Related papers: Spread Flows for Manifold Modelling

Learning mappings of data on manifolds is an important topic in contemporary machine learning, with applications in astrophysics, geophysics, statistical physics, medical diagnosis, biochemistry, 3D object analysis. This paper studies the…

Flow Matching has recently gained attention in generative modeling as a simple and flexible alternative to diffusion models. While existing statistical guarantees adapt tools from the analysis of diffusion models, we take a different…

We introduce a novel generative model for the representation of joint probability distributions of a possibly large number of discrete random variables. The approach uses measure transport by randomized assignment flows on the statistical…

To model manifold data using normalizing flows, we employ isometric autoencoders to design embeddings with explicit inverses that do not distort the probability distribution. Using isometries separates manifold learning and density…

Statistical models are an essential tool to model, forecast and understand the hydrological processes in watersheds. In particular, the understanding of time lags associated with the delay between rainfall occurrence and subsequent changes…

The latent space of diffusion model mostly still remains unexplored, despite its great success and potential in the field of generative modeling. In fact, the latent space of existing diffusion models are entangled, with a distorted mapping…

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…

We derive a deterministic, non-asymptotic upper bound on the Kullback-Leibler (KL) divergence of the flow-matching distribution approximation. In particular, if the $L_2$ flow-matching loss is bounded by $\epsilon^2 > 0$, then the KL…

Longitudinal Dispersion(LD) is the dominant process of scalar transport in natural streams. An accurate prediction on LD coefficient(Dl) can produce a performance leap in related simulation. The emerging machine learning(ML) techniques…

A common belief in high-dimensional data analysis is that data are concentrated on a low-dimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide an algorithm for learning gradients on…

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…

Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step…

Generative models that can model and predict sequences of future events can, in principle, learn to capture complex real-world phenomena, such as physical interactions. However, a central challenge in video prediction is that the future is…

In this work we explore the advantages of end-to-end learning of multilayer maps offered by feed forward neural-networks (FFNN) for learning and predicting dynamics from transient fluid flow data.While machine learning in general depends on…

In autonomous driving scenarios, the collected LiDAR point clouds can be challenged by occlusion and long-range sparsity, limiting the perception of autonomous driving systems. Scene completion methods can infer the missing parts of…

Drawing motivation from the manifold hypothesis, which posits that most high-dimensional data lies on or near low-dimensional manifolds, we apply manifold learning to the space of neural networks. We learn manifolds where datapoints are…

Formal verification has emerged as a promising method to ensure the safety and reliability of neural networks. However, many relevant properties, such as fairness or global robustness, pertain to the entire input space. If one applies…

Recent advances in diffusion and flow matching models have highlighted a shift in the preferred prediction target -- moving from noise ($\varepsilon$) and velocity (v) to direct data (x) prediction -- particularly in high-dimensional…

In this manuscript, we consider the problem of learning a flow or diffusion-based generative model parametrized by a two-layer auto-encoder, trained with online stochastic gradient descent, on a high-dimensional target density with an…

Transformer models have consistently achieved remarkable results in various domains such as natural language processing and computer vision. However, despite ongoing research efforts to better understand these models, the field still lacks…