Related papers: Simple simulation of diffusion bridges with applic…
We consider the problem of inference for nonlinear, multivariate diffusion processes, satisfying It\^o stochastic differential equations (SDEs), using data at discrete times that may be incomplete and subject to measurement error. Our…
We describe a new, surprisingly simple algorithm, that simulates exact sample paths of a class of stochastic differential equations. It involves rejection sampling and, when applicable, returns the location of the path at a random…
This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…
Let X be the mild solution to a semilinear stochastic partial differential equation. In this article, we develop methodology to sample from the infinite-dimensional diffusion bridge that arises from conditioning X on a linear transformation…
We present a novel approximate inference method for diffusion processes, based on the Wasserstein gradient flow formulation of the diffusion. In this formulation, the time-dependent density of the diffusion is derived as the limit of…
Modelling random dynamical systems in continuous time, diffusion processes are a powerful tool in many areas of science. Model parameters can be estimated from time-discretely observed processes using Markov chain Monte Carlo (MCMC) methods…
In this paper we describe a novel framework for diffusion-based generative modeling on constrained spaces. In particular, we introduce manual bridges, a framework that expands the kinds of constraints that can be practically used to form…
The marginal likelihood plays an important role in many areas of Bayesian statistics such as parameter estimation, model comparison, and model averaging. In most applications, however, the marginal likelihood is not analytically tractable…
We propose a discrete time discrete space Markov chain approximation with a Brownian bridge correction for computing curvilinear boundary crossing probabilities of a general diffusion process on a finite time interval. For broad classes of…
Given an unconditional diffusion model targeting a joint model $\pi(x, y)$, using it to perform conditional simulation $\pi(x \mid y)$ is still largely an open question and is typically achieved by learning conditional drifts to the…
Pore-scale simulations accurately describe transport properties of fluids in the subsurface. These simulations enhance our understanding of applications such as assessing hydrogen storage efficiency and forecasting CO$_2$ sequestration…
Recent advances have introduced diffusion models for probabilistic streamflow forecasting, demonstrating strong early flood-warning skill. However, current implementations rely on recurrent Long Short-Term Memory (LSTM) backbones and…
We consider the problem of making nonparametric inference in a class of multi-dimensional diffusions in divergence form, from low-frequency data. Statistical analysis in this setting is notoriously challenging due to the intractability of…
We propose a hybrid generative model for efficient sampling of high-dimensional, multimodal probability distributions for Bayesian inference. Traditional Monte Carlo methods, such as the Metropolis-Hastings and Langevin Monte Carlo sampling…
Hourly predictions are critical for issuing flood warnings as the flood peaks on the hourly scale can be distinctly higher than the corresponding daily ones. Currently a popular hourly data-driven prediction scheme is multi-time-scale long…
Diffusion bridge models in both continuous and discrete state spaces have recently become powerful tools in the field of generative modeling. In this work, we leverage the discrete state space formulation of bridge matching models to…
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…
We provide the first generic exact simulation algorithm for multivariate diffusions. Current exact sampling algorithms for diffusions require the existence of a transformation which can be used to reduce the sampling problem to the case of…
Diffusion models offer stable training and state-of-the-art performance for deep generative modeling tasks. Here, we consider their use in the context of multivariate subsurface modeling and probabilistic inversion. We first demonstrate…
The dynamic Schr\"odinger bridge problem seeks a stochastic process that defines a transport between two target probability measures, while optimally satisfying the criteria of being closest, in terms of Kullback-Leibler divergence, to a…