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.
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.
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.
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.
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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Unifying Deep Stochastic Processes for Image Enhancement
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Stabilizing, Scaling & Enhancing MeanFlow for Large-scale Diffusion Distillation
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