Related papers: Parameter Inference via Differentiable Diffusion B…

Diffusion-based generative models have achieved promising results recently, but raise an array of open questions in terms of conceptual understanding, theoretical analysis, algorithm improvement and extensions to discrete, structured,…

Dynamical behaviors of complex interacting systems, including brain activities, financial price movements, and physical collective phenomena, are associated with underlying interactions between the system's components. The issue of…

Analyzing time series in the frequency domain enables the development of powerful tools for investigating the second-order characteristics of multivariate processes. Parameters like the spectral density matrix and its inverse, the coherence…

In recent years, diffusion models, and more generally score-based deep generative models, have achieved remarkable success in various applications, including image and audio generation. In this paper, we view diffusion models as an implicit…

We consider a lognormal diffusion process having a multisigmoidal logistic mean, useful to model the evolution of a population which reaches the maximum level of the growth after many stages. Referring to the problem of statistical…

This paper presents a parameter scan technique for BSM signal models based on normalizing flow. Normalizing flow is a type of deep learning model that transforms a simple probability distribution into a complex probability distribution as…

Diffusion Bridge and Flow Matching have both demonstrated compelling empirical performance in transformation between arbitrary distributions. However, there remains confusion about which approach is generally preferable, and the substantial…

Inference of the network structure (e.g., routing topology) and dynamics (e.g., link performance) is an essential component in many network design and management tasks. In this paper we propose a new, general framework for analyzing and…

This tutorial provides an in-depth guide on inference-time guidance and alignment methods for optimizing downstream reward functions in diffusion models. While diffusion models are renowned for their generative modeling capabilities,…

We consider the problem of statistical inference for a class of partially-observed diffusion processes, with discretely-observed data and finite-dimensional parameters. We construct unbiased estimators of the score function, i.e. the…

Interpreting data with mathematical models is an important aspect of real-world industrial and applied mathematical modeling. Often we are interested to understand the extent to which a particular set of data informs and constrains model…

Diffusion models (DMs) have become the dominant paradigm of generative modeling in a variety of domains by learning stochastic processes from noise to data. Recently, diffusion denoising bridge models (DDBMs), a new formulation of…

Parameter estimation in diffusion processes from discrete observations up to a first-hitting time is clearly of practical relevance, but does not seem to have been studied so far. In neuroscience, many models for the membrane potential…

Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…

Dynamical modelling lies at the heart of our understanding of physical systems. Its role in science is deeper than mere operational forecasting, in that it allows us to evaluate the adequacy of the mathematical structure of our models.…

Pathogen genome data offers valuable structure for spatial models, but its utility is limited by incomplete sequencing coverage. We propose a probabilistic framework for inferring genetic distances between unsequenced cases and known…

Ordinary differential equation models have become a standard tool for the mechanistic description of biochemical processes. If parameters are inferred from experimental data, such mechanistic models can provide accurate predictions about…

Cognitive processes undergo various fluctuations and transient states across different temporal scales. Superstatistics are emerging as a flexible framework for incorporating such non-stationary dynamics into existing cognitive model…

Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…

We propose a new algorithm for learning bridged diffusion processes using score-matching methods. Our method relies on reversing the dynamics of the forward process and using this to learn a score function, which, via Doob's $h$-transform,…