Normalizing flows are constructed by learning the velocity of a stochastic interpolant via a quadratic loss derived from its probability current, yielding an efficient ODE-based alternative to diffusion models.
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Rectified Flow: A Marginal Preserving Approach to Optimal Transport
23 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We present a flow-based approach to the optimal transport (OT) problem between two continuous distributions $\pi_0,\pi_1$ on $\mathbb{R}^d$, of minimizing a transport cost $\mathbb{E}[c(X_1-X_0)]$ in the set of couplings $(X_0,X_1)$ whose marginal distributions on $X_0,X_1$ equals $\pi_0,\pi_1$, respectively, where $c$ is a cost function. Our method iteratively constructs a sequence of neural ordinary differentiable equations (ODE), each learned by solving a simple unconstrained regression problem, which monotonically reduce the transport cost while automatically preserving the marginal constraints. This yields a monotonic interior approach that traverses inside the set of valid couplings to decrease the transport cost, which distinguishes itself from most existing approaches that enforce the coupling constraints from the outside. The main idea of the method draws from rectified flow, a recent approach that simultaneously decreases the whole family of transport costs induced by convex functions $c$ (and is hence multi-objective in nature), but is not tailored to minimize a specific transport cost. Our method is a single-object variant of rectified flow that guarantees to solve the OT problem for a fixed, user-specified convex cost function $c$.
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representative citing papers
A control-theoretic linear program yields value-driven transport policies for generative modeling with straight paths and simulation-free training.
Discrete MeanFlow parameterizes CTMC conditional transition kernels with a boundary-by-construction design to enable exact one-step generation in discrete state spaces.
A2A flow matching starts action generation from prior proprioceptive actions in latent space to enable single-step high-quality predictions in robotic policies.
A geometric latent-subspace model on Riemannian manifolds of categorical distributions enables low-dimensional generative modeling of discrete data via isometries and geometric PCA for flow 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.
DRIFT enables stable offline-to-online fine-tuning of CTMC policies in discrete RL via advantage-weighted discrete flow matching, path-space regularization, and candidate-set approximation.
Discrete flow matching on Z_m^d achieves non-asymptotic KL bounds for early-stopped targets and explicit TV convergence to the true target under an approximation error assumption, with improved scaling in dimension d and vocabulary size m.
Embedding Loss aligns feature distributions via MMD in random network embeddings to boost one-step diffusion distillation, reaching SOTA FID of 1.475 on CIFAR-10 unconditional generation.
Pose-VLA uses a decoupled two-stage pre-training with discrete pose tokens to extract universal 3D spatial priors from 3D datasets and robotic trajectories, achieving 79.5% success on RoboTwin 2.0 and 96.0% on LIBERO.
SPEAR-1 combines a 3D-enriched VLM with embodied control to match or exceed existing robotic foundation models using 20 times fewer robot demonstrations.
SmolVLA is a small efficient VLA model that achieves performance comparable to 10x larger models while training on one GPU and deploying on consumer hardware via community data and chunked asynchronous action prediction.
π_{0.5} is a VLA model that achieves long-horizon dexterous manipulation in entirely new homes through co-training on heterogeneous tasks and multi-source data including web and semantic predictions.
GenFocal uses probabilistic ML to downscale coarse climate projections to fine-scale weather events without paired training data and samples rare high-impact events more accurately than prior methods.
π₀ is a vision-language-action flow model trained on diverse multi-platform robot data that supports zero-shot task performance, language instruction following, and efficient fine-tuning for dexterous tasks.
C²FG provides a time-dependent guidance controller for diffusion models derived from score discrepancy upper bounds, implemented as an exponential decay function without retraining.
GR-3 is a VLA model that generalizes to novel objects, environments, and abstract instructions, outperforms the π0 baseline, and integrates with the new ByteMini bi-manual mobile robot.
Category theory proves prompt-based learning on perfect foundation models works only for representable tasks, fine-tuning solves tasks in the pretext category, and models can represent unseen target-category objects using source-category structure.
OmniVLA-RL uses a mix-of-transformers architecture and flow-matching reformulated as SDE with group segmented policy optimization to surpass prior VLA models on LIBERO benchmarks.
Generative models via pushforward maps, Fokker-Planck equations, and Wasserstein geometry enable learning nominal uncertainty, stressed distributions for robustness, and conditional posteriors under distributional shift.
A mathematical review of flow matching techniques for generative models, showing characterizations via couplings, kernels, and processes, with application to inverse problems.
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Building Normalizing Flows with Stochastic Interpolants
Normalizing flows are constructed by learning the velocity of a stochastic interpolant via a quadratic loss derived from its probability current, yielding an efficient ODE-based alternative to diffusion models.
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Generative Modeling by Value-Driven Transport
A control-theoretic linear program yields value-driven transport policies for generative modeling with straight paths and simulation-free training.
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Discrete MeanFlow: One-Step Generation via Conditional Transition Kernels
Discrete MeanFlow parameterizes CTMC conditional transition kernels with a boundary-by-construction design to enable exact one-step generation in discrete state spaces.
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Action-to-Action Flow Matching
A2A flow matching starts action generation from prior proprioceptive actions in latent space to enable single-step high-quality predictions in robotic policies.
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Generative Modeling of Discrete Data Using Geometric Latent Subspaces
A geometric latent-subspace model on Riemannian manifolds of categorical distributions enables low-dimensional generative modeling of discrete data via isometries and geometric PCA for flow 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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Discrete Flow Matching for Offline-to-Online Reinforcement Learning
DRIFT enables stable offline-to-online fine-tuning of CTMC policies in discrete RL via advantage-weighted discrete flow matching, path-space regularization, and candidate-set approximation.
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Discrete Flow Matching: Convergence Guarantees Under Minimal Assumptions
Discrete flow matching on Z_m^d achieves non-asymptotic KL bounds for early-stopped targets and explicit TV convergence to the true target under an approximation error assumption, with improved scaling in dimension d and vocabulary size m.
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Efficient Diffusion Distillation via Embedding Loss
Embedding Loss aligns feature distributions via MMD in random network embeddings to boost one-step diffusion distillation, reaching SOTA FID of 1.475 on CIFAR-10 unconditional generation.
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Universal Pose Pretraining for Generalizable Vision-Language-Action Policies
Pose-VLA uses a decoupled two-stage pre-training with discrete pose tokens to extract universal 3D spatial priors from 3D datasets and robotic trajectories, achieving 79.5% success on RoboTwin 2.0 and 96.0% on LIBERO.
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SPEAR-1: Scaling Beyond Robot Demonstrations via 3D Understanding
SPEAR-1 combines a 3D-enriched VLM with embodied control to match or exceed existing robotic foundation models using 20 times fewer robot demonstrations.
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SmolVLA: A Vision-Language-Action Model for Affordable and Efficient Robotics
SmolVLA is a small efficient VLA model that achieves performance comparable to 10x larger models while training on one GPU and deploying on consumer hardware via community data and chunked asynchronous action prediction.
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$\pi_{0.5}$: a Vision-Language-Action Model with Open-World Generalization
π_{0.5} is a VLA model that achieves long-horizon dexterous manipulation in entirely new homes through co-training on heterogeneous tasks and multi-source data including web and semantic predictions.
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Regional climate risk assessment from climate models using probabilistic machine learning
GenFocal uses probabilistic ML to downscale coarse climate projections to fine-scale weather events without paired training data and samples rare high-impact events more accurately than prior methods.
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$\pi_0$: A Vision-Language-Action Flow Model for General Robot Control
π₀ is a vision-language-action flow model trained on diverse multi-platform robot data that supports zero-shot task performance, language instruction following, and efficient fine-tuning for dexterous tasks.
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C$^2$FG: Control Classifier-Free Guidance via Score Discrepancy Analysis
C²FG provides a time-dependent guidance controller for diffusion models derived from score discrepancy upper bounds, implemented as an exponential decay function without retraining.
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GR-3 Technical Report
GR-3 is a VLA model that generalizes to novel objects, environments, and abstract instructions, outperforms the π0 baseline, and integrates with the new ByteMini bi-manual mobile robot.
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On the Power of Foundation Models
Category theory proves prompt-based learning on perfect foundation models works only for representable tasks, fine-tuning solves tasks in the pretext category, and models can represent unseen target-category objects using source-category structure.
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OmniVLA-RL: A Vision-Language-Action Model with Spatial Understanding and Online RL
OmniVLA-RL uses a mix-of-transformers architecture and flow-matching reformulated as SDE with group segmented policy optimization to surpass prior VLA models on LIBERO benchmarks.
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Generative models for decision-making under distributional shift
Generative models via pushforward maps, Fokker-Planck equations, and Wasserstein geometry enable learning nominal uncertainty, stressed distributions for robustness, and conditional posteriors under distributional shift.
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Flow Matching: Markov Kernels, Stochastic Processes and Transport Plans
A mathematical review of flow matching techniques for generative models, showing characterizations via couplings, kernels, and processes, with application to inverse problems.
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