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Markov jump processes are continuous-time stochastic processes which describe dynamical systems evolving in discrete state spaces. These processes find wide application in the natural sciences and machine learning, but their inference is…

Nanoscopic diffusion at surfaces normally takes place when an adsorbate jumps from one adsorption site to the other. Jump diffusion can be measured via quasi-elastic scattering experiments, and the results can often be interpreted in terms…

Diffusion models rely on a high-dimensional latent space of initial noise seeds, yet it remains unclear whether this space contains sufficient structure to predict properties of the generated samples, such as their classes. In this work, we…

Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…

Latent diffusion models offer an attractive alternative to discrete diffusion for non-autoregressive text generation by operating on continuous text representations and denoising entire sequences in parallel. The major challenge in latent…

This paper addresses the problem of distributed state estimation for discrete-time linear time-invariant systems. Building on the framework proposed in Gao & Yang (2025), we exploit the Jordan canonical form of the system matrix to develop…

We introduce a nonparametric model for inferring time-evolving, unobserved probability distributions from discrete-time data consisting of unlabelled partitions. The latent process is a two-parameter Poisson-Dirichlet diffusion, and…

In this paper, we propose a non-parametric method for state estimation of high-dimensional nonlinear stochastic dynamical systems, which evolve according to gradient flows with isotropic diffusion. We combine diffusion maps, a manifold…

This paper is the first part of a series of papers on filtering for partially observed jump diffusions satisfying a stochastic differential equation driven by Wiener processes and Poisson martingale measures. The coefficients of the…

Wireless channels in motion-rich urban microcell (UMi) settings are non-stationary; mobility and scatterer dynamics shift the distribution over time, degrading classical and deep estimators. This work proposes conditional prior diffusion…

News might trigger jump arrivals in financial time series. The "bad" and "good" news seems to have distinct impact. In the research, a double exponential jump distribution is applied to model downward and upward jumps. Bayesian double…

The growing sophistication of synthetic image and deepfake generation models has turned source attribution and authenticity verification into a critical challenge for modern computer vision systems. Recent studies suggest that diffusion…

In this paper, we address the problem of distributed state estimation for a discrete-time, linear time-invariant system. Building on the framework proposed in [2], we exploit the Jordan canonical form of the system matrix to develop a…

A continuously measured quantum system with multiple jump channels gives rise to a stochastic process described by random jump times and random emitted symbols, representing each jump channel. While much is known about the waiting time…

In recent years, diffusion based methods have emerged as a powerful paradigm for generative modeling. Although discrete diffusion for natural language processing has been explored to a lesser extent, it shows promise for tasks requiring…

We seek a computationally efficient model for a collection of time series arising from multiple interacting entities (a.k.a. "agents"). Recent models of temporal patterns across individuals fail to incorporate explicit system-level…

The behaviour of many real-world phenomena can be modelled by nonlinear dynamical systems whereby a latent system state is observed through a filter. We are interested in interacting subsystems of this form, which we model by a set of…

We evaluate the significance of a recently proposed bivariate jump-diffusion model for a data-driven characterization of interactions between complex dynamical systems. For various coupled and non-coupled jump-diffusion processes, we find…

Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they…

Deep learning (DL)-based Semantic Communications (SemCom) is becoming critical to maximize overall efficiency of communication networks. Nevertheless, SemCom is sensitive to wireless channel uncertainties, source outliers, and suffer from…