Related papers: Simple, Fast and Efficient Injective Manifold Dens…

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…

Leveraging representation encoders for generative modeling offers a path for efficient, high-fidelity synthesis. However, standard diffusion transformers fail to converge on these representations directly. While recent work attributes this…

Recently, studies on machine learning have focused on methods that use symmetry implicit in a specific manifold as an inductive bias. Grassmann manifolds provide the ability to handle fundamental shapes represented as shape spaces, enabling…

Random Projection is a foundational research topic that connects a bunch of machine learning algorithms under a similar mathematical basis. It is used to reduce the dimensionality of the dataset by projecting the data points efficiently to…

Many areas in science and engineering now have access to technologies that enable the rapid collection of overwhelming data volumes. While these datasets are vital for understanding phenomena from physical to biological and social systems,…

Likelihood-based deep generative models have been widely investigated for Image Anomaly Detection (IAD), particularly Normalizing Flows, yet their strict architectural invertibility needs often constrain scalability, particularly in…

Recent advances suggest that encoding images through Symmetric Positive Definite (SPD) matrices and then interpreting such matrices as points on Riemannian manifolds can lead to increased classification performance. Taking into account…

Normalizing flows model probability distributions through an expressive tractable density. They transform a simple base distribution, such as a Gaussian, through a sequence of invertible functions, which are referred to as layers. These…

Object pose estimation is a fundamental problem in computer vision and plays a critical role in virtual reality and embodied intelligence, where agents must understand and interact with objects in 3D space. Recently, score based generative…

Randomized orthogonal projection methods (ROPMs) can be used to speed up the computation of Krylov subspace methods in various contexts. Through a theoretical and numerical investigation, we establish that these methods produce…

Kernel methods represent one of the most powerful tools in machine learning to tackle problems expressed in terms of function values and derivatives due to their capability to represent and model complex relations. While these methods show…

Current density modeling approaches suffer from at least one of the following shortcomings: expensive training, slow inference, approximate likelihood, mode collapse or architectural constraints like bijective mappings. We propose a simple…

Flow Matching (FM) is a recent generative modelling technique: we aim to learn how to sample from distribution $\mathfrak{X}_1$ by flowing samples from some distribution $\mathfrak{X}_0$ that is easy to sample from. The key trick is that…

Normalizing flows model a complex target distribution in terms of a bijective transform operating on a simple base distribution. As such, they enable tractable computation of a number of important statistical quantities, particularly…

Normalizing Flows (NFs) are able to model complicated distributions p(y) with strong inter-dimensional correlations and high multimodality by transforming a simple base density p(z) through an invertible neural network under the change of…

Probabilistic power flow (PPF) is essential for quantifying operational uncertainty in modern distribution systems with high penetration of renewable generation and flexible loads. Conventional PPF methods primarily rely on Monte Carlo (MC)…

We present Riemannian Gaussian Variational Flow Matching (RG-VFM), a geometric extension of Variational Flow Matching (VFM) for generative modeling on manifolds. Motivated by the benefits of VFM, we derive a variational flow matching…

Interesting data often concentrate on low dimensional smooth manifolds inside a high dimensional ambient space. Random projections are a simple, powerful tool for dimensionality reduction of such data. Previous works have studied bounds on…

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…

Bayesian inference with computationally expensive likelihood evaluations remains a significant challenge in many scientific domains. We propose normalizing flow regression (NFR), a novel offline inference method for approximating posterior…