TAKO demonstrates real-time adversarial takeover of robotic diffusion policies via reusable universal patches on visual inputs, achieving 100% success in steering attacker-chosen trajectories across multiple tasks, encoders, and diffusion methods.
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Flow Matching for Generative Modeling
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abstract
We introduce a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale. Specifically, we present the notion of Flow Matching (FM), a simulation-free approach for training CNFs based on regressing vector fields of fixed conditional probability paths. Flow Matching is compatible with a general family of Gaussian probability paths for transforming between noise and data samples -- which subsumes existing diffusion paths as specific instances. Interestingly, we find that employing FM with diffusion paths results in a more robust and stable alternative for training diffusion models. Furthermore, Flow Matching opens the door to training CNFs with other, non-diffusion probability paths. An instance of particular interest is using Optimal Transport (OT) displacement interpolation to define the conditional probability paths. These paths are more efficient than diffusion paths, provide faster training and sampling, and result in better generalization. Training CNFs using Flow Matching on ImageNet leads to consistently better performance than alternative diffusion-based methods in terms of both likelihood and sample quality, and allows fast and reliable sample generation using off-the-shelf numerical ODE solvers.
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- abstract We introduce a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale. Specifically, we present the notion of Flow Matching (FM), a simulation-free approach for training CNFs based on regressing vector fields of fixed conditional probability paths. Flow Matching is compatible with a general family of Gaussian probability paths for transforming between noise and data samples -- which subsumes existing diffusion paths as specific instances. Interestingly, we find that employing FM with diffusion paths results in a more
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representative citing papers
WavTTS is the first raw-waveform diffusion TTS model using DiT flow matching and multi-scale mel supervision that approaches SOTA latent zero-shot performance while beating prior end-to-end models.
AnyFlow enables any-step video diffusion by distilling flow-map transitions over arbitrary time intervals with on-policy backward simulation.
TrackCraft3R is the first method to repurpose a video diffusion transformer as a feed-forward dense 3D tracker via dual-latent representations and temporal RoPE alignment, achieving SOTA performance with lower compute.
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.
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.
A-CODE presents a fully atomic one-stage multimodal diffusion model for protein co-design that claims superior unconditional generation performance over prior one- and two-stage models plus a tenfold success-rate gain on hard binder-design tasks.
Derives closed-form posterior covariance for flow matching from divergence of velocity field, enabling post-hoc uncertainty on pre-trained models including one-step generators.
FMRG reformulates guidance as deterministic optimal control, deriving a single-trajectory method using the flow map that matches or exceeds baselines on reward-guided generation and inverse problems with 3 NFEs at text-to-image scale.
ReConText3D is the first replay-memory framework for continual text-to-3D generation that prevents catastrophic forgetting on new textual categories while preserving quality on previously seen classes.
Diffusion sampling from d-dimensional distributions requires at least ~sqrt(d) adaptive score queries when score estimates have polynomial accuracy.
OP-GRPO is the first off-policy GRPO method for flow-matching models that reuses trajectories via replay buffer and importance sampling corrections, matching on-policy performance with 34.2% of the training steps.
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.
Flow-GRPO is the first online RL method for flow matching models, raising GenEval accuracy from 63% to 95% and text-rendering accuracy from 59% to 92% with little reward hacking.
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.
QWERTY enables training-free motion control in pretrained image-to-video DiTs by warping the frame-invariant semantic subspace of queries in 3D full attention and using the predicted noise as self-guidance for latent optimization.
Proposes diffeomorphic optimization for manifold-constrained problems in generative models via flow maps, with Lie-group extensions for protein design showing metric improvements.
Self-conditioned flow language models solve fixed-point iterations, enabling fixed-point flow maps that distill into FMLM* which outperforms SOTA in few-step generation on OpenWebText.
Flow-Map GRPO uses anchored stochastic flow map composition to enable GRPO-based RL alignment of deterministic few-step flow-map generators while preserving their marginal paths.
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.
OOPSIEVERSE is a new damage-aware simulation benchmark for household robot manipulation that converts contact, thermal, and fluid signals into task-agnostic damage metrics and demonstrates uses in safer policy learning and benchmarking.
FlexiSLM is the first spoken language model supporting dynamic and controllable frame rates on speech input and output, outperforming fixed-rate 7B models at high quality and enabling faster inference at lower rates like 6.25 Hz.
MUSE shows that the native timestep embedding in diffusion models acts as a parameter-free steering signal for multi-task monocular depth and normal estimation via manifold decoupling in latent space.
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.
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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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Divergence is Uncertainty: A Closed-Form Posterior Covariance for Flow Matching
Derives closed-form posterior covariance for flow matching from divergence of velocity field, enabling post-hoc uncertainty on pre-trained models including one-step generators.
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How to Guide Your Flow: Few-Step Alignment via Flow Map Reward Guidance
FMRG reformulates guidance as deterministic optimal control, deriving a single-trajectory method using the flow map that matches or exceeds baselines on reward-guided generation and inverse problems with 3 NFEs at text-to-image scale.
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Query Lower Bounds for Diffusion Sampling
Diffusion sampling from d-dimensional distributions requires at least ~sqrt(d) adaptive score queries when score estimates have polynomial accuracy.
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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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Diffeomorphic Optimization
Proposes diffeomorphic optimization for manifold-constrained problems in generative models via flow maps, with Lie-group extensions for protein design showing metric improvements.
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Flow-Map GRPO: Reinforcement Learning for Few-Step Flow-Map Generators via Anchored Stochastic Composition
Flow-Map GRPO uses anchored stochastic flow map composition to enable GRPO-based RL alignment of deterministic few-step flow-map generators while preserving their marginal paths.
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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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Execution-State Capsules: Graph-Bound Execution-State Checkpoint and Restore for Low-Latency, Small-Batch, On-Device Physical-AI Serving
Execution-state capsules enable graph-bound full-state checkpointing and sub-millisecond restore for LLMs including KV and recurrent states, yielding 3.9x-27x TTFT speedups in on-device physical-AI serving.
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The Reward Was in Your Data All Along: Correcting Flow Matching with Discriminator-Guided RL
DRL trains a discriminator on data versus base-model samples in pretrained representation space and uses its logit as reward in KL-regularized RL, cutting guidance-free FID from 9.38 to 2.62 on SiT and similar gains on other backbones.
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Net-Ev$^2$: A Generative Simulator for Network Event Evolution
Net-Ev² proposes a two-stage generative simulator with structure-guided masked pre-training and topology-aware diffusion using graph U-Net down/upsampling to model network event evolution from text inputs, plus a new 6.5M multimodal benchmark and JL-MMD metric.
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Flow Matching with In-Context Priors for Out-of-Distribution Brain Dynamics
A per-timestep conditioned diffusion transformer generates realistic fMRI dynamics for unseen cognitive tasks by injecting compositional language and optional spatial priors in-context.
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Spectrally Regularized Latent Flow Matching for Turbulence Generation
Spectrally regularized compression in latent flow matching raises retained deep-dissipation spectral power from 20% to 79% in generated turbulence on a 256^2 DNS dataset at Re_f ≈ 2250.
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Test-Time Gradient Guidance of Flow Policies in Reinforcement Learning
QGF performs test-time policy optimization for flow models in RL by guiding a behavior-cloned reference policy with value-function gradients, achieving strong results on high-dimensional offline RL benchmarks without additional policy training.
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Reinforcement Learning for Flow-Matching Policies with Density Transport
RLDT fine-tunes pretrained flow-matching policies for continuous control by aligning them to a max-entropy RL transport field constructed via SVGD, using expected-target estimation for stable multi-step updates.
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Balancing Image Compression and Generation with Bootstrapped Tokenization
SelfBootTok decomposes image tokens into global and local groups via self-bootstrapped learning, enabling generators to use only global tokens for ~40% less computation and a new SOTA gFID of 1.56 with 64 tokens.
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Midpoint Generative Models
Midpoint Generative Models define a midpoint divergence from flow matching symmetry and derive its variational form as a tractable objective for training competitive one-step generators.
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Spectral Guidance for Flexible and Efficient Control of Diffusion Models
Spectral Guidance learns singular functions via self-supervised objective to project guidance signals onto diffusion sampling trajectories, enabling stable control without retraining or backpropagation and improving CIFAR-10 accuracy by 37 points with 4x faster sampling.
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Parameter-Efficient Generative Modeling with Controlled Vector Fields
Presents a controlled vector field framework for continuous generative modeling where velocity is formed from fixed bracket-generating fields modulated by scalar controls, with an expressivity principle under controllability assumptions.
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Beyond the Bellman Recursion: A Pontryagin-Guided Framework for Non-Exponential Discounting
PG-DPO is a new variational framework that replaces Bellman recursion with a Pontryagin-guided adjoint-MC projection for RL under non-exponential discounting and shows gains on hyperbolic and survival benchmarks.
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CAdam: Context-Adaptive Moment Estimation for 3D Gaussian Densification in Generative Distillation
CAdam reinterprets densification in generative 3DGS as signal verification via gradient-moment interference, quantile context, and SNR gating to achieve large reductions in primitive count with comparable quality.
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Inference-Time Scaling in Diffusion Models through Iterative Partial Refinement
IPR improves valid solution rates on MNIST Sudoku from 55.8% to 75.0% by iteratively refining partial regions in sequential diffusion models without external verifiers or reward models.
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Rethinking Muon Beyond Pretraining: Spectral Failures and High-Pass Remedies for VLA and RLVR
Pion modifies Muon's Newton-Schulz iterations into a controllable high-pass filter that anchors dominant singular values at 1 while suppressing noisy tails, outperforming Muon and AdamW in VLA and RLVR regimes.
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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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A Mutual Information Lower Bound for Multimodal Regression Active Learning
Derives MI-LB acquisition function from mutual information in a two-index epistemic-aleatoric framework and shows it outperforms baselines on multimodal regression benchmarks.
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Sampling from Flow Language Models via Marginal-Conditioned Bridges
Marginal-conditioned bridges enable training-free sampling from Flow Language Models by drawing clean one-hot endpoints from factorized posteriors and using Ornstein-Uhlenbeck bridges, preserving token marginals and reducing denoising error versus conditional-mean bridges.
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Constraint-Aware Flow Matching: Decision Aligned End-to-End Training for Constrained Sampling
Constraint-Aware Flow Matching integrates constraint projections into the flow matching training objective to align model dynamics with constrained sampling and reduce distributional shift.
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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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Physics-Informed Neural PDE Solvers via Spatio-Temporal MeanFlow
Spatio-Temporal MeanFlow adapts MeanFlow to PDEs by replacing the generative velocity field with the physical operator and extending the integral constraint to the spatio-temporal domain, yielding a unified solver for time-dependent and stationary equations with improved accuracy and generalization.
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Generative Actor-Critic with Soft Bridge Policies
SoftGAC defines a stochastic bridge from base to action latent that converts the MaxEnt objective into a tractable relative-entropy term reducible to control energy, achieving competitive returns with one-pass sampling.
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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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Geometry-Aware Discretization Error of Diffusion Models
First-order asymptotic expansions of weak and Fréchet discretization errors in diffusion sampling are derived, explicit under Gaussian data through covariance geometry and robust to other data geometries.
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Arbitrarily Conditioned Hierarchical Flows for Spatiotemporal Events
ARCH is a hierarchical flow-based generative model that enables tractable conditional intensity computation and arbitrary conditioning for spatiotemporal event distributions.
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ABC: Any-Subset Autoregression via Non-Markovian Diffusion Bridges in Continuous Time and Space
ABC enables any-subset autoregressive generation of continuous stochastic processes via non-Markovian diffusion bridges that track physical time and allow path-dependent conditioning.
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Frequency-Forcing: From Scaling-as-Time to Soft Frequency Guidance
Frequency-Forcing guides pixel flow-matching with a data-derived low-frequency auxiliary stream to softly enforce scale-ordered generation, improving FID on ImageNet-256 over baselines.
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Guiding Distribution Matching Distillation with Gradient-Based Reinforcement Learning
GDMD replaces raw-sample rewards with distillation-gradient rewards in RL-guided diffusion distillation, yielding 4-step models that surpass their multi-step teachers on GenEval and human preference metrics.
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${\pi}_{0.7}$: a Steerable Generalist Robotic Foundation Model with Emergent Capabilities
π₀.₇ is a steerable generalist robotic model that uses rich multimodal prompts including language, subgoal images, and performance metadata to achieve out-of-the-box generalization across tasks and robot bodies.
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Reinforcement Learning via Value Gradient Flow
VGF solves behavior-regularized RL by transporting particles from a reference distribution to the value-induced optimal policy via discrete value-guided gradient flow.
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Isokinetic Flow Matching for Pathwise Straightening of Generative Flows
Isokinetic Flow Matching adds a lightweight regularization term to flow matching that penalizes acceleration along paths via self-guided finite differences, yielding straighter trajectories and large gains in few-step sampling quality on CIFAR-10.
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SetFlow: Generating Structured Sets of Representations for Multiple Instance Learning
SetFlow is a flow-matching generative model for permutation-invariant MIL bags in representation space that produces synthetic data improving classification performance and enabling training on synthetic data alone.
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From Baselines to Transport Geodesics: Axiomatic Attribution via Optimal Generative Flows
Transport-geodesic attribution via optimal generative flows selects principled paths for feature attributions by minimizing kinetic action.
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QuantVLA: Scale-Calibrated Post-Training Quantization for Vision-Language-Action Models
QuantVLA is the first post-training quantization framework for VLA models that quantizes the diffusion transformer action head and reports higher task success rates than full-precision baselines with roughly 70% memory savings on the quantized components.
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SplineFlow: Flow Matching for Dynamical Systems with B-Spline Interpolants
SplineFlow uses B-spline interpolation inside flow matching to jointly construct stable conditional paths that satisfy multi-marginal constraints for dynamical systems with irregular observations.
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DiffusionNFT: Online Diffusion Reinforcement with Forward Process
DiffusionNFT performs online RL for diffusion models on the forward process via flow matching and positive-negative contrasts, delivering up to 25x efficiency gains and rapid benchmark improvements over prior reverse-process methods.
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An Analytical Theory of Spectral Bias in the Learning Dynamics of Diffusion Models
Analytic solution of full-batch gradient flow for linear and convolutional denoisers in diffusion models yields a universal inverse-variance spectral law for learning times of eigenmodes.
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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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One Step Diffusion via Shortcut Models
Shortcut models enable high-quality single or few-step sampling in diffusion models with one network and training phase by conditioning on desired step size.
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Optimizing Visual Generative Models via Distribution-wise Rewards
Distribution-wise rewards with subset-replace strategy and post-hoc merging improve FID-50K on SiT (8.30 to 5.77) and EDM2 (3.74 to 3.52) while preserving diversity.
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Sequentially-Controlled Interactive Multi-Particle Flow-Maps for Online Feedback-Driven Search
IMPFM is a multi-particle flow-map sampling method with sequential posterior sharing and interaction-aware correction that targets a KL-tilted distribution for global exploration in online feedback search.