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.
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.
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AssetGen: Deployable 3D Asset Generation at Interactive Speed
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From Snapshots to Trajectories: Learning Single-Cell Gene Expression Dynamics via Conditional Flow Matching
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Jointly Learning Predicates and Actions Enables Zero-Shot Skill Composition
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Divergence-Suppressing Couplings for Rectified Flow
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SynVA: A Modular Toolkit for Vessel Generation and Aneurysm Editing
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PixelFlowCast: Latent-Free Precipitation Nowcasting via Pixel Mean Flows
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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
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Unifying Deep Stochastic Processes for Image Enhancement
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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
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Flow Matching Guide and Code
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