Related papers: Generative Modeling with Orbit-Space Particle Flow…

Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…

Reconstructing PDE solutions from sparse observations is a core challenge in scientific computing. We present FM4PDE, a flow-matching generative framework that learns the joint distribution of PDE coefficients (or initial states) and…

Porous and heterogeneous materials are found in many applications from composites, membranes, chemical reactors, and other engineered materials to biological matter and natural subsurface structures. In this work we propose an integrated…

Particle flow (PFL) is an effective method for overcoming particle degeneracy, the main limitation of particle filtering. In PFL, particles are migrated towards regions of high likelihood based on the solution of a partial differential…

This letter presents a continuous probabilistic modeling methodology for spatial point cloud data using finite Gaussian Mixture Models (GMMs) where the number of components are adapted based on the scene complexity. Few hierarchical and…

We present GOFMM (geometry-oblivious FMM), a novel method that creates a hierarchical low-rank approximation, "compression," of an arbitrary dense symmetric positive definite (SPD) matrix. For many applications, GOFMM enables an approximate…

Gaussian processes (GPs) are instrumental in modeling spatial processes, offering precise interpolation and prediction capabilities across fields such as environmental science and biology. Recently, there has been growing interest in…

Conventional image motion based structure from motion methods first compute optical flow, then solve for the 3D motion parameters based on the epipolar constraint, and finally recover the 3D geometry of the scene. However, errors in optical…

Conventional methods of 3D object generative modeling learn volumetric predictions using deep networks with 3D convolutional operations, which are direct analogies to classical 2D ones. However, these methods are computationally wasteful in…

Despite recent advances, estimating optical flow remains a challenging problem in the presence of illumination change, large occlusions or fast movement. In this paper, we propose a novel optical flow estimation framework which can provide…

The ability to compare two degenerate probability distributions (i.e. two probability distributions supported on two distinct low-dimensional manifolds living in a much higher-dimensional space) is a crucial problem arising in the…

Score-based generative models, which transform noise into data by learning to reverse a diffusion process, have become a cornerstone of modern generative AI. This paper contributes to establishing theoretical guarantees for the probability…

Diffusion models are promising for joint trajectory prediction and controllable generation in autonomous driving, but they face challenges of inefficient inference steps and high computational demands. To tackle these challenges, we…

With the discovery of Wasserstein GANs, Optimal Transport (OT) has become a powerful tool for large-scale generative modeling tasks. In these tasks, OT cost is typically used as the loss for training GANs. In contrast to this approach, we…

This paper addresses the practical challenge in Entropic Optimal Transport (EOT) where the underlying ground cost function is typically latent and unobserved. Rather than assuming a fixed geometric cost, we adopt a data-driven approach…

We study how to generate molecule conformations (i.e., 3D structures) from a molecular graph. Traditional methods, such as molecular dynamics, sample conformations via computationally expensive simulations. Recently, machine learning…

We investigate properties of the particle distribution near the tip of one-dimensional branching random walks at large times $t$, focusing on unusual realizations in which the rightmost lead particle is very far ahead of its expected…

Diffusion-based generative models have reformed generative AI, and also enabled new capabilities in the science domain, e.g., fast generation of 3D structures of molecules. In such tasks, there is often a symmetry in the system, identifying…

Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied…

Optimal transport (OT) provides powerful tools for comparing probability measures in various types. The Wasserstein distance which arises naturally from the idea of OT is widely used in many machine learning applications. Unfortunately,…