Related papers: Diffusion bridges for stochastic Hamiltonian syste…

The diffusion bridge, which is a diffusion process conditioned on hitting a specific state within a finite period, has found broad applications in various scientific and engineering fields. However, simulating diffusion bridges for modeling…

We propose simple methods for multivariate diffusion bridge simulation, which plays a fundamental role in simulation-based likelihood and Bayesian inference for stochastic differential equations. By a novel application of classical coupling…

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…

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…

Diffusion bridge models and stochastic interpolants enable high-quality image-to-image (I2I) translation by creating paths between distributions in pixel space. However, the proliferation of techniques based on incompatible mathematical…

Simulation of conditioned diffusion processes is an essential tool in inference for stochastic processes, data imputation, generative modelling, and geometric statistics. Whilst simulating diffusion bridge processes is already difficult on…

We provide a general framework for learning diffusion bridges that transport prior to target distributions. It includes existing diffusion models for generative modeling, but also underdamped versions with degenerate diffusion matrices,…

Stochastic processes of evolving shapes are used in applications including evolutionary biology, where morphology changes stochastically as a function of evolutionary processes. Due to the non-linear and often infinite-dimensional nature of…

This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation…

Diffusion models are powerful generative models that map noise to data using stochastic processes. However, for many applications such as image editing, the model input comes from a distribution that is not random noise. As such, diffusion…

We consider the problem of simulating diffusion bridges, which are diffusion processes that are conditioned to initialize and terminate at two given states. The simulation of diffusion bridges has applications in diverse scientific fields…

Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…

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…

Recent innovations in diffusion probabilistic models have paved the way for significant progress in image, text and audio generation, leading to their applications in generative time series forecasting. However, leveraging such abilities to…

We study a generalization of the Brownian bridge as a stochastic process that models the position and velocity of inertial particles between the two end-points of a time interval. The particles experience random acceleration and are assumed…

Diffusion-based generative models have achieved promising results recently, but raise an array of open questions in terms of conceptual understanding, theoretical analysis, algorithm improvement and extensions to discrete, structured,…

Diffusion models (DMs) have become the dominant paradigm of generative modeling in a variety of domains by learning stochastic processes from noise to data. Recently, diffusion denoising bridge models (DDBMs), a new formulation of…

In recent years, diffusion models have become the leading approach for distribution learning. This paper focuses on structure-preserving diffusion models (SPDM), a specific subset of diffusion processes tailored for distributions with…

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…

This work presents a comprehensive framework for enhanced diffusion modeling in fluid-structure interactions by combining the Immersed Boundary Method (IBM) with stochastic trajectories and high-order spectral boundary conditions. Using…