Related papers: Telegrapher's Generative Model via Kac Flows

In this work, we propose a novel generative learning paradigm, K-Flow, an algorithm that flows along the $K$-amplitude. Here, $k$ is a scaling parameter that organizes frequency bands (or projected coefficients), and amplitude describes the…

Consider $n$ independent Goldstein-Kac telegraph processes $X_1(t), \dots ,X_n(t), \; n\ge 2, \; t\ge 0,$ on the real line $\Bbb R$. Each the process $X_k(t), \; k=1,\dots,n,$ describes a stochastic motion at constant finite speed $c_k>0$…

Diffusion-based generative models have achieved remarkable performance across various domains, yet their practical deployment is often limited by high sampling costs. While prior work focuses on training objectives or individual solvers,…

Many scientific systems, such as cellular populations or economic cohorts, are naturally described by probability distributions that evolve over time. Predicting how such a system would have evolved under different forces or initial…

The blooming diffusion probabilistic models (DPMs) have garnered significant interest due to their impressive performance and the elegant inspiration they draw from physics. While earlier DPMs relied upon the Markovian assumption, recent…

Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…

The default Gaussian latent in flow-based generative models poses challenges when learning certain distributions such as heavy-tailed ones. We introduce a general framework for learning data-adaptive latent distributions using…

In the current work we construct a multimolecule random process which leads to the Boltzmann equation in the appropriate limit, and which is different from the deterministic real gas dynamics process. We approximate the statistical…

Despite the remarkable empirical success of generative models, the available theory on their statistical accuracy in scientific computing remains largely pessimistic. This paper develops a theoretical framework for understanding the…

By building upon the recent theory that established the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algorithm for learning the underlying distributions of…

We study a variant of the dynamical optimal transport problem in which the energy to be minimised is modulated by the covariance matrix of the distribution. Such transport metrics arise naturally in mean-field limits of certain ensemble…

We reveal a precise mathematical framework about a new family of generative models which we call Gradient Flow Drifting. With this framework, we prove an equivalence between the recently proposed Drifting Model and the Wasserstein gradient…

Reconstructing near-wall turbulence from wall-based measurements is a critical yet inherently ill-posed problem in wall-bounded flows, where limited sensing and spatially heterogeneous flow-wall coupling challenge deterministic estimation…

This paper provides an elementary, self-contained analysis of diffusion-based sampling methods for generative modeling. In contrast to existing approaches that rely on continuous-time processes and then discretize, our treatment works…

We study the problem of estimating a sequence of evolving probability distributions from historical data, where the underlying distribution changes over time in a nonstationary and nonparametric manner. To capture gradual changes, we…

Many generative models synthesize data by transforming a standard Gaussian random variable using a deterministic neural network. Among these models are the Variational Autoencoders and the Generative Adversarial Networks. In this work, we…

We study the existence of the stochastic flow associated to a linear stochastic evolution equation $$d X= AX\,d t +\sum_{k} B_k X\,d W_k, $$ on a Hilbert space. Our first result covers the case where $A$ is the generator of a…

Continuous Normalizing Flows (CNFs) enable elegant generative modeling but remain bottlenecked by slow sampling: producing a single sample requires solving a nonlinear ODE with hundreds of function evaluations. Recent approaches such as…

In this paper, we investigate the training process of generative networks that use a type of probability density distance named particle-based distance as the objective function, e.g. MMD GAN, Cram\'er GAN, EIEG GAN. However, these GANs…

We consider the discretization of a semilinear damped wave equation arising, for instance, in the modeling of gas transport in pipeline networks. For time invariant boundary data, the solutions of the problem are shown to converge…