Related papers: Using Ornstein-Uhlenbeck Process to understand Den…
Due to the dynamics of underlying physics and external influences, the uncertainty of time series often varies over time. However, existing Denoising Diffusion Probabilistic Models (DDPMs) often fail to capture this non-stationary nature,…
ODE solvers with randomly sampled timestep sizes appear in the context of chaotic dynamical systems, differential equations with low regularity, and, implicitly, in stochastic optimisation. In this work, we propose and study the stochastic…
Score-based diffusion methods provide a powerful strategy to solve image restoration tasks by flexibly combining a pre-trained foundational prior model with a likelihood function specified during test time. Such methods are predominantly…
To investigate the complex dynamics of a biological neuron that is subject to small random perturbations we can use stochastic neuron models. While many techniques have already been developed to study properties of such models, especially…
The paper considers the problem of robust estimating a periodic function in a continuous time regression model with dependent disturbances given by a general square integrable semimartingale with unknown distribution. An example of such a…
We provide the first polynomial-time convergence guarantees for the probability flow ODE implementation (together with a corrector step) of score-based generative modeling. Our analysis is carried out in the wake of recent results obtaining…
Diffusion probabilistic models (DPMs) and their extensions have emerged as competitive generative models yet confront challenges of efficient sampling. We propose a new bilateral denoising diffusion model (BDDM) that parameterizes both the…
Many processes, such as discrete event systems in engineering or population dynamics in biology, evolve in discrete space and continuous time. We consider the problem of optimal decision making in such discrete state and action space…
Generative AI has received significant attention among a spectrum of diverse industrial and academic domains, thanks to the magnificent results achieved from deep generative models such as generative pre-trained transformers (GPT) and…
Generative models for quantum data pose significant challenges but hold immense potential in fields such as chemoinformatics and quantum physics. Quantum denoising diffusion probabilistic models (QuDDPMs) enable efficient learning of…
The Ornstein-Uhlenbeck (OU) process, a mean-reverting stochastic process, has been widely applied as a time series model in various domains. This paper describes the design and implementation of a model-based synthetic time series model…
We propose Riemannian Denoising Diffusion Probabilistic Models (RDDPMs) for learning distributions on submanifolds of Euclidean space that are level sets of functions, including most of the manifolds relevant to applications. Existing…
We consider the discrete-time filtering problem in scenarios where the observation noise is low or degenerate. We focus on the case where the observation equation is a linear function of the state and the data involve additive noise.…
Standard Ornstein-Uhlenbeck (OU) models often yield biased parameter estimates when measurement error is ignored. While the Ornstein-Uhlenbeck State Space Model (OUSSM) addresses this in univariate settings, multidimensional extensions…
We derive the Markov-modulated generalized Ornstein-Uhlenbeck process by embedding a Markov-modulated random recurrence equation in continuous time. The obtained process turns out to be the unique solution of a certain stochastic…
Diffusion Probabilistic Models (DPMs) have demonstrated exceptional capability of generating high-quality and diverse images, but their practical application is hindered by the intensive computational cost during inference. The DPM…
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…
Masked diffusion models (MDMs) have recently emerged as a novel framework for language modeling. MDMs generate sentences by iteratively denoising masked sequences, filling in [MASK] tokens step by step. Although MDMs support any-order…
Distributional properties -including Laplace transforms- of integrals of Markov processes received a lot of attention in the literature. In this paper, we complete existing results in several ways. First, we provide the analytical solution…
Dissipative Particle Dynamics (DPD) is a popular simulation model for investigating hydrodynamic behavior of systems with non-negligible equilibrium thermal fluctuations. DPD employs soft core repulsive interactions between the system…