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
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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.
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.
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.
UniGeo unifies geometric guidance across three levels in video models to reduce geometric drift and improve consistency in camera-controllable image editing.
A conditional diffusion model using proprioception and multi-contact touch produces metric-scale, physically consistent 3D object reconstructions under hand occlusion.
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.
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.
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.
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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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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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.
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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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.
-
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.
-
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.
-
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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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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UniGeo: Unifying Geometric Guidance for Camera-Controllable Image Editing via Video Models
UniGeo unifies geometric guidance across three levels in video models to reduce geometric drift and improve consistency in camera-controllable image editing.
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Physically Grounded 3D Generative Reconstruction under Hand Occlusion using Proprioception and Multi-Contact Touch
A conditional diffusion model using proprioception and multi-contact touch produces metric-scale, physically consistent 3D object reconstructions under hand occlusion.
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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.
-
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.
-
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.
-
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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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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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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Free Energy Surface Sampling via Reduced Flow Matching
FES-FM applies reduced flow matching with a Hessian-derived prior to directly sample free energy surfaces in collective variable space, claiming lower computational cost and higher accuracy per unit time than standard methods.
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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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Allo{SR}$^2$: Rectifying One-Step Super-Resolution to Stay Real via Allomorphic Generative Flows
Allo{SR}^2 rectifies one-step super-resolution trajectories with allomorphic generative flows via SNR initialization, velocity supervision, and self-adversarial matching to deliver state-of-the-art fidelity and realism.
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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.
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Frequency-Aware Flow Matching for High-Quality Image Generation
FreqFlow introduces frequency-aware conditioning and a two-branch architecture to flow matching, reaching FID 1.38 on ImageNet-256 and outperforming DiT and SiT.
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LiveMoments: Reselected Key Photo Restoration in Live Photos via Reference-guided Diffusion
LiveMoments restores reselected key photos in Live Photos via reference-guided diffusion and motion alignment, yielding higher perceptual quality and fidelity than prior methods especially under fast motion.
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Region-Constrained Group Relative Policy Optimization for Flow-Based Image Editing
RC-GRPO-Editing constrains GRPO exploration to editing regions via localized noise and attention rewards, improving instruction adherence and non-target preservation in flow-based image editing.
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Monte Carlo Event Generation with Continuous Normalizing Flows
Continuous normalizing flows improve unweighting efficiency in Monte Carlo event generation for high-jet-multiplicity collider processes by factors up to 184, with wall-time gains of about ten when combined with coupling-layer flows.
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Conditional flow matching for physics-constrained inverse problems with finite training data
Conditional flow matching learns a velocity field to sample from measurement-conditioned posteriors in physics inverse problems, with early stopping to prevent variance collapse and selective memorization under finite training data.
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ContextFlow: Context-Aware Flow Matching For Trajectory Inference From Spatial Omics Data
ContextFlow regularizes flow matching with a transition plausibility matrix built from local tissue organization and ligand-receptor patterns to produce statistically and biologically coherent trajectories from longitudinal spatial omics data.
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Flow-based Generative Modeling of Potential Outcomes and Counterfactuals
PO-Flow uses continuous normalizing flows trained via flow matching to jointly model potential outcome distributions and enable factual-conditioned counterfactual prediction for causal inference tasks including CATE estimation.
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Mean Flows for One-step Generative Modeling
MeanFlow uses a derived identity between average and instantaneous velocities to train one-step flow models, achieving FID 3.43 on ImageNet 256x256 with 1-NFE from scratch.
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MAGI-1: Autoregressive Video Generation at Scale
MAGI-1 is a 24B-parameter autoregressive video world model that predicts denoised frame chunks sequentially with increasing noise to enable causal, scalable, streaming generation up to 4M token contexts.
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DanceGRPO: Unleashing GRPO on Visual Generation
DanceGRPO applies GRPO to visual generation tasks to achieve stable policy optimization across diffusion models, rectified flows, multiple tasks, and diverse reward models, outperforming prior RL methods.
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Long-Context Autoregressive Video Modeling with Next-Frame Prediction
FAR baseline plus asymmetric kernels for long short-term context modeling achieves SOTA short and long video generation in autoregressive setups.
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ConjNorm: Tractable Density Estimation for Out-of-Distribution Detection
ConjNorm reframes OOD detection score design as optimizing norm p in an exponential family density model via a Bregman divergence theorem, with a tractable Monte Carlo estimator, claiming SOTA gains on CIFAR-100 and ImageNet-1K.
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Improved DDIM Sampling with Moment Matching Gaussian Mixtures
Moment-matched GMM kernels in DDIM yield lower FID and higher IS than Gaussian kernels at small sampling steps on CelebA-HQ, FFHQ, ImageNet, and Stable Diffusion tasks.
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Multiscale Supervised Unbalanced Optimal Transport Flow Matching
MUST-FM is a simulation-free multiscale supervised framework that scales unbalanced optimal transport flow matching for trajectory inference in single-cell data by exploiting hierarchical structure and transition priors.
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CaloArt: Large-Patch x-Prediction Diffusion Transformers for High-Granularity Calorimeter Shower Generation
CaloArt achieves top FPD, high-level, and classifier metrics on CaloChallenge datasets 2 and 3 while keeping single-GPU generation at 9-11 ms per shower by combining large-patch tokenization, x-prediction, and conditional flow matching.
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Neural Posterior Estimation of Terrain Parameters from Radar Sounder Data
Neural posterior estimation trained on simulated radar data enables probabilistic inference of terrain parameters from real Mars radar sounder profiles while conditioning on reference surface assumptions.
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Self-Improving Tabular Language Models via Iterative Reward-Guided Post-Training
TabGRAA applies group-relative advantage alignment in an iterative reward-guided post-training loop to improve tabular language model generators on fidelity, utility, and privacy trade-offs across five benchmarks.
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SubFlow: Sub-mode Conditioned Flow Matching for Diverse One-Step Generation
SubFlow restores full mode coverage in one-step flow matching by conditioning on sub-modes from semantic clustering, yielding higher diversity on ImageNet-256 while preserving FID.
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Efficient Hierarchical Implicit Flow Q-learning for Offline Goal-conditioned Reinforcement Learning
Proposes mean flow policies and LeJEPA loss to overcome Gaussian policy limits and weak subgoal generation in hierarchical offline GCRL, reporting strong results on OGBench state and pixel tasks.