Related papers: On the Exact Simulation of (Jump) Diffusion Bridge…
We derive a universal, exact asymptotic form of the splitting probability for symmetric continuous jump processes, which quantifies the probability $ \pi_{0,\underline{x}}(x_0)$ that the process crosses $x$ before 0 starting from a given…
In this manuscript, we present a novel approach for sampling from a continuous multivariate probability distribution, which may either be explicitly known (up to a normalization factor) or represented via empirical samples. Our method…
Continuous time stochastic processes are useful models especially for financial and insurance purposes. The numerical simulation of such models is dependant of the time discrete discretization, of the parametric estimation and of the choice…
Conditional diffusion models serve as the foundation of modern image synthesis and find extensive application in fields like computational biology and reinforcement learning. In these applications, conditional diffusion models incorporate…
In this paper we construct numerical schemes to approximate linear transport equations with slab geometry by diffusion equations. We treat both the case of pure diffusive scaling and the case where kinetic and diffusive scalings coexist.…
Denoising diffusion models have recently emerged as a powerful class of generative models. They provide state-of-the-art results, not only for unconditional simulation, but also when used to solve conditional simulation problems arising in…
Connecting optimal transport and variational inference, we present a principled and systematic framework for sampling and generative modelling centred around divergences on path space. Our work culminates in the development of the…
Safe trajectory planning in complex environments must balance stringent collision avoidance with real-time efficiency, which is a long-standing challenge in robotics. In this work, we present a diffusion-based trajectory planning framework…
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…
We propose a new Monte Carlo method for efficiently sampling trajectories with fixed initial and final conditions in a system with discrete degrees of freedom. The method can be applied to any stochastic process with local interactions,…
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…
We introduce the use of the Zig-Zag sampler to the problem of sampling conditional diffusion processes (diffusion bridges). The Zig-Zag sampler is a rejection-free sampling scheme based on a non-reversible continuous piecewise deterministic…
We consider the task of generating discrete-time realisations of a nonlinear multivariate diffusion process satisfying an It\^o stochastic differential equation conditional on an observation taken at a fixed future time-point. Such…
In this work, we propose FastDPM, a unified framework for fast sampling in diffusion probabilistic models. FastDPM generalizes previous methods and gives rise to new algorithms with improved sample quality. We systematically investigate the…
We develop diffusion-based samplers for target distributions known up to a normalising constant. To this end, we rely on the well-known diffusion path that smoothly interpolates between a simple base distribution and the target, popularised…
The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to combine random walk on squares or rectangles methods with…
For one-dimensional Jump-Drift and Jump-Diffusion processes converging towards some steady state, the large deviations of a long dynamical trajectory are described from two perspectives. Firstly, the joint probability of the empirical…
The diffusion model has shown success in generating high-quality and diverse solutions to trajectory optimization problems. However, diffusion models with neural networks inevitably make prediction errors, which leads to constraint…
Sparse parametric models are of great interest in statistical learning and are often analyzed by means of regularized estimators. Pathwise methods allow to efficiently compute the full solution path for penalized estimators, for any…
The existing literature on stochastic simulation of chemical reaction networks has a tendency to move as quickly as possible to the abstract formulation of the stochastic dynamics in terms of probabilities based on the concept of the…