Related papers: From Snapshots to Trajectories: Learning Single-Ce…

We survey continuous-time generative modeling methods based on transporting a simple reference distribution to a data distribution via stochastic or deterministic dynamics. We present a unified framework in which diffusion models,…

Flow matching has recently emerged as a principled framework for learning continuous-time transport maps, enabling efficient ODE-based sampling without relying on stochastic diffusion processes. While generative modeling has shown promise…

We introduce Statistical Flow Matching (SFM), a novel and mathematically rigorous flow-matching framework on the manifold of parameterized probability measures inspired by the results from information geometry. We demonstrate the…

Strong semantic representations improve the convergence and generation quality of diffusion and flow models. Existing approaches largely rely on external models, which require separate training, operate on misaligned objectives, and exhibit…

Streamflow plays an essential role in the sustainable planning and management of national water resources. Traditional hydrologic modeling approaches simulate streamflow by establishing connections across multiple physical processes, such…

Straightening the probability flow of the continuous-time generative models, such as diffusion models or flow-based models, is the key to fast sampling through the numerical solvers, existing methods learn a linear path by directly…

Spatial transcriptomics (ST) enables spot-level in situ expression profiling, but its high cost and limited throughput motivate predicting expression directly from HE-stained histology. Recent advances explore using score- or flow-based…

Single-cell RNA sequencing (scRNA-seq) allows transcriptional profiling, and cell-type annotation of individual cells. However, sample preparation in typical scRNA-seq experiments often homogenizes the samples, thus spatial locations of…

Single-cell RNA-sequencing captures a temporal slice, or a snapshot, of a cell differentiation process. A major bioinformatical challenge is the inference of differentiation trajectories from a single snapshot, and methods that account for…

Computational modeling of single-cell gene expression is crucial for understanding cellular processes, but generating realistic expression profiles remains a major challenge. This difficulty arises from the count nature of gene expression…

Spatial transcriptomics (ST) has emerged as a powerful technology for bridging histology imaging with gene expression profiling. However, its application has been limited by low throughput and the need for specialized experimental…

Flow Matching (FM) is a simulation-free method for learning a continuous and invertible flow to interpolate between two distributions, and in particular to generate data from noise. Inspired by the variational nature of the diffusion…

Over the several recent years, there has been a boom in development of Flow Matching (FM) methods for generative modeling. One intriguing property pursued by the community is the ability to learn flows with straight trajectories which…

Single-cell RNA sequencing (scRNA-seq) is a fast growing approach to measure the genome-wide transcriptome of many individual cells in parallel, but results in noisy data with many dropout events. Existing methods to learn molecular…

Clustering analysis is fundamental in single-cell RNA sequencing (scRNA-seq) data analysis for elucidating cellular heterogeneity and diversity. Recent graph-based scRNA-seq clustering methods, particularly graph neural networks (GNNs),…

In recent years, the advances in single-cell RNA-seq techniques have enabled us to perform large-scale transcriptomic profiling at single-cell resolution in a high-throughput manner. Unsupervised learning such as data clustering has become…

In a previous paper [CSIAM Trans. Appl. Math. 2 (2021), 1-55], the authors proposed a theoretical framework for the analysis of RNA velocity, which is a promising concept in scRNA-seq data analysis to reveal the cell state-transition…

Single-cell RNA sequencing (scRNA-seq) data analysis is pivotal for understanding cellular heterogeneity. However, the high sparsity and complex noise patterns inherent in scRNA-seq data present significant challenges for traditional…

Comparisons of single-cell RNA sequencing (scRNA-seq) data across species can reveal links between cellular gene expression and the evolution of cell functions, features, and phenotypes. These comparisons invoke evolutionary histories, as…

Flow matching has recently emerged as a promising alternative to diffusion-based generative models, offering faster sampling and simpler training by learning continuous flows governed by ordinary differential equations. Despite growing…