AnyFlow enables any-step video diffusion by distilling flow-map transitions over arbitrary time intervals with on-policy backward simulation.
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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
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.
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.
Geo-Align applies RL with a perceptual reward derived from 3D camera trajectory estimation to improve controllability and fidelity in video generation without paired training data.
GenRecon lifts object-level generative priors to scene-scale reconstruction by chunking scenes and using projection-based conditioning on multi-view features, claiming 16% better results than prior methods.
VINS-120K supplies the first large-scale set of instruction-image-edited-image triplets at ultra-high resolution together with an adaptation strategy that improves detail synthesis.
VDE accelerates rectified flow models like Flux by 3.22x with LPIPS of 0.069 via velocity decomposition into parallel/orthogonal components plus periodic full-pass anchoring.
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.
JET is a conditional flow matching framework that generates EEG as continuous raw sequences with added constraints for spectral and temporal properties, achieving over 40% lower TS-FID than prior discrete denoising methods on three benchmarks.
Linear-DPO replaces sigmoid utility with linear utility and adds EMA reference to improve preference alignment in diffusion and flow-matching text-to-image models.
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.
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.
MetaEarth-MM unifies multi-modal remote sensing image generation and any-to-any translation across five modalities via scene-centered joint modeling on the new EarthMM dataset.
AdaMaG is a guidance rule for generative models derived from decomposing continuity-equation effects into divergence and score-parallel terms, with a proof that divergence diverges near the manifold and a time-dependent bound that improves realism at no extra cost.
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.
citing papers explorer
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AnyFlow: Any-Step Video Diffusion Model with On-Policy Flow Map Distillation
AnyFlow enables any-step video diffusion by distilling flow-map transitions over arbitrary time intervals with on-policy backward simulation.
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TrackCraft3R: Repurposing Video Diffusion Transformers for Dense 3D Tracking
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.
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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.
-
A-CODE: Fully Atomic Protein Co-Design with Unified Multimodal Diffusion
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.
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ReConText3D: Replay-based Continual Text-to-3D Generation
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.
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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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OP-GRPO: Efficient Off-Policy GRPO for Flow-Matching Models
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.
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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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Flow-GRPO: Training Flow Matching Models via Online RL
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.
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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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Geo-Align: Video Generation Alignment via Metric Geometry Reward
Geo-Align applies RL with a perceptual reward derived from 3D camera trajectory estimation to improve controllability and fidelity in video generation without paired training data.
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GenRecon: Bridging Generative Priors for Multi-View 3D Scene Reconstruction
GenRecon lifts object-level generative priors to scene-scale reconstruction by chunking scenes and using projection-based conditioning on multi-view features, claiming 16% better results than prior methods.
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VINS-120K: Ultra High-Resolution Image Editing with A Large-Scale Dataset
VINS-120K supplies the first large-scale set of instruction-image-edited-image triplets at ultra-high resolution together with an adaptation strategy that improves detail synthesis.
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VDE: Training-Free Accelerating Rectified Flow Model via Velocity Decomposition and Estimation
VDE accelerates rectified flow models like Flux by 3.22x with LPIPS of 0.069 via velocity decomposition into parallel/orthogonal components plus periodic full-pass anchoring.
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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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Let EEG Models Learn EEG
JET is a conditional flow matching framework that generates EEG as continuous raw sequences with added constraints for spectral and temporal properties, achieving over 40% lower TS-FID than prior discrete denoising methods on three benchmarks.
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Linear-DPO: Linear Direct Preference Optimization for Diffusion and Flow-Matching Generative Models
Linear-DPO replaces sigmoid utility with linear utility and adds EMA reference to improve preference alignment in diffusion and flow-matching text-to-image models.
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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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MetaEarth-MM: Unified Multimodal Remote Sensing Image Generation with Scene-centered Joint Modeling
MetaEarth-MM unifies multi-modal remote sensing image generation and any-to-any translation across five modalities via scene-centered joint modeling on the new EarthMM dataset.
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Probability-Conserving Flow Guidance
AdaMaG is a guidance rule for generative models derived from decomposing continuity-equation effects into divergence and score-parallel terms, with a proof that divergence diverges near the manifold and a time-dependent bound that improves realism at no extra cost.
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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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Mat\'ern Noise for Triangulation-Agnostic Flow Matching on Meshes
Proposes discretized Matérn process noise for triangulation-agnostic flow matching on meshes with PoissonNet denoiser, tested on elastic states and humanoid poses for meshes exceeding one million triangles.
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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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StableHand: Quality-Aware Flow Matching for World-Space Dual-Hand Motion Estimation from Egocentric Video
StableHand introduces a quality-aware flow matching framework conditioned on predicted four-channel per-frame hand observation quality to estimate dual-hand world-space motion from egocentric video, achieving SOTA results with 20-25% W-MPJPE reduction on HOT3D and ARCTIC benchmarks.
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Nested-GPT for variable-multiplicity parton showers: A case study in the resummation of non-global logarithms
Nested-GPT is an autoregressive Transformer surrogate that generates variable-multiplicity parton showers while enforcing ordered Markovian branching and matches reference Monte Carlo results for leading-log non-global logarithm resummation in the large-Nc limit.
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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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HASTE: Training-Free Video Diffusion Acceleration via Head-Wise Adaptive Sparse Attention
HASTE delivers up to 1.93x speedup on Wan2.1 video DiTs via head-wise adaptive sparse attention using temporal mask reuse and error-guided per-head calibration while preserving video quality.
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TeDiO: Temporal Diagonal Optimization for Training-Free Coherent Video Diffusion
TeDiO regularizes temporal diagonals in diffusion transformer attention maps to produce smoother video motion while keeping per-frame quality intact.
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Realtime-VLA FLASH: Speculative Inference Framework for Diffusion-based VLAs
A new speculative inference system speeds up diffusion VLAs to 19.1 ms average latency (3.04x faster) on LIBERO by replacing most full 58 ms inferences with 7.8 ms draft rounds while preserving task performance.
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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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OP4KSR: One-Step Patch-Free 4K Super-Resolution with Periodic Artifact Suppression
OP4KSR enables efficient one-step 4K super-resolution without patches by adapting Flux with RoPE rescaling and periodicity loss to suppress artifacts.
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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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OmniNFT: Modality-wise Omni Diffusion Reinforcement for Joint Audio-Video Generation
OmniNFT introduces modality-wise advantage routing, layer-wise gradient surgery, and region-wise loss reweighting in an online diffusion RL framework to improve audio-video quality, alignment, and synchronization.
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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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Morphologically Equivariant Flow Matching for Bimanual Mobile Manipulation
A morphologically equivariant flow matching policy for bimanual robots enforces reflective symmetry to improve sample efficiency and enable zero-shot generalization to mirrored task configurations.
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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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Zero-couplings of infinite measures with cyclically monotone support and multivariate regular variation
Existence and uniqueness of cyclically monotone zero-couplings are established for arbitrary pairs of infinite measures in M_0(R^d) under a Hausdorff-dimension condition, with the tail limit of such couplings for regularly varying distributions coinciding with the unique proper zero-coupling of the
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SABER: A Scalable Action-Based Embodied Dataset for Real-World VLA Adaptation
SABER provides 44.8K multi-representation action samples from unscripted retail environments that raise a VLA model's mean success rate on ten manipulation tasks from 13.4% to 29.3%.
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Offline Preference Optimization for Rectified Flow with Noise-Tracked Pairs
PNAPO augments preference data with prior noise pairs and uses straight-line interpolation to create a tighter surrogate objective for offline alignment of rectified flow models.
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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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From Articulated Kinematics to Routed Visual Control for Action-Conditioned Surgical Video Generation
A kinematic-to-visual lifting paradigm combined with hierarchically routed control generates action-conditioned surgical videos with better faithfulness, fidelity, and efficiency.
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ACWM-Phys: Investigating Generalized Physical Interaction in Action-Conditioned Video World Models
ACWM-Phys is a controllable simulator benchmark with in- and out-of-distribution protocols for evaluating action-conditioned world models across rigid, kinematic, deformable, and particle dynamics.
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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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One Token Per Frame: Reconsidering Visual Bandwidth in World Models for VLA Policy
Reducing visual input to one token per frame in VLA world models maintains or improves long-horizon performance on MetaWorld, LIBERO, and real-robot tasks.
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Path-Coupled Bellman Flows for Distributional Reinforcement Learning
Path-Coupled Bellman Flows use source-consistent Bellman-coupled paths and a lambda-parameterized control-variate to learn return distributions via flow matching, improving fidelity and stability over prior DRL approaches.