Related papers: One-step data-driven generative model via Schr\"od…
Stochastic bridges are commonly used to impute missing data with a lower sampling rate to generate data with a higher sampling rate, while preserving key properties of the dynamics involved in an unbiased way. While the generation of…
Diffusion models have emerged as powerful generative tools, rivaling GANs in sample quality and mirroring the likelihood scores of autoregressive models. A subset of these models, exemplified by DDIMs, exhibit an inherent asymmetry: they…
This work introduces a novel nonlinear optimal filtering method, termed the Ensemble Schr{\"o}dinger Bridge nonlinear filter. The proposed filter combines the standard prediction step with a diffusion-generative-modeling-based analysis…
In this work, we revisit the discrete-time Schr\"{o}dinger Bridge (SB) and Density Steering (DS) problems for Gaussian mixture model (GMM) boundary distributions. Building on the existing literature, we construct a set of feasible Markovian…
Bridge models in image restoration construct a diffusion process from degraded to clear images. However, existing methods typically require training a bridge model from scratch for each specific type of degradation, resulting in high…
A new approach of obtaining stratified random samples from statistically dependent random variables is described. The proposed method can be used to obtain samples from the input space of a computer forward model in estimating expectations…
Time series generation is widely used in real-world applications such as simulation, data augmentation, and hypothesis testing. Recently, diffusion models have emerged as the de facto approach to time series generation, enabling diverse…
Diffusions are a fundamental class of models in many fields, including finance, engineering, and biology. Simulating diffusions is challenging as their sample paths are infinite-dimensional and their transition functions are typically…
Discrete diffusion models are a class of generative models that produce samples from an approximated data distribution within a discrete state space. Often, there is a need to target specific regions of the data distribution. Current…
Modeling the dynamics from sparsely time-resolved snapshot data is crucial for understanding complex cellular processes and behavior. Existing methods leverage optimal transport, Schr\"odinger bridge theory, or their variants to…
We propose the characteristic generator, a novel one-step generative model that combines the efficiency of sampling in Generative Adversarial Networks (GANs) with the stable performance of flow-based models. Our model is driven by…
Geophysical inverse problems are often ill-posed and admit multiple solutions. Conventional discriminative methods typically yield a single deterministic solution, which fails to model the posterior distribution, cannot generate diverse…
This paper introduces a new approach to generating sample paths of unknown Markovian stochastic differential equations (SDEs) using diffusion models, a class of generative AI methods commonly employed in image and video applications. Unlike…
The advance of diffusion-based generative models in recent years has revolutionized state-of-the-art (SOTA) techniques in a wide variety of image analysis and synthesis tasks, whereas their adaptation on image restoration, particularly…
Score-based generative models (SGMs) have recently emerged as a promising class of generative models. However, a fundamental limitation is that their inference is very slow due to a need for many (e.g., 2000) iterations of sequential…
Stochastic flows of an advective-diffusive nature are ubiquitous in physical sciences. Of particular interest is the problem to reconcile observed marginal distributions with a given prior posed by E. Schrodinger in 1932/32 and known as the…
Despite their ability to generate high-resolution and diverse images from text prompts, text-to-image diffusion models often suffer from slow iterative sampling processes. Model distillation is one of the most effective directions to…
Motivation: Single-cell RNA sequencing (scRNA-seq) is a groundbreaking technology extensively utilized in biological research, facilitating the examination of gene expression at the individual cell level within a given tissue sample. While…
We propose DiffSep, a new single channel source separation method based on score-matching of a stochastic differential equation (SDE). We craft a tailored continuous time diffusion-mixing process starting from the separated sources and…
Graph generative models have broad applications in biology, chemistry and social science. However, modelling and understanding the generative process of graphs is challenging due to the discrete and high-dimensional nature of graphs, as…