Related papers: Trajectory Inference with Smooth Schr\"odinger Bri…
The dynamic Schr\"odinger bridge problem provides an appealing setting for solving constrained time-series data generation tasks posed as optimal transport problems. It consists of learning non-linear diffusion processes using efficient…
Practitioners often aim to infer an unobserved population trajectory using sample snapshots at multiple time points. E.g., given single-cell sequencing data, scientists would like to learn how gene expression changes over a cell's life…
Consider a reference Markov process with initial distribution $\pi_{0}$ and transition kernels $\{M_{t}\}_{t\in[1:T]}$, for some $T\in\mathbb{N}$. Assume that you are given distribution $\pi_{T}$, which is not equal to the marginal…
Score-based generative models have recently attracted significant attention for their ability to generate high-fidelity data by learning maps from simple Gaussian priors to complex data distributions. A natural generalization of this idea…
Despite the recent advances in the field of computational Schr\"odinger Bridges (SB), most existing SB solvers are still heavy-weighted and require complex optimization of several neural networks. It turns out that there is no principal…
We consider the Schr\"odinger bridge problem which, given ensemble measurements of the initial and final configurations of a stochastic dynamical system and some prior knowledge on the dynamics, aims to reconstruct the "most likely"…
Understanding the continuous evolution of populations from discrete temporal snapshots is a critical research challenge, particularly in fields like developmental biology and systems medicine where longitudinal tracking of individual…
Recent diffusion probabilistic models (DPM) in the field of pansharpening have been gradually gaining attention and have achieved state-of-the-art (SOTA) performance. In this paper, we identify shortcomings in directly applying DPMs to the…
At the core of modern generative modeling frameworks, including diffusion models, score-based models, and flow matching, is the task of transforming a simple prior distribution into a complex target distribution through stochastic paths in…
The Schr\"odinger Bridge (SB) problem offers a powerful framework for combining optimal transport and diffusion models. A promising recent approach to solve the SB problem is the Iterative Markovian Fitting (IMF) procedure, which alternates…
The purpose of the present work is to expand substantially the type of control and estimation problems that can be addressed following the paradigm of Schr\"odinger bridges, by incorporating termination (killing) of stochastic flows.…
We study the Schr\"odinger bridge problem when the endpoint distributions are available only through samples. Classical computational approaches estimate Schr\"odinger potentials via Sinkhorn iterations on empirical measures and then…
Compared to the existing function-based models in deep generative modeling, the recently proposed diffusion models have achieved outstanding performance with a stochastic-process-based approach. But a long sampling time is required for this…
Machine learning-based simulations, especially calorimeter simulations, are promising tools for approximating the precision of classical high energy physics simulations with a fraction of the generation time. Nearly all methods proposed so…
It is a crucial challenge to reconstruct population dynamics using unlabeled samples from distributions at coarse time intervals. Recent approaches such as flow-based models or Schr\"odinger Bridge (SB) models have demonstrated appealing…
Given two boundary distributions, the Schr\"odinger Bridge (SB) problem seeks the ``most likely`` random evolution between them with respect to a reference process. It has revealed rich connections to recent machine learning methods for…
This paper introduces a novel theoretical simplification of the Diffusion Schr\"odinger Bridge (DSB) that facilitates its unification with Score-based Generative Models (SGMs), addressing the limitations of DSB in complex data generation…
Many natural dynamic processes -- such as in vivo cellular differentiation or disease progression -- can only be observed through the lens of static sample snapshots. While challenging, reconstructing their temporal evolution to decipher…
Generating samples from a probability distribution is a fundamental task in machine learning and statistics. This article proposes a novel scheme for sampling from a distribution for which the probability density $\mu({\bf x})$ for ${\bf…
Denoising diffusion models have recently emerged as a powerful class of generative models. They provide state-of-the-art results, not only for unconditional simulation, but also when used to solve conditional simulation problems arising in…