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.
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 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.
Talker-T2AV achieves better lip-sync accuracy, video quality, and audio quality than dual-branch baselines by separating high-level shared autoregressive modeling from modality-specific low-level diffusion refinement in a joint audio-video generation framework.
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.
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.
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.
Stochastic interpolants unify flow-based and diffusion-based generative models by bridging target densities exactly via latent-variable processes whose drifts minimize quadratic objectives.
Constructs continuous sign conversation data from isolated signs using retrieval and diffusion models to train a direct sign-to-sign conversational AI.
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.
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.
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.
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.
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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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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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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Talker-T2AV: Joint Talking Audio-Video Generation with Autoregressive Diffusion Modeling
Talker-T2AV achieves better lip-sync accuracy, video quality, and audio quality than dual-branch baselines by separating high-level shared autoregressive modeling from modality-specific low-level diffusion refinement in a joint audio-video generation framework.
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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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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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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.
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Flow marching for a generative PDE foundation model
Flow Marching jointly samples noise and physical time to learn a velocity field for generative PDE modeling, paired with a latent autoencoder and efficient transformer for large-scale pretraining on 2.5M trajectories.
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Latent Stochastic Interpolants
Latent Stochastic Interpolants jointly optimize encoder-decoder and a latent-space stochastic interpolant using a continuous-time ELBO to transform arbitrary priors into aggregated posteriors.
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Fully Guided Neural Schr\"odinger bridge for Brain MR image synthesis
FGSB is a two-stage neural Schrödinger bridge that generates missing MRI modalities from limited paired data and preserves lesions via expert priors.
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From Snapshots to Trajectories: Learning Single-Cell Gene Expression Dynamics via Conditional Flow Matching
scFM learns bidirectional velocity fields from entropically regularized OT couplings between snapshots, with added alignment and regularization to reduce drift in long-horizon predictions of single-cell trajectories.
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Jointly Learning Predicates and Actions Enables Zero-Shot Skill Composition
PACTS jointly model action trajectories and predicate belief trajectories in a single generative policy, enabling zero-shot skill composition via symbolic planning without retraining.
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Divergence-Suppressing Couplings for Rectified Flow
Divergence-suppressing couplings attenuate the divergent part of the velocity field when generating training couplings for Rectified Flow, yielding straighter paths and better generation quality at no extra inference cost.
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SynVA: A Modular Toolkit for Vessel Generation and Aneurysm Editing
SynVA toolkit generates realistic vascular meshes and anatomically plausible aneurysms, releasing 50,000 labeled samples for medical vision tasks.
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PixelFlowCast: Latent-Free Precipitation Nowcasting via Pixel Mean Flows
PixelFlowCast delivers high-fidelity precipitation nowcasts from radar sequences using a latent-free Pixel Mean Flows predictor guided by a deterministic coarse stage and KANCondNet features.
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Deterministic Decomposition of Stochastic Generative Dynamics
Stochastic generative dynamics are decomposed into transport and osmotic parts via b_t = u_t + d_t, with Bridge Matching proposed to learn the components for controllable sampling.
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Trajectory-Consistent Flow Matching for Robust Visuomotor Policy Learning
Trajectory consistency training, smoothness regularization, and higher-order integration for flow matching policies deliver 60-70% success on long-horizon real-robot tasks where baselines achieve 0%.
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FluxFlow: Conservative Flow-Matching for Astronomical Image Super-Resolution
FluxFlow uses conservative pixel-space flow-matching with uncertainty weights and Wiener test-time correction to outperform baselines on photometric and scientific accuracy for ground-to-space super-resolution, validated on a new real 19,500-pair DESI-HST dataset.
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Unifying Deep Stochastic Processes for Image Enhancement
Stochastic image enhancement methods are shown to be variants of a shared SDE differing in drift, diffusion, terminal distributions and boundary conditions, with controlled experiments revealing no single dominant family and a new modular library released.
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Self-Improving Tabular Language Models via Iterative Reward-Guided Post-Training
TabGRAA applies group-relative advantage alignment in an iterative reward-guided post-training loop to improve tabular language model generators on fidelity, utility, and privacy trade-offs across five benchmarks.
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The Amazing Stability of Flow Matching
Flow matching generative models preserve sample quality, diversity, and latent representations despite pruning 50% of the CelebA-HQ dataset or altering architecture and training configurations.
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PRiMeFlow: Capturing Complex Expression Heterogeneity in Perturbation Response Modelling
PRiMeFlow applies flow matching in gene expression space with a U-Net velocity field and pretraining-finetuning to model perturbation-induced heterogeneity, showing strong benchmark performance on PerturBench and the ARC Virtual Cell Challenge.
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SubFlow: Sub-mode Conditioned Flow Matching for Diverse One-Step Generation
SubFlow restores full mode coverage in one-step flow matching by conditioning on sub-modes from semantic clustering, yielding higher diversity on ImageNet-256 while preserving FID.
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Stabilizing, Scaling & Enhancing MeanFlow for Large-scale Diffusion Distillation
Stabilizes MeanFlow for large-scale diffusion distillation via discrete warm-up and trajectory alignment, reporting better results on FLUX.1-dev and HunyuanImage 3.0.
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A Survey of Advancing Audio Super-Resolution and Bandwidth Extension from Discriminative to Generative Models
A structured survey of audio bandwidth extension that organizes the transition from deterministic discriminative DNNs to generative approaches including GANs, diffusion models, and flow-based methods.
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Flow Matching Guide and Code
Flow Matching is a generative modeling framework with mathematical foundations, design choices, extensions, and open-source PyTorch code for applications like image and text generation.
- SURGE: Approximation and Training Free Particle Filter for Diffusion Surrogate