New algorithm solves complex mean-field Schrödinger bridge problem.
problem Designing a controller for diffusion processes with nonlocal interaction.
method Generalized Hopf-Cole transform and Sinkhorn-type algorithm.
result Convergence guarantees for the proposed algorithm under mild assumptions.
DeepGSB solves MFGs with non-differentiable preferences.
problem Solving MFGs with non-differentiable preferences and exact population convergence.
method Generalized Schrödinger Bridge via Forward-Backward SDEs and Temporal Difference learning.
result DeepGSB provides necessary and sufficient conditions for mean-field problems.
Kernel-based mean-field games use MMD penalties for interaction and target costs.
problem Optimizing mean-field games with specific cost functions.
method Kernel structure, random Fourier U-statistics, neural network training.
result Sample-level convergence theorem and rate of convergence proved.
Paper develops a new method for solving complex problems in generative modeling and mean-field games.
problem Solving complex problems in generative modeling and mean-field games.
method Reinterpreting Generalized Schrödinger Bridges (GSBs) as probabilistic models and using the nonlinear Feynman-Kac lemma.
result Demonstrates the efficacy of the new method in generative modeling and mean-field games.
A new method for steering large agent populations efficiently.
problem Controlling the configuration of a swarm of identical, interacting cooperative agents.
method Mean-Field Schrodinger Bridges with Gaussian Mixture Models.
result A highly efficient parameterization to approximate optimal solutions of the MFSB problem in closed form.
New method infers population dynamics from snapshots using path space optimization.
problem Recover dynamics of a population from its temporal marginals.
method Grid-free algorithm using Schrödinger bridges coupled via noisy gradient descent in mean-field limit.
result Global convergence to min-entropy estimator with end-to-end theoretical guarantees.
Paper adds Fisher Information to mean field optimization for faster convergence.
problem Mean field optimization in neural networks training.
method Developed energy-dissipation method and gradient flow on probability space.
result Marginal distributions converge exponentially to minimizer.
Mean-field neural nets approximate functions using a free energy functional and controlled dynamics.
problem Function approximation by two-layer neural nets in the mean-field regime.
method Phrasing function approximation as global minimization of a free energy functional, examining dynamics in the space of probability measures over weights.
result Characterization of the unique global minimizer and dynamics achieving it, including the Föllmer drift.
Extends martingale Schrödinger bridge to arbitrary dimensions and characterizes it.
problem Tackles the martingale Schrödinger bridge in arbitrary dimensions.
method Identifies continuous-time counterpart and relates to variational problems.
result Continuous martingale Schrödinger bridge coincides with Föllmer martingale in irreducible case.
BM2 learns Schrödinger bridges using neural networks.
problem Learning dynamic transport maps between two distributions.
method Coupled Bridge Matching (BM2) with neural networks. result Preliminary theoretical analysis and numerical experiments show BM2's effectiveness. We solve a Schrödinger bridge with a quadratic state cost, finding a closed-form solution.
problem Optimizing diffusion processes between given distributions.
method Regularized Schrödinger bridge with a quadratic state cost.
result Closed-form solution for the Markov kernel of the regularized Schrödinger bridge.
Unified framework extends adjoint Schrödinger bridge sampler to discrete spaces.
problem Challenges in learning discrete neural samplers due to gradients and combinatorial complexity.
method Introduces discrete ASBS, a unified framework that extends adjoint Schrödinger bridge sampler to discrete spaces.
result Empirically, discrete ASBS achieves competitive sample quality with significant advantages in training efficiency and scalability.
Smooth Schrödinger Bridges improve trajectory inference by smoothing Gaussian processes.
problem Improving trajectory inference in applications like particle tracking.
method Generalizes Schrödinger Bridge problem to smooth Gaussian processes, solving the problem on phase space.
result The method outperforms existing methods on real datasets.
A new method estimates Schrödinger bridges without iterative simulations or neural networks.
problem Estimating the time-dependent drift between two probability distributions.
method Solving the static entropic optimal transport problem and modifying the potentials.
result The Sinkhorn bridge method provably estimates Schrödinger bridges with a rate of convergence dependent on the target measure's intrinsic dimensionality.
New algorithm computes Schrödinger Bridge for unpaired data translation.
problem Computing optimal transport maps for unpaired data translation.
method Schrödinger Bridge Flow, a discretization of a flow of path measures.
result Eliminates the need to train multiple DDM-like models.
A new diffusion method approximates Schrödinger bridge with improved convergence.
problem Approximating Schrödinger bridge with Langevin diffusion.
method Leveraging Langevin diffusion to approximate Schrödinger bridge.
result The difference between the two approximations is proportional to the score function.
Study finds optimal martingale coupling between two distributions with minimal entropy.
problem Finding the optimal martingale coupling between two distributions with minimal relative entropy.
method Solving a dual problem to find the log-density of the optimal coupling, which represents the marginal and martingale constraints.
result The log-density of the optimal coupling is given by a triplet of real functions representing the marginal and martingale constraints.
New method estimates Schrödinger bridges using ML techniques.
problem Finding most likely stochastic evolution between two distributions.
method Equivalence with maximum likelihood estimation, numerical Gaussian process approach.
result Direct application of ML techniques for SBP estimation.
Schrödinger bridge solved with Weyl calculus for quadratic state cost.
problem Optimal control policy to steer joint state statistics.
method Weyl calculus in quantum mechanics for reaction-diffusion PDEs.
result Explicit Markov kernel for quadratic state cost found.
This work studies the contraction coefficients of Schrödinger bridge problems in linear systems.
problem Optimally controlling the evolution of a system's state density over time.
method Analyzes and improves the convergence rates of dynamic Schrödinger systems via geometric and control-theoretic interpretations.
result New insights into improving computation of worst-case contraction coefficients by preconditioning.
New method estimates Schrödinger bridge potentials via empirical risk minimization.
problem Estimating Schrödinger bridge potentials from samples.
method Rewriting Schrödinger system as a fixed-point equation and estimating the potential via empirical risk minimization.
result Uniform concentration of empirical risk around population counterpart under sub-Gaussian assumptions.
Extends diffusion-based Schrödinger bridge models to handle time-dependent potentials.
problem Approximating optimal transport dynamics between two boundary distributions with a twisted Brownian motion reference.
method Introduces Twisted Schrödinger Bridge Matching (TSBM) using the Iterative Markovian Fitting (IMF) paradigm, incorporating a gradient-dependent bridge-matching loss.
result Improves trajectory inference across high-dimensional settings, including crowd navigation and single-cell data.
Paper proposes a new method to solve Schrödinger Bridge Problem using kernel regression.
problem Schrödinger Bridge Problem in the context of entropic optimal transport.
method Forward-reverse iterative Monte Carlo procedure using kernel regression.
result Developed a provably convergent algorithm for approximating Schrödinger potentials.
New algorithm solves Schrödinger bridge problem with mismatched channels.
problem Solving Schrödinger bridge problem with input and noise channel mismatch.
method Design of a Sinkhorn recursion with memory for nonlinear PDEs.
result Demonstrates solving control-affine Schrödinger bridge problem.
Generative models use Schrödinger bridges for faster conditional simulation.
problem Efficiently simulate conditional scenarios in generative models.
method Extend Schrödinger bridge framework to conditional simulation.
result Demonstrated on various applications, including image super-resolution.
Generative model for time series using Schrödinger bridges with jumps.
problem Creating realistic synthetic time series from observed data.
method Entropic optimal transport, Schrödinger bridge framework, jump-diffusion process.
result Jump-diffusion Schrödinger bridge model generates more realistic time series.
New discretization scheme for Wasserstein gradient flows using Schrödinger bridges.
problem Computing Wasserstein gradient flows efficiently and without score functions.
method Iterated Schrödinger bridge approximation with particle-based Sinkhorn algorithm.
result The scheme converges to Wasserstein gradient flows for certain flows, including heat flow.
Clarifies relation for solving control-affine Schrödinger bridge problems.
problem Solving control-affine Schrödinger bridge problems via Hopf-Cole transform.
method Applies Hopf-Cole transform to conditions of optimality, resulting in nonlinear PDEs.
result Generic control-affine Schrödinger bridge requires further algorithmic development.
Localized sampler tackles high-dimensional sampling with fewer samples.
problem Sampling from unknown distributions with limited data.
method Combining Schrödinger bridges and plug & play Langevin samplers with localization strategy.
result Localized sampler reduces dimensionality, making sampling more efficient.
This work studies the statistical performance of Sinkhorn iterations in estimating Schrödinger bridges.
problem Estimating Schrödinger bridges with limited samples.
method Intermediate Sinkhorn iterations applied to the time-dependent drifts of SDEs.
result Established a statistical bound on the squared total variation error of Sinkhorn bridge iterations.
UNSB uses neural Schrödinger Bridge to solve unpaired image-to-image translation.
problem Difficulties in unpaired image-to-image translation with diffusion models.
method Expresses SB problem as adversarial learning problems, incorporating advanced discriminators and regularization.
result Successfully solves various unpaired image-to-image translation tasks.
IDBM solves Schrödinger bridge problems with iterative sampling.
problem Optimizing transport between probability measures.
method Iterated diffusion bridge mixture (IDBM) procedure.
result IDBM realizes valid transport between target measures at each iteration.
Proposes a new algorithm for robust learning in Schrödinger bridge problems.
problem Uncertainty in estimated learning signals in Schrödinger bridge problems.
method Variational Online Mirror Descent (OMD) framework for Schrödinger bridge problems.
result Formally proves convergence and a regret bound for the OMD formulation of Schrödinger bridge acquisition.
PA reinterpreted as SB problem, unifying thermodynamics and optimal transport.
problem Optimizing discrete-time paths between probability distributions.
method Schrödinger Bridge theory, solving variational problems.
result PA's reweighting step derived from Schrödinger system.
New method synthesizes data on curved spaces for better interpolation.
problem Synthesizing data on curved spaces for better interpolation.
method Riemannian Diffusion Schrödinger Bridge
result Generalizes Diffusion Schrödinger Bridge to curved spaces for better interpolation.
New framework for Bayesian inference using neural Schrödinger-Föllmer flows.
problem Approximate Bayesian inference in large datasets.
method Stochastic control, Schrödinger bridges, SDE-based models.
result Advocates stochastic control as a finite time and low variance alternative to SGLD.
Generative AI connects to Schrödinger bridge problems with soft constraints for stability.
problem Stability issues in generative AI due to hard terminal constraints.
method Soft-constrained Schrödinger bridge formulation and convergence analysis.
result Existence and convergence of optimal solutions as penalty grows.
New algorithm improves on existing methods for solving transport problems.
problem Finding a map to transport one distribution to another.
method Iterative Markovian Fitting (IMF) and Diffusion Schrödinger Bridge Matching (DSBM).
result DSBM significantly improves over previous SB numerics and recovers various transport methods.
New framework models non-conservative stochastic processes without energy conservation constraints.
problem Existing Schrödinger Bridge methods are limited by energy-conservation assumptions.
method Introduces non-conservative generalized Schrödinger bridge (NCGSB) based on contact Hamiltonian mechanics.
result Contact Wasserstein geodesic (CWG) provides a broader class of real-world stochastic processes.
Study optimal semistatic portfolios using martingale Schrödinger bridges.
problem Optimizing semistatic portfolios in a dynamic stock market.
method Minimizing entropy among calibrated martingale measures.
result Explicit solution for optimal semistatic portfolios exists.
LightSBB-M improves generative diffusion modeling with lower 2-Wasserstein distances.
problem Improving generative diffusion models using Schrödinger Bridge and Bass methods.
method Optimizes SBB transport plan with dual representation and tunable beta parameter.
result Achieves up to 32% improvement in 2-Wasserstein distance on synthetic datasets.
QDSB accelerates Schrödinger bridge learning with quantized approximations.
problem Learning generative models from unpaired samples.
method Quantized diffusion Schrödinger bridges (QDSB) using anchor-quantized distributions and cell-wise sampling.
result QDSB achieves sample quality similar to existing methods but with significantly less computational time.
New method trains reflected Schrödinger bridges without complex derivatives.
problem Training reflected Schrödinger bridges efficiently in high dimensions.
method Partially simulation-free framework with new sampling method.
result Generative performance maintained or slightly improved with reflected dynamics.
Develops new samplers to approximate target distributions via modified Markov processes.
problem Approximating a target distribution with a modified Markov process.
method Iterative proportional fitting and Sinkhorn algorithm to modify transition kernels.
result Schrödinger bridge samplers can approximate target distributions and estimate their normalizing constants.
Following closely the construction of the Schrodinger bridge, we build a new class of Stochastic Volatility Models exactly calibrated to market instruments such as for example Vanillas, options on realized variance or VIX options. These models differ strongly from the well-known local stochastic volatility models, in p…
Generative model uses Schrödinger bridges for stable sampling.
problem Sampling from unknown distributions with limited training samples.
method Combines Schrödinger bridges and Langevin dynamics.
result Effective stability and generation of samples within convex hull.
New method solves tree-structured Schrödinger Bridge problems.
problem Computing Schrödinger Bridge between tree-structured distributions.
method Iterative Markovian Fitting (IMF) procedure for tree-structured costs.
result Extends IMF to tree-structured Schrödinger Bridge problems.
New approach to control diffusion processes with soft constraints.
problem Finding an optimal diffusion process with a target terminal distribution.
method Generalized Schrödinger bridge problem with soft constraints, solving for a geometric mixture of target and other distributions.
result The terminal distribution of the optimally controlled process is a geometric mixture of the target and another distribution.