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Related papers: Schr\"odinger Bridge Samplers

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The Schr\"odinger bridge problem (SBP) is gaining increasing attention in generative modeling and showing promising potential even in comparison with the score-based generative models (SGMs). SBP can be interpreted as an entropy-regularized…

The Schr\"odinger bridge problem (SBP) finds the most likely stochastic evolution between two probability distributions given a prior stochastic evolution. As well as applications in the natural sciences, problems of this kind have…

Machine Learning · Statistics 2022-05-31 Francisco Vargas , Pierre Thodoroff , Neil D. Lawrence , Austen Lamacraft

The Schr\"odinger Bridge (SB) problem has become a fundamental tool in computational optimal transport and generative modeling. To address this problem, ideal methods such as Iterative Proportional Fitting and Iterative Markovian Fitting…

Machine Learning · Statistics 2025-10-27 Marta Gentiloni Silveri , Giovanni Conforti , Alain Durmus

The Iterative Markovian Fitting (IMF) procedure, which iteratively projects onto the space of Markov processes and the reciprocal class, successfully solves the Schr\"odinger Bridge (SB) problem. However, an efficient practical…

Modern methods of generative modelling and unpaired data translation based on Schr\"odinger bridges and stochastic optimal control theory aim to transform an initial density to a target one in an optimal way. In the present paper, we assume…

Machine Learning · Computer Science 2026-03-24 Nikita Puchkin , Denis Suchkov , Alexey Naumov , Denis Belomestny

We introduce a novel discretization scheme for Wasserstein gradient flows that involves successively computing Schr\"{o}dinger bridges with the same marginals. This is different from both the forward/geodesic approximation and the…

Probability · Mathematics 2024-06-18 Medha Agarwal , Zaid Harchaoui , Garrett Mulcahy , Soumik Pal

Entropy-regularized optimal transport, which has strong links to the Schr\"odinger bridge problem in statistical mechanics, enjoys a variety of applications from trajectory inference to generative modeling. A major driver of renewed…

Machine Learning · Statistics 2026-01-27 Anand Srinivasan , Jean-Jacques Slotine

Consider the problem of matching two independent i.i.d. samples of size $N$ from two distributions $P$ and $Q$ in $\mathbb{R}^d$. For an arbitrary continuous cost function, the optimal assignment problem looks for the matching that…

Probability · Mathematics 2023-01-03 Zaid Harchaoui , Lang Liu , Soumik Pal

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…

Machine Learning · Computer Science 2025-12-08 Thomas Gravier , Thomas Boyer , Auguste Genovesio

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…

Machine Learning · Computer Science 2024-11-06 Nikita Gushchin , Daniil Selikhanovych , Sergei Kholkin , Evgeny Burnaev , Alexander Korotin

Recent advances in flow-based generative modelling have provided scalable methods for computing the Schr\"odinger Bridge (SB) between distributions, a dynamic form of entropy-regularised Optimal Transport (OT) for the quadratic cost. The…

Machine Learning · Statistics 2025-11-04 Samuel Howard , Peter Potaptchik , George Deligiannidis

Modern distribution matching algorithms for training diffusion or flow models directly prescribe the time evolution of the marginal distributions between two boundary distributions. In this work, we consider a generalized distribution…

Predicting the intermediate trajectories between an initial and target distribution is a central problem in generative modeling. Existing approaches, such as flow matching and Schr\"odinger bridge matching, effectively learn mappings…

Machine Learning · Computer Science 2026-03-03 Sophia Tang , Yinuo Zhang , Alexander Tong , Pranam Chatterjee

Schr\"odinger bridges (SBs) provide an elegant framework for modeling the temporal evolution of populations in physical, chemical, or biological systems. Such natural processes are commonly subject to changes in population size over time…

Machine Learning · Computer Science 2023-06-16 Matteo Pariset , Ya-Ping Hsieh , Charlotte Bunne , Andreas Krause , Valentin De Bortoli

In this work, we study a discrete Schr\"odinger bridge problem with partial marginal observations. A main difficulty compared to the classical Schr\"odinger bridge formulation is that our problem is not strictly convex and standard…

Optimization and Control · Mathematics 2026-04-08 Michele Mascherpa , Victor Molnö , Carsten Skovmose Kallesøe , Johan Karlsson

We address the problem of Schr\"odinger potential estimation, which plays a crucial role in modern generative modelling approaches based on Schr\"odinger bridges and stochastic optimal control for SDEs. Given a simple prior diffusion…

Machine Learning · Computer Science 2025-06-04 Nikita Puchkin , Iurii Pustovalov , Yuri Sapronov , Denis Suchkov , Alexey Naumov , Denis Belomestny

Diffusion Schr\"odinger bridges (DSB) have recently emerged as a powerful framework for recovering stochastic dynamics via their marginal observations at different time points. Despite numerous successful applications, existing algorithms…

We characterize the Schr\"odinger bridge problems by a family of Mckean-Vlasov stochastic control problems with no terminal time distribution constraint. In doing so, we use the theory of Hilbert space embeddings of probability measures and…

Optimization and Control · Mathematics 2025-12-10 Yumiharu Nakano

A Schr\"odinger bridge is the most probable time-dependent probability distribution that connects an initial probability distribution $w_{i}$ to a final one $w_{f}$. The problem has been solved and widely used for the case of simple…

Statistical Mechanics · Physics 2025-07-02 Henri Orland

The unbalanced Schr\"odinger bridge problem (uSBP) seeks to interpolate between a probability measure $\rho_0$ and a sub-probability measure $\rho_T$ while minimizing KL divergence to a reference measure $\mathbf{R}$ on a path space. In…

Probability · Mathematics 2025-12-16 Andrei Zlotchevski , Linan Chen