Data geometry makes time identifiable from noisy interpolants at rate O(1/sqrt(d-k)), rendering the time-blindness gap asymptotically negligible relative to coupling variance.
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Improving and generalizing flow-based generative models with minibatch optimal transport
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abstract
Continuous normalizing flows (CNFs) are an attractive generative modeling technique, but they have been held back by limitations in their simulation-based maximum likelihood training. We introduce the generalized conditional flow matching (CFM) technique, a family of simulation-free training objectives for CNFs. CFM features a stable regression objective like that used to train the stochastic flow in diffusion models but enjoys the efficient inference of deterministic flow models. In contrast to both diffusion models and prior CNF training algorithms, CFM does not require the source distribution to be Gaussian or require evaluation of its density. A variant of our objective is optimal transport CFM (OT-CFM), which creates simpler flows that are more stable to train and lead to faster inference, as evaluated in our experiments. Furthermore, we show that when the true OT plan is available, our OT-CFM method approximates dynamic OT. Training CNFs with CFM improves results on a variety of conditional and unconditional generation tasks, such as inferring single cell dynamics, unsupervised image translation, and Schr\"odinger bridge inference.
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representative citing papers
Flux Matching generalizes score-based generative modeling by using a weaker objective that admits infinitely many non-conservative vector fields with the data as stationary distribution, enabling new design choices beyond traditional score matching.
Generative diffusion and flow models are constructed to remain exactly on the Lorentz-invariant massless N-particle phase space manifold during sampling for particle physics applications.
FlowHijack is the first dynamics-aware backdoor attack on flow-matching VLAs that achieves high success rates with stealthy triggers while preserving benign performance and making malicious actions kinematically indistinguishable from normal ones.
Introduces a Bridge latent interface that maps mismatched student latents into teacher space, enabling distillation from modern diffusion teachers to compact one-step students and raising SD 1.5 HPSv3 from 5.4 to 9.4 while keeping one-step speed.
Introduces structured DRO for learned inverse problem reconstructions with ambiguity sets aligned to the forward operator, yielding explicit dual representations and a worst-case bound that induces Tikhonov regularization on the operator Lipschitz constant.
OTF-CBM replaces static cosine similarity in vision-language CBMs with data-driven optimal transport flow to improve concept alignment, accuracy, and faithfulness.
Patched Flow Matching reconstructs full-resolution wall-pressure fields on domains four times larger than training data from 0.25% sensor coverage by fusing short-domain DNS patch priors with sparse measurements via training-free posterior sampling.
IFM learns deterministic tangent velocity fields on CP^{d-1} via Pancharatnam phase-aligned paths, recovering marginal transport with endpoint and stability guarantees while showing empirical gains over Euclidean flow matching on quantum benchmarks.
TriFlow synthesizes nearest-vertex vector fields via flow-matching to generate artist-like 3D mesh topology, then extracts meshes via clustering and topology-aware QEM simplification.
PAINT reframes asynchronous flow-based action chunking as an initial noise selection problem solved via backward Euler inversion and a repainting rule.
A weakly-supervised image quality transfer method generates synthetic distorted DWI images from quality labels to train improved distortion correction models for prostate MRI.
CADENCE recovers individualized continuous-time trajectories from cross-sectional snapshots via context-anchored latent dynamics, a bijective score-based encoder, and SMoE routing, with claimed identifiability guarantees and benchmark performance matching dense-data models.
A flow matching generative model produces weak lensing mass maps with fidelity improved to below 1% and 5% on basic and higher-order statistics relative to GAN benchmarks.
PermFlow applies conditional flow matching on the affine subspace of doubly stochastic matrices with a closed-form tangent projector and nearest-target coupling to capture multimodal permutation distributions.
Flow matching underestimates velocities due to MSE loss leading to integration lag; Initial Energy Injection corrects the start-end asymmetry, improving FID by 44.6% and achieving 5x speedup on ImageNet-1k.
Flow map policies enable fast one-step inference for flow-based RL policies, and FMQ provides an optimal closed-form Q-guided target for offline-to-online adaptation under trust-region constraints, achieving SOTA performance.
A generative transfer framework using iterative path-wise tilting integrated with conditional flow matching recovers target entropic optimal transport couplings from reference samples, achieving O(δ) convergence in Wasserstein-1 distance.
Wasserstein Lagrangian Mechanics formalizes second-order dynamics in Wasserstein space and provides an algorithm to learn them from observed marginals without specifying the Lagrangian, outperforming gradient flows on various dynamics.
STMD distills the full transition map of diffusion sampling SDEs into a conditional Mean Flow model to enable fast one- or few-step stochastic sampling without teacher models or bi-level optimization.
OGPP is a particle flow-matching method using orbit-space canonicalization and geometric paths that achieves lower error and fewer steps than prior approaches on 3D benchmarks.
Flow matching on time series targets a closed-form nonparametric velocity field that is a similarity-weighted mixture of observed transition velocities, making neural models approximations to an ideal memory-augmented dynamical system sampler.
DisRFM uses polar Riemannian flow matching on constant-curvature manifolds to align graph domains while preserving label-relevant topology via radial Wasserstein and angular confidence matching.
Empirical flow matching introduces coupled biases from plug-in estimation, including altered statistical targets, non-gradient minimizers, and non-unique dynamics via flux-null fields, with base distribution controlling kinetic energy tails.
citing papers explorer
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What Time Is It? How Data Geometry Makes Time Conditioning Optional for Flow Matching
Data geometry makes time identifiable from noisy interpolants at rate O(1/sqrt(d-k)), rendering the time-blindness gap asymptotically negligible relative to coupling variance.
-
Generative Modeling with Flux Matching
Flux Matching generalizes score-based generative modeling by using a weaker objective that admits infinitely many non-conservative vector fields with the data as stationary distribution, enabling new design choices beyond traditional score matching.
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Generative models on phase space
Generative diffusion and flow models are constructed to remain exactly on the Lorentz-invariant massless N-particle phase space manifold during sampling for particle physics applications.
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FlowHijack: A Dynamics-Aware Backdoor Attack on Flow-Matching Vision-Language-Action Models
FlowHijack is the first dynamics-aware backdoor attack on flow-matching VLAs that achieves high success rates with stealthy triggers while preserving benign performance and making malicious actions kinematically indistinguishable from normal ones.
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Cross-Space Distillation: Teaching One-Step Students with Modern Diffusion Teachers
Introduces a Bridge latent interface that maps mismatched student latents into teacher space, enabling distillation from modern diffusion teachers to compact one-step students and raising SD 1.5 HPSv3 from 5.4 to 9.4 while keeping one-step speed.
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A Distributionally Robust Framework for Learned Reconstructions in Inverse Problems
Introduces structured DRO for learned inverse problem reconstructions with ambiguity sets aligned to the forward operator, yielding explicit dual representations and a worst-case bound that induces Tikhonov regularization on the operator Lipschitz constant.
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Bridging Vision and Language Concepts through Optimal Transport Semantic Flow
OTF-CBM replaces static cosine similarity in vision-language CBMs with data-driven optimal transport flow to improve concept alignment, accuracy, and faithfulness.
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Patched Flow Matching: Generative Wall-Pressure Reconstruction Beyond Training-Domain Scales from Sparse Sensors
Patched Flow Matching reconstructs full-resolution wall-pressure fields on domains four times larger than training data from 0.25% sensor coverage by fusing short-domain DNS patch priors with sparse measurements via training-free posterior sampling.
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Intrinsic Flow Matching on Quantum Pure-State Manifolds with Phase-Aligned Transport
IFM learns deterministic tangent velocity fields on CP^{d-1} via Pancharatnam phase-aligned paths, recovering marginal transport with endpoint and stability guarantees while showing empirical gains over Euclidean flow matching on quantum benchmarks.
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TriFlow: Generating Artist-Like 3D Mesh Topology via Nearest-Vertex Vector Fields
TriFlow synthesizes nearest-vertex vector fields via flow-matching to generate artist-like 3D mesh topology, then extracts meshes via clustering and topology-aware QEM simplification.
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Start Right, Arrive Right: Asynchronous Execution via Initial Noise Selection
PAINT reframes asynchronous flow-based action chunking as an initial noise selection problem solved via backward Euler inversion and a repainting rule.
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Learning to Distort: Weakly-Supervised Image Quality Transfer for Prostate DWI Correction
A weakly-supervised image quality transfer method generates synthetic distorted DWI images from quality labels to train improved distortion correction models for prostate MRI.
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Learning Individual Dynamics from Sparse Cross-Sectional Snapshots
CADENCE recovers individualized continuous-time trajectories from cross-sectional snapshots via context-anchored latent dynamics, a bijective score-based encoder, and SMoE routing, with claimed identifiability guarantees and benchmark performance matching dense-data models.
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Increasing the Precision of Surrogate Models for Weak Lensing Mass Maps with Flow Matching
A flow matching generative model produces weak lensing mass maps with fidelity improved to below 1% and 5% on basic and higher-order statistics relative to GAN benchmarks.
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Learning Unbiased Permutations via Flow Matching
PermFlow applies conditional flow matching on the affine subspace of doubly stochastic matrices with a closed-form tangent projector and nearest-target coupling to capture multimodal permutation distributions.
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The Velocity Deficit: Initial Energy Injection for Flow Matching
Flow matching underestimates velocities due to MSE loss leading to integration lag; Initial Energy Injection corrects the start-end asymmetry, improving FID by 44.6% and achieving 5x speedup on ImageNet-1k.
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Aligning Flow Map Policies with Optimal Q-Guidance
Flow map policies enable fast one-step inference for flow-based RL policies, and FMQ provides an optimal closed-form Q-guided target for offline-to-online adaptation under trust-region constraints, achieving SOTA performance.
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Generative Transfer for Entropic Optimal Transport with Unknown Costs
A generative transfer framework using iterative path-wise tilting integrated with conditional flow matching recovers target entropic optimal transport couplings from reference samples, achieving O(δ) convergence in Wasserstein-1 distance.
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A Call to Lagrangian Action: Learning Population Mechanics from Temporal Snapshots
Wasserstein Lagrangian Mechanics formalizes second-order dynamics in Wasserstein space and provides an algorithm to learn them from observed marginals without specifying the Lagrangian, outperforming gradient flows on various dynamics.
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Stochastic Transition-Map Distillation for Fast Probabilistic Inference
STMD distills the full transition map of diffusion sampling SDEs into a conditional Mean Flow model to enable fast one- or few-step stochastic sampling without teacher models or bi-level optimization.
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Generative Modeling with Orbit-Space Particle Flow Matching
OGPP is a particle flow-matching method using orbit-space canonicalization and geometric paths that achieves lower error and fewer steps than prior approaches on 3D benchmarks.
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Is Flow Matching Just Trajectory Replay for Sequential Data?
Flow matching on time series targets a closed-form nonparametric velocity field that is a similarity-weighted mixture of observed transition velocities, making neural models approximations to an ideal memory-augmented dynamical system sampler.
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DisRFM: Polar Riemannian Flow Matching for Structure-Preserving Graph Domain Adaptation
DisRFM uses polar Riemannian flow matching on constant-curvature manifolds to align graph domains while preserving label-relevant topology via radial Wasserstein and angular confidence matching.
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On The Hidden Biases of Flow Matching Samplers
Empirical flow matching introduces coupled biases from plug-in estimation, including altered statistical targets, non-gradient minimizers, and non-unique dynamics via flux-null fields, with base distribution controlling kinetic energy tails.
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NEAT: Neighborhood-Guided, Efficient, Autoregressive Set Transformer for 3D Molecular Generation
NEAT achieves state-of-the-art 3D molecular generation on QM9 and GEOM-Drugs via a neighborhood-guided autoregressive set transformer that ensures atom-level permutation invariance and offers a significant speed advantage.
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Sundial: A Family of Highly Capable Time Series Foundation Models
Sundial uses TimeFlow Loss for native pre-training of Transformers on continuous time series from TimeBench, achieving SOTA point and probabilistic forecasting with millisecond inference.
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Stochastic Interpolants: A Unifying Framework for Flows and Diffusions
Stochastic interpolants unify flow-based and diffusion-based generative models by bridging target densities exactly via latent-variable processes whose drifts minimize quadratic objectives.
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FlowEqProp: Training Flow Matching Generative Models with Gradient Equilibrium Propagation
GradEP extends Equilibrium Propagation to train velocity fields, yielding the first EP-trained flow-matching generative model that produces recognizable digits without backpropagation.
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Generative modeling of granular flow on inclined planes using conditional flow matching
Conditional flow matching with sparsity-aware gradient guidance recovers interior granular kinematics and stresses from as little as 16% boundary coverage or 11% spatial data, beating a CNN baseline in the most ill-posed regime.
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Unified Audio Intelligence Without Regressing on Text Intelligence
Audex unifies audio understanding and generation on a strong text MoE backbone with multi-stage SFT plus text-only Cascade RL, matching open SOTA audio scores while mostly retaining text capability.
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Generative Models on Analog Hardware with Dynamics
AIS framework with time-varying piecewise parameters and hidden states enables analog hardware to perform generative modeling, achieving FID 27.6 on MNIST and 80.8 on Fashion-MNIST with 23uJ per image using 4-bit sparse architectures.
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CurvSegFlow: Time-Conditioned Flow Matching for Robust Segmentation of Curvilinear Structures in Noisy Biomedical Images
CurvSegFlow applies time-conditioned flow matching with a U-Net backbone and triple-term loss to progressively refine segmentations of thin structures in noisy images, reporting competitive performance on microtubule, vessel, and nerve datasets.
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Benchmarking Neural Speech Compression from a Rate-Distortion Perspective
ECC integrates hyperprior side information, channel-wise context, latent residual prediction, temporal modeling, and entropy skip into a learned entropy model, yielding 39.9% and 76.3% average BD-rate reductions on ViSQOL and PESQ over baselines.
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GenPO++: Generative Policy Optimization with Jacobian-free Likelihood Ratios
GenPO++ achieves exact Jacobian-free likelihood ratio computation for generative flow policies by embedding history states as auxiliary memory in a high-order reversible ODE solver.
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CaloTrilogy: Toward a Breakthrough in One-Step, End-to-End, Physics-Guided Shower Generation for Modern Calorimeters
A one-step generative model for calorimeter showers, using MeanFlow, a learned Gaussian-mixture prior, and a physics-constrained loss, matches diffusion-model quality at far fewer evaluations.
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GenSBI: Generative Methods for Simulation-Based Inference in JAX
GenSBI delivers JAX-native implementations of generative SBI methods with transformer backbones and reports near-ideal calibration scores on standard benchmarks.
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SURGE: Approximation and Training Free Particle Filter for Diffusion Surrogate
SURGE is an unbiased particle filter that fuses diffusion-model simulations with noisy observations via sequential Monte Carlo reweighting over diffusion trajectories.
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PACE: Geometry-Aware Bridge Transport for Single-Cell Trajectory Inference
PACE recovers geometry-consistent continuous transport dynamics from destructive single-cell snapshots via anisotropic metrics and neural bridges, reducing reconstruction distances by 23.7% on average across seven datasets.
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Towards Continuous Sign Language Conversation from Isolated Signs
Constructs continuous sign conversation data from isolated signs using retrieval and diffusion models to train a direct sign-to-sign conversational AI.
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Intervention-Based Time Series Causal Discovery via Simulator-Generated Interventional Distributions
SVAR-FM uses simulator clamping to produce interventional distributions and flow matching to identify time series causal structures, with an error bound that predicts sign reversal of causal effects below a simulator accuracy threshold.
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Curated Synthetic Data Doesn't Have to Collapse: A Theoretical Study of Generative Retraining with Pluralistic Preferences
Recursive generative retraining with heterogeneous rewards converges to a stable distribution satisfying a weighted Nash bargaining solution, preserving diversity under stated conditions.
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Debiased Counterfactual Generation via Flow Matching from Observations
Observational and counterfactual distributions are linked by identical support and invariant features, enabling a flow-matching estimator with semiparametric efficiency correction to generate debiased counterfactuals from observations.
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SDFlow: Similarity-Driven Flow Matching for Time Series Generation
SDFlow learns a global transport map via similarity-driven flow matching in VQ latent space, using low-rank manifold decomposition and a categorical posterior to handle discreteness, yielding SOTA long-horizon performance and inference speedups.
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SixthSense: Task-Agnostic Proprioception-Only Whole-Body Wrench Estimation for Humanoids
SixthSense infers whole-body contact events and wrenches in humanoids from proprioception and IMU data alone by tokenizing histories and estimating a sparse contact-event flow with conditional flow matching.
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FlowS: One-Step Motion Prediction via Local Transport Conditioning
FlowS achieves state-of-the-art single-step motion prediction on Waymo Open Motion Dataset by using scene-conditioned anchor trajectories and a step-consistent displacement field to make local transport accurate in one Euler step.
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Fisher Decorator: Refining Flow Policy via a Local Transport Map
Fisher Decorator refines flow policies in offline RL via a local transport map and Fisher-matrix quadratic approximation of the KL constraint, yielding controllable error near the optimum and SOTA benchmark results.
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Monte Carlo Event Generation with Continuous Normalizing Flows
Continuous normalizing flows improve unweighting efficiency in Monte Carlo event generation for high-jet-multiplicity collider processes by factors up to 184, with wall-time gains of about ten when combined with coupling-layer flows.
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FluxMC: Rapid and High-Fidelity Inference for Space-Based Gravitational-Wave Observations
FluxMC integrates flow matching with parallel tempering MCMC to converge in under five hours on high-fidelity IMRPhenomHM waveforms for massive black hole binaries, where standard methods fail after hundreds of hours and produce two to three orders of magnitude higher distributional error.
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MIOFlow 2.0: A unified framework for inferring cellular stochastic dynamics from single cell and spatial transcriptomics data
MIOFlow 2.0 learns stochastic cellular trajectories from transcriptomics data via neural SDEs, unbalanced optimal transport for growth, and a joint latent space unifying gene expression with spatial features.
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Flow Matching is Adaptive to Manifold Structures
Flow matching achieves near-minimax optimal statistical consistency for manifold-supported distributions, with convergence rates governed by intrinsic dimension and smoothness rather than ambient dimension.