gained recent traction in medical image translation given improved training stability over adversarial models. DDMs learn a multi-step denoising transformation to progressively map random Gaussian-noise…
Denoising diffusion bridge models (DDBMs) are a powerful variant of diffusion models for interpolating between two arbitrary paired distributions given as endpoints. Despite their promising performance in tasks like image translation, DDBMs…
Existing deterministic variational inference approaches for diffusion processes use simple proposals and target the marginal density of the posterior. We construct the variational process as a controlled version of the prior process and…
In this paper we study a reflected Markov-modulated Brownian motion with a two sided reflection in which the drift, diffusion coefficient and the two boundaries are (jointly) modulated by a finite state space irreducible continuous time…
We develop two-dimensional Brownian dynamics simulations to examine the motion of disks under thermal fluctuations and Hookean forces. Our simulations are designed to be experimental-like, since the experimental conditions define the…