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Dynamical generative models that produce samples through an iterative process, such as Flow Matching and denoising diffusion models, have seen widespread use, but there have not been many theoretically-sound methods for improving these…
Recent advances in generative artificial intelligence have enabled the creation of high-quality synthetic data that closely mimics real-world data. This paper explores the adaptation of the Stable Diffusion 2.0 model for generating…
We consider here probabilistic models of transportation flows. The main goal of this introduction is rather not to present various techniques for problem solving but to present some intuition to invent adequate and natural models having…
A practical introduction to stochastic modelling of reaction-diffusion processes is presented. No prior knowledge of stochastic simulations is assumed. The methods are explained using illustrative examples. The article starts with the…
Normalizing flows, diffusion normalizing flows and variational autoencoders are powerful generative models. This chapter provides a unified framework to handle these approaches via Markov chains. We consider stochastic normalizing flows as…
Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a…
Despite Flow Matching and diffusion models having emerged as powerful generative paradigms for continuous variables such as images and videos, their application to high-dimensional discrete data, such as language, is still limited. In this…
Normalizing flows provide a general mechanism for defining expressive probability distributions, only requiring the specification of a (usually simple) base distribution and a series of bijective transformations. There has been much recent…
Modeling dynamical systems and unraveling their underlying causal relationships is central to many domains in the natural sciences. Various physical systems, such as those arising in cell biology, are inherently high-dimensional and…
Diffusion models have recently attained significant interest within the community owing to their strong performance as generative models. Furthermore, its application to inverse problems have demonstrated state-of-the-art performance.…
Deep generative models have made rapid progress in image, text, audio, and video generation, and are increasingly being applied to structured records. For tabular data, however, generative modeling remains difficult: a dataset may contain…
We present a method for enhanced sampling of molecular dynamics simulations using stochastic resetting. Various phenomena, ranging from crystal nucleation to protein folding, occur on timescales that are unreachable in standard simulations.…
In many scientific applications, the target probability distribution cannot be evaluated in closed form or sampled from directly. Instead, it can often be decomposed into multiple components, some of which are accessible only through…
Predicting the distribution of future states in a stochastic system, known as belief propagation, is fundamental to reasoning under uncertainty. However, nonlinear dynamics often make analytical belief propagation intractable, requiring…
Training a generative model with limited number of samples is a challenging task. Current methods primarily rely on few-shot model adaption to train the network. However, in scenarios where data is extremely limited (less than 10), the…
Guidance is a cornerstone of modern diffusion models, playing a pivotal role in conditional generation and enhancing the quality of unconditional samples. However, current approaches to guidance scheduling--determining the appropriate…
Sampling from unnormalized densities is analogous to the generative modeling problem, but the target distribution is defined by a known energy function instead of data samples. Because evaluating the energy function is often costly, a…
Mainstream flow matching methods typically focus on learning the local velocity field, which inherently requires multiple integration steps during generation. In contrast, Mean Velocity Flow models establish a relationship between the local…
In this study, we introduce a novel method for generating new synthetic samples that are independent and identically distributed (i.i.d.) from high-dimensional real-valued probability distributions, as defined implicitly by a set of Ground…
Generative foundation models like Stable Diffusion comprise a diverse spectrum of knowledge in computer vision with the potential for transfer learning, e.g., via generating data to train student models for downstream tasks. This could…