Related papers: On residual and guided proposals for diffusion bri…

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…

We propose the Bayesian bridge estimator for regularized regression and classification. Two key mixture representations for the Bayesian bridge model are developed: (1) a scale mixture of normals with respect to an alpha-stable random…

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…

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…

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…

Time series generation is widely used in real-world applications such as simulation, data augmentation, and hypothesis testing. Recently, diffusion models have emerged as the de facto approach to time series generation, enabling diverse…

Stochastically evolving geometric systems are studied in shape analysis and computational anatomy for modelling random evolutions of human organ shapes. The notion of geodesic paths between shapes is central to shape analysis and has a…

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…

Microstructure reconstruction, a major component of inverse computational materials engineering, is currently advancing at an unprecedented rate. While various training-based and training-free approaches are developed, the majority of…

In this article we consider the estimation of static parameters for partially observed diffusion processes with discrete-time observations over a fixed time interval. In particular, when one only has access to time-discretized solutions of…

Simulating the conditioned dynamics of diffusion processes, given their initial and terminal states, is an important but challenging problem in the sciences. The difficulty is particularly pronounced for rare events, for which the…

We present a method to downscale idealized geophysical fluid simulations using generative models based on diffusion maps. By analyzing the Fourier spectra of images drawn from different data distributions, we show how one can chain together…

Diffusion models, known for their strong generative capability derived from iterative noising and denoising processes, have recently emerged as a promising paradigm for sequential recommendation. To incorporate user history for…

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…

We revisit the work of Mitter and Newton on an information-theoretic interpretation of Bayes' formula through the Gibbs variational principle. This formulation allowed them to pose nonlinear estimation for diffusion processes as a problem…

We propose a novel method for simulating conditioned diffusion processes (diffusion bridges) in Euclidean spaces. By training a neural network to approximate bridge dynamics, our approach eliminates the need for computationally intensive…

Diffusion models have risen as a promising approach to data-driven planning, and have demonstrated impressive robotic control, reinforcement learning, and video planning performance. Given an effective planner, an important question to…

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…

We present a scheme for simulating conditioned semimartingales taking values in Riemannian manifolds. Extending the guided bridge proposal approach used for simulating Euclidean bridges, the scheme replaces the drift of the conditioned…

Diffusion bridge models have recently become a powerful tool in the field of generative modeling. In this work, we leverage their power to address another important problem in machine learning and information theory, the estimation of the…