Related papers: Normalizing Flows on Quotient Manifolds via Bounda…

Normalizing Flows (NFs) are emerging as a powerful class of generative models, as they not only allow for efficient sampling, but also deliver, by construction, density estimation. They are of great potential usage in High Energy Physics…

We propose Riemannian Flow Matching (RFM), a simple yet powerful framework for training continuous normalizing flows on manifolds. Existing methods for generative modeling on manifolds either require expensive simulation, are inherently…

The aim of this paper is to provide a mathematical analysis of transformer architectures using a self-attention mechanism with layer normalization. In particular, observed patterns in such architectures resembling either clusters or uniform…

Estimating normals for noisy point clouds is a persistent challenge in 3D geometry processing, particularly for end-to-end oriented normal estimation. Existing methods generally address relatively clean data and rely on supervised priors to…

Manifold learning flows are a class of generative modelling techniques that assume a low-dimensional manifold description of the data. The embedding of such a manifold into the high-dimensional space of the data is achieved via learnable…

Normalizing flow is a generative modeling approach with efficient sampling. However, Flow-based models suffer two issues: 1) If the target distribution is manifold, due to the unmatch between the dimensions of the latent target distribution…

Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies…

We propose an algorithm for learning a conditional generative model of a molecule given a target. Specifically, given a receptor molecule that one wishes to bind to, the conditional model generates candidate ligand molecules that may bind…

We consider fixed boundary flow with canonical interpretability as principal components extended on non-linear Riemannian manifolds. We aim to find a flow with fixed starting and ending points for noisy multivariate data sets lying on an…

We introduce in this paper new and very effective numerical methods based on neural networks for the approximation of the mean curvature flow of either oriented or non-orientable surfaces. To learn the correct interface evolution law, our…

We develop a theory of surfaces with boundary moving by mean curvature flow. In particular, we prove a general existence theorem by elliptic regularization, and we prove boundary regularity at all positive times under very mild hypotheses.

We introduce Random Projection Flows (RPFs), a principled framework for injective normalizing flows that leverages tools from random matrix theory and the geometry of random projections. RPFs employ random semi-orthogonal matrices, drawn…

Normalizing flow (NF) has gained popularity over traditional maximum likelihood based methods due to its strong capability to model complex data distributions. However, the standard approach, which maps the observed data to a normal…

A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent)…

We reinterpret multiplicative noise in neural networks as auxiliary random variables that augment the approximate posterior in a variational setting for Bayesian neural networks. We show that through this interpretation it is both efficient…

This paper introduces a generative model equivariant to Euclidean symmetries: E(n) Equivariant Normalizing Flows (E-NFs). To construct E-NFs, we take the discriminative E(n) graph neural networks and integrate them as a differential…

We present a framework for modeling complex, high-dimensional distributions on convex polytopes by leveraging recent advances in discrete and continuous normalizing flows on Riemannian manifolds. We show that any full-dimensional polytope…

A machine learning method to predict steady external fluid flows using elliptic input features is introduced. Using data from as few as one high-fidelity simulation, the proposed method produces models generalizable under changes to…

Quantization lowers memory usage, computational requirements, and latency by utilizing fewer bits to represent model weights and activations. In this work, we investigate the generalization properties of quantized neural networks, a…

Flow-based generative models are composed of invertible transformations between two random variables of the same dimension. Therefore, flow-based models cannot be adequately trained if the dimension of the data distribution does not match…