mlsanityData to 7 Oct 2026

Dynamic Conditional Optimal Transport through Simulation-Free Flows

arXiv 2404.04240 ↗First posted 5 Apr 2024cs.LGcited by 24

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Abstract (arXiv)

We study the geometry of conditional optimal transport (COT) and prove a dynamical formulation which generalizes the Benamou-Brenier Theorem. Equipped with these tools, we propose a simulation-free flow-based method for conditional generative modeling. Our method couples an arbitrary source distribution to a specified target distribution through a triangular COT plan, and a conditional generative model is obtained by approximating the geodesic path of measures induced by this COT plan. Our theory and methods are applicable in infinite-dimensional settings, making them well suited for a wide class of Bayesian inverse problems. Empirically, we demonstrate that our method is competitive on several challenging conditional generation tasks, including an infinite-dimensional inverse problem.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). Builds on 61 of its 92 references that are in the map. First posted on arXiv 5 Apr 2024.

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61 of 92 references.

References · 61

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38 more
  1. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
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Citing papers per year: 2024: 2; 2025: 13; 2026: 9.

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  1. 2025Guided Diffusion Sampling on Function Spaces with Applications to PDEscited by 33
  2. 2025Flow Matching: Markov Kernels, Stochastic Processes and Transport Planscited by 16
  3. 2025Stochastic Process Learning via Operator Flow Matchingcited by 14
  4. 2025Flow Matching with Semidiscrete Couplingscited by 12
  5. 2024Conditional simulation via entropic optimal transport: Toward non-parametric estimation of conditional Brenier mapscited by 9
  6. 2025Fast Flow-based Visuomotor Policies via Conditional Optimal Transport Couplingscited by 8
  7. 2025Source Separation by Flow Matchingcited by 8
  8. 2025Composite Flow Matching for Reinforcement Learning with Shifted-Dynamics Datacited by 8
  9. 2024Modeling Stochastic Conditional Dynamics from Sparse Observations via Kernel-Stabilized Flow Matchingcited by 3
  10. 2025Conditional Flow Matching for Bayesian Posterior Inferencecited by 3
  11. 2025A Geometric Approach to Optimal Experimental Designcited by 2
  12. 2025GRASP: Guided Residual Adapters with Sample-wise Partitioningcited by 2
12 more
  1. 2025Pairwise Optimal Transports for Training All-to-All Flow-Based Condition Transfer Modelcited by 1
  2. 2025Weighted Conditional Flow Matchingcited by 1
  3. 2025Bridging Simulators with Conditional Optimal Transportcited by 0
  4. 2026Conditional Normalizing Flows for Forward and Backward Joint State and Parameter Estimationcited by 0
  5. 2026Conditional Unbalanced Optimal Transport Maps: An Outlier-Robust Framework for Conditional Generative Modelingcited by 0
  6. 2026Prior-Fitted Functional Flow: In-Context Generative Models for Pharmacokineticscited by 0
  7. 2026Intrinsic Flow Matching on Quantum Pure-State Manifolds with Phase-Aligned Transportcited by 0
  8. 2026Optimal Transport Q-Learning for Flow Policy Steering and Accelerationcited by 0
  9. 2026Restoration Flow Matching-Based Channel Refinement and Equalization Correction for MIMO Semantic Communicationscited by 0
  10. 2026Approximating Measures on Function Spaces: Transport and Truncationcited by 0
  11. 2026One-Step Generative Surrogate Models via Block-Triangular Joint Driftingcited by 0
  12. 2026DRIFT: Disentangled Responsive-Invariant Flow Transport for Single-Cell Perturbation Predictioncited by 0