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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Building Normalizing Flows with Stochastic Interpolants
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abstract
A generative model based on a continuous-time normalizing flow between any pair of base and target probability densities is proposed. The velocity field of this flow is inferred from the probability current of a time-dependent density that interpolates between the base and the target in finite time. Unlike conventional normalizing flow inference methods based the maximum likelihood principle, which require costly backpropagation through ODE solvers, our interpolant approach leads to a simple quadratic loss for the velocity itself which is expressed in terms of expectations that are readily amenable to empirical estimation. The flow can be used to generate samples from either the base or target, and to estimate the likelihood at any time along the interpolant. In addition, the flow can be optimized to minimize the path length of the interpolant density, thereby paving the way for building optimal transport maps. In situations where the base is a Gaussian density, we also show that the velocity of our normalizing flow can also be used to construct a diffusion model to sample the target as well as estimate its score. However, our approach shows that we can bypass this diffusion completely and work at the level of the probability flow with greater simplicity, opening an avenue for methods based solely on ordinary differential equations as an alternative to those based on stochastic differential equations. Benchmarking on density estimation tasks illustrates that the learned flow can match and surpass conventional continuous flows at a fraction of the cost, and compares well with diffusions on image generation on CIFAR-10 and ImageNet $32\times32$. The method scales ab-initio ODE flows to previously unreachable image resolutions, demonstrated up to $128\times128$.
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- abstract A generative model based on a continuous-time normalizing flow between any pair of base and target probability densities is proposed. The velocity field of this flow is inferred from the probability current of a time-dependent density that interpolates between the base and the target in finite time. Unlike conventional normalizing flow inference methods based the maximum likelihood principle, which require costly backpropagation through ODE solvers, our interpolant approach leads to a simple quadratic loss for the velocity itself which is expressed in terms of expectations that are readily ame
co-cited works
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.
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.
MF-PID turns independent diffusion samples into mean-field interacting agents, proving that quadratic interactions yield exact linear mean interpolation and delivering 19-24% energy savings in demand-response control.
Active lifting of data distributions via latent-sequence sampling and max-rate uncertainty reduction formally derives slow-thinking LLMs and places them on representation and sampler hierarchies that can be climbed.
Proposes diffeomorphic optimization for manifold-constrained problems in generative models via flow maps, with Lie-group extensions for protein design showing metric improvements.
OTF-CBM replaces static cosine similarity in vision-language CBMs with data-driven optimal transport flow to improve concept alignment, accuracy, and faithfulness.
Provides a posterior-transport analysis of flow-based inverse solvers, demonstrating that source reweighting yields exact posteriors while trajectory guidance methods are zeroth-order/Gaussian/proximal approximations incurring Wasserstein bias, and proposes a competitive velocity-correction solver.
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.
FTM learns the probability current velocity from trajectories to deliver fast, trajectory-aware ensemble predictions for stochastic dynamical systems and PDEs.
Recasts covariance shrinkage as risk minimization over stochastic interpolants between distributions, recovering known estimators via scheduling, couplings, and early stopping, and proposing a neural estimator with quadratic risk bounds.
By designing the prior as the low-frequency projection of data images, flow matching achieves OT-optimal identity couplings without explicit OT computation, reducing trajectory curvature over 2x and improving few-step quality.
A two-stage diffusion framework decomposes MAP inference for MIMO-FAS into continuous-flow channel estimation and discrete diffusion port selection, claiming superior accuracy and rates via simulations.
Orthogonal Negative Guidance subtracts only the orthogonal component of negative-prompt attention features from positive ones in FLUX models to suppress concepts while preserving semantics and quality.
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.
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.
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.
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.
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
A general framework reduces flow matching on symmetric spaces to flow matching on a Lie algebra subspace, linearizing geodesics.
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.
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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.
FMA introduces flow matching for multi-step cross-modal feature alignment in few-shot learning, using fixed coupling, noise augmentation, and early-stopping to outperform one-step PEFT methods.
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.
-
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.
-
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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Mean-Field Path-Integral Diffusion: From Samples to Interacting Agents
MF-PID turns independent diffusion samples into mean-field interacting agents, proving that quadratic interactions yield exact linear mean interpolation and delivering 19-24% energy savings in demand-response control.
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A First-Principles Theory of Slow Thinking and Active Perception
Active lifting of data distributions via latent-sequence sampling and max-rate uncertainty reduction formally derives slow-thinking LLMs and places them on representation and sampler hierarchies that can be climbed.
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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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Bridging Vision and Language Concepts through Optimal Transport Semantic Flow
OTF-CBM replaces static cosine similarity in vision-language CBMs with data-driven optimal transport flow to improve concept alignment, accuracy, and faithfulness.
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What Do Flow-Based Inverse Solvers Approximate? A Posterior-Transport View
Provides a posterior-transport analysis of flow-based inverse solvers, demonstrating that source reweighting yields exact posteriors while trajectory guidance methods are zeroth-order/Gaussian/proximal approximations incurring Wasserstein bias, and proposes a competitive velocity-correction solver.
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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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First-Order Trajectory Matching: Fast Ensemble Predictions of Chaotic, Turbulent, Stochastic Systems
FTM learns the probability current velocity from trajectories to deliver fast, trajectory-aware ensemble predictions for stochastic dynamical systems and PDEs.
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Covariance Shrinkage via Stochastic Interpolation
Recasts covariance shrinkage as risk minimization over stochastic interpolants between distributions, recovering known estimators via scheduling, couplings, and early stopping, and proposing a neural estimator with quadratic risk bounds.
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Optimal Transport Flow Matching by Design
By designing the prior as the low-frequency projection of data images, flow matching achieves OT-optimal identity couplings without explicit OT computation, reducing trajectory curvature over 2x and improving few-step quality.
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A Unified Two-Stage Generative Diffusion Framework for Channel Estimation and Port Selection in Multiuser MIMO-FAS
A two-stage diffusion framework decomposes MAP inference for MIMO-FAS into continuous-flow channel estimation and discrete diffusion port selection, claiming superior accuracy and rates via simulations.
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Orthogonal Negative Guidance in Attention Feature Space for Text-to-Image Generation
Orthogonal Negative Guidance subtracts only the orthogonal component of negative-prompt attention features from positive ones in FLUX models to suppress concepts while preserving semantics and quality.
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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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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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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.
-
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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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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Flow Matching on Symmetric Spaces
A general framework reduces flow matching on symmetric spaces to flow matching on a Lie algebra subspace, linearizing geodesics.
-
Generative Modeling with Orbit-Space Particle Flow Matching
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.
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GVCC: Zero-Shot Video Compression via Codebook-Driven Stochastic Rectified Flow
GVCC achieves the lowest LPIPS on UVG at bitrates down to 0.003 bpp by encoding stochastic innovations in a marginal-preserving stochastic process derived from a pretrained rectified-flow video model, with 65% LPIPS reduction over DCVC-RT.
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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.
-
Exploring Cross-Modal Flows for Few-Shot Learning
FMA introduces flow matching for multi-step cross-modal feature alignment in few-shot learning, using fixed coupling, noise augmentation, and early-stopping to outperform one-step PEFT methods.
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Steering Your Diffusion Policy with Latent Space Reinforcement Learning
DSRL steers pretrained diffusion policies for robotics by applying RL to their latent noise inputs, achieving sample-efficient real-world adaptation with only black-box access.
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In-context Region-based Drag: Drag Any Region to Any Shape
ICRDrag performs region-based drag editing in diffusion models by feeding source image, source mask, and target mask into an in-context framework with image-mask attention consistency and source-target attention correspondence regularizations, plus a new Paired Region Dataset.
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EAGG: Embodiment-Aligned Grasp Generation via Geometry-Aware Graph Conditioning
EAGG uses embodiment-specific graphs and iterative geometry injection in a shared generator to achieve 56.17% average success across six end-effectors on MultiGripperGrasp, within 1.10 pp of specialized models.
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Flexible Flows for Biological Sequence Design
Enhances Discrete Flow Matching with domain-specific couplings, latent edit-based rates, latent classifier-free guidance, and temperature scaling to reach SOTA on DNA and peptide sequence tasks.
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A Theory on Flow Matching with Neural Networks
Establishes convergence guarantees for overparameterized 2-layer ReLU networks in flow matching, generalization bounds for the velocity-field objective, and Wasserstein guarantees for generated samples, using multi-task representation learning bounds.
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Reactive Flux Matching: Mechanism Discovery and Adaptive Sampling of Rare Events
Flux Matching learns current velocity u(z) and scalar potential h(z) from reactive trajectories via quadratic minimization to trace pathways and provide reaction coordinates for adaptive sampling.
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ReCache: Learning Budget-Aware Caching Schedules for Diffusion Models via REINFORCE
ReCache learns recomputation schedules via policy gradients to maximize quality under a target compute budget for any caching mechanism in diffusion models.
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Spectral-Progressive Thought Flow for Lightweight Multimodal Reasoning
SpecFlow represents intermediate visual thoughts in fixed-size DCT space and uses classifier-free guidance to steer updates from textual thoughts, achieving up to 2.1x lower computation and KV cache costs.
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Colored Noise Diffusion Sampling
CNS is a plug-and-play stochastic sampler for diffusion models that uses timestep- and frequency-dependent colored noise to allocate energy to unresolved bands, producing lower FID scores than standard ODE/SDE baselines on ImageNet-256.
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SCRIPT: Scalable Diffusion Policy with Multi-stage Training for Language-driven Physics-based Humanoid Control
SCRIPT presents a scalable diffusion policy with JAST-DiT architecture, nonlinear history conditioning, and RLHR post-training that claims to outperform prior methods on text alignment, motion quality, and physical realism while scaling on a 1200-hour dataset.
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Spatial Gram Alignment for Ultra-High-Resolution Image Synthesis
Spatial Gram Alignment aligns internal self-similarities of LDM features with foundation priors to reconcile global structure and fine details in ultra-high-resolution text-to-image synthesis.
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DEFLECT: Delay-Robust Execution via Flow-matching Likelihood-Estimated Counterfactual Tuning for VLA Policies
DEFLECT is an offline post-training method that improves async VLA policy success rates under high inference delays by using flow-matching likelihood ratios on counterfactual fresh/stale action pairs from a frozen reference policy.
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WavFlow: Audio Generation in Waveform Space
WavFlow performs direct waveform audio generation via flow matching on 2D token grids from raw patches plus amplitude lifting, matching latent-based methods on VGGSound and AudioCaps without intermediate compression.
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SURGE: Approximation and Training Free Particle Filter for Diffusion Surrogate
SURGE is an unbiased particle filter that fuses diffusion-model simulations with noisy observations via sequential Monte Carlo reweighting over diffusion trajectories.
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Vision Foundation Models as Generalist Tokenizers for Image Generation
VFMTok builds a generalist image tokenizer on frozen VFMs using adaptive quantization and semantic alignment, delivering gFID 1.36 for autoregressive and 1.25 for continuous generation on ImageNet with 3x faster convergence.
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Simple Approximation and Derivative Free Inference-Time Scaling for Diffusion Models via Sequential Monte Carlo on Path Measures
URGE performs unbiased inference-time scaling for diffusion models by attaching multiplicative path weights from Girsanov estimation and resampling trajectories, with a proven equivalence to prior particle-wise SMC schemes.
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Aligning Latent Geometry for Spherical Flow Matching in Image Generation
Projecting VAE latents to a fixed spherical radius and replacing linear interpolation with spherical linear interpolation improves class-conditional ImageNet-256 FID while leaving the diffusion architecture unchanged.
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One-Step Generative Modeling via Wasserstein Gradient Flows
W-Flow compresses a Wasserstein gradient flow defined via Sinkhorn divergence into a single-step neural generator, reporting 1.29 FID on ImageNet 256x256 with improved mode coverage.
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HorizonDrive: Self-Corrective Autoregressive World Model for Long-horizon Driving Simulation
HorizonDrive is a new anti-drifting autoregressive training and distillation method that enables minute-scale stable driving video rollouts by making the teacher model rollout-capable via scheduled rollout recovery and teacher rollout DMD.
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Intervention-Based Time Series Causal Discovery via Simulator-Generated Interventional Distributions
SVAR-FM uses simulator clamping to produce interventional distributions and flow matching to identify time series causal structures, with an error bound that predicts sign reversal of causal effects below a simulator accuracy threshold.
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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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Conservative Flows: A New Paradigm of Generative Models
Conservative flows generate by running probability-preserving stochastic dynamics initialized at data points rather than noise, using corrected Langevin or predictor-corrector mechanisms on top of any pretrained flow model and showing gains on Swiss-roll, ImageNet-256 and Oxford Flowers-102.
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SDFlow: Similarity-Driven Flow Matching for Time Series Generation
SDFlow learns a global transport map via similarity-driven flow matching in VQ latent space, using low-rank manifold decomposition and a categorical posterior to handle discreteness, yielding SOTA long-horizon performance and inference speedups.
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Towards Efficient and Expressive Offline RL via Flow-Anchored Noise-conditioned Q-Learning
FAN simplifies expressive flow policies and distributional critics in offline RL via single-iteration behavior regularization and single-sample noise conditioning to claim SOTA performance with lower training and inference time.
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Quantum Dynamics via Score Matching on Bohmian Trajectories
Neural networks learn the score of the probability density on Bohmian trajectories to recover exact Schrödinger dynamics via self-consistent minimization for nodeless wave functions, demonstrated on double-well splitting and Morse chain vibrations.
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Fisher Decorator: Refining Flow Policy via a Local Transport Map
Fisher Decorator refines flow policies in offline RL via a local transport map and Fisher-matrix quadratic approximation of the KL constraint, yielding controllable error near the optimum and SOTA benchmark results.