Related papers: Affine forward variance models
Diffusion models have emerged as one of the most promising frameworks for deep generative modeling. In this work, we explore the potential of non-uniform diffusion models. We show that non-uniform diffusion leads to multi-scale diffusion…
In this article we consider affine generalizations of the Merton jump diffusion model [Merton, J. Fin. Econ., 1976] and the respective pricing of European options. On the one hand, the Brownian motion part in the Merton model may be…
Variational Autoencoders (VAEs) are powerful generative models widely used for learning interpretable latent spaces, quantifying uncertainty, and compressing data for downstream generative tasks. VAEs typically rely on diagonal Gaussian…
We obtain a first order extension of the large deviation estimates in the G\"{a}rtner-Ellis theorem. In addition, for a given family of measures, we find a special family of functions having a similar Laplace principle expansion up to order…
Sampling from high-dimensional, multi-modal distributions remains a fundamental challenge across domains such as statistical Bayesian inference and physics-based machine learning. In this paper, we propose Annealing Flow (AF), a method…
Rectified flow and reflow procedures have significantly advanced fast generation by progressively straightening ordinary differential equation (ODE) flows. They operate under the assumption that image and noise pairs, known as couplings,…
Flow matching models have emerged as a powerful framework for realistic image generation by learning to reverse a corruption process that progressively adds Gaussian noise. However, because noise is injected in the latent domain, its impact…
Diffusion models have revolutionized generative tasks through high-fidelity outputs, yet flow matching (FM) offers faster inference and empirical performance gains. However, current foundation FM models are computationally prohibitive for…
Normalizing Flows (NFs) are a class of generative models distinguished by a mathematically invertible architecture, where the forward pass transforms data into a latent space for density estimation, and the reverse pass generates new…
Over the past few years quadratic Backward Stochastic Differential Equations (BSDEs) have been a popular field of research. However there are only very few examples where explicit solutions for these equations are known. In this paper we…
We investigate the compilation of general multilinear variational forms over affines simplices and prove a representation theorem for the representation of the element tensor (element stiffness matrix) as the contraction of a constant…
In this paper we demonstrate a new technique for deriving discrete adjoint and tangent linear models of finite element models. The technique is significantly more efficient and automatic than standard algorithmic differentiation techniques.…
Normalizing flows are among the most popular paradigms in generative modeling, especially for images, primarily because we can efficiently evaluate the likelihood of a data point. This is desirable both for evaluating the fit of a model,…
A latent force model is a Gaussian process with a covariance function inspired by a differential operator. Such covariance function is obtained by performing convolution integrals between Green's functions associated to the differential…
We propose a principled and effective framework for one-step generative modeling. We introduce the notion of average velocity to characterize flow fields, in contrast to instantaneous velocity modeled by Flow Matching methods. A…
We introduce a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale. Specifically, we present the notion of Flow Matching (FM), a simulation-free approach for…
Generative modelling has seen significant advances through simulation-free paradigms such as Flow Matching, and in particular, the MeanFlow framework, which replaces instantaneous velocity fields with average velocities to enable efficient…
We introduce a harmonic analysis for a class of affine iteration models in $\br^d$. Using Hilbert-space geometry, we develop a new duality notion for affine and contractive iterated function systems (IFSs) and we construct some identities…
Inside the discipline of graph theory exists an extension known as the hypergraph. This generalization of graphs includes vertices along with hyperedges consisting of collections of two or more vertices. One well-studied application of this…
We consider stochastic (partial) differential equations appearing as Markovian lifts of affine Volterra processes with jumps from the point of view of the generalized Feller property which was introduced in e.g.~\cite{doetei:10}. In…