In flow matching, the uncertainty of the clean data given the current state is exactly the divergence of the velocity field (up to a known scalar).
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Stochastic Interpolants: A Unifying Framework for Flows and Diffusions
43 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
A class of generative models that unifies flow-based and diffusion-based methods is introduced. These models extend the framework proposed in Albergo and Vanden-Eijnden (2023), enabling the use of a broad class of continuous-time stochastic processes called stochastic interpolants to bridge any two probability density functions exactly in finite time. These interpolants are built by combining data from the two prescribed densities with an additional latent variable that shapes the bridge in a flexible way. The time-dependent density function of the interpolant is shown to satisfy a transport equation as well as a family of forward and backward Fokker-Planck equations with tunable diffusion coefficient. Upon consideration of the time evolution of an individual sample, this viewpoint leads to both deterministic and stochastic generative models based on probability flow equations or stochastic differential equations with an adjustable level of noise. The drift coefficients entering these models are time-dependent velocity fields characterized as the unique minimizers of simple quadratic objective functions, one of which is a new objective for the score. We show that minimization of these quadratic objectives leads to control of the likelihood for generative models built upon stochastic dynamics, while likelihood control for deterministic dynamics is more stringent. We also construct estimators for the likelihood and the cross entropy of interpolant-based generative models, and we discuss connections with other methods such as score-based diffusion models, stochastic localization, probabilistic denoising, and rectifying flows. In addition, we demonstrate that stochastic interpolants recover the Schr\"odinger bridge between the two target densities when explicitly optimizing over the interpolant. Finally, algorithmic aspects are discussed and the approach is illustrated on numerical examples.
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- abstract A class of generative models that unifies flow-based and diffusion-based methods is introduced. These models extend the framework proposed in Albergo and Vanden-Eijnden (2023), enabling the use of a broad class of continuous-time stochastic processes called stochastic interpolants to bridge any two probability density functions exactly in finite time. These interpolants are built by combining data from the two prescribed densities with an additional latent variable that shapes the bridge in a flexible way. The time-dependent density function of the interpolant is shown to satisfy a transport e
co-cited works
representative citing papers
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.
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.
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.
Non-monotonic sampling schedules never improve upon monotonic baselines in diffusion models, with performance gaps ranging from substantial to negligible depending on the denoiser.
TMPO uses Softmax Trajectory Balance to match policy probabilities over multiple trajectories to a Boltzmann reward distribution, improving diversity by 9.1% in diffusion alignment tasks.
FLUX reconstructs longitudinal transport and recovers interpretable regime structure from unpaired biological snapshots by combining geometry-aware flow matching with mixture-of-experts velocity decomposition.
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.
Diffusion model priors enable training-free Bayesian sampling for more accurate rain field reconstruction from path-integrated commercial microwave link measurements than Gaussian process baselines.
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.
ABC enables any-subset autoregressive generation of continuous stochastic processes via non-Markovian diffusion bridges that track physical time and allow path-dependent conditioning.
FMRG is a training-free, single-trajectory guidance method for flow models derived from optimal control that achieves strong reward alignment with only 3 NFEs.
ALMC-ODE uses annealed Langevin Monte Carlo with Jarzynski reweighting to produce a low-variance velocity estimator for flow ODE sampling, with an O(1/n) MSE bound and superior performance on multimodal benchmarks.
ScoRe-Flow achieves decoupled mean-variance control in stochastic flow matching by deriving a closed-form score for drift modulation plus learned variance, yielding faster RL convergence and higher success rates on locomotion and manipulation benchmarks.
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.
MixGRPO speeds up GRPO for flow-based image generators by restricting SDE sampling and optimization to a sliding window while using ODE elsewhere, cutting training time by up to 71% with better alignment performance.
Generative models learn rules before memorizing data, creating an innovation window whose width depends on dataset size and rule complexity, observed in both diffusion and autoregressive architectures.
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.
AuxPath-FM extends flow matching to arbitrary auxiliary distributions while preserving the continuity equation and marginal training objective.
Distilled one-step consistency model from optimal-transport flow-matching teacher reconstructs high-fidelity dynamical system flows from low-fidelity data with 12x speedup, half the parameters, and 23.1% better SSIM than scratch-trained baselines.
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.
Training and sampling in static scalar energy generative models are two instances of the same Lyapunov-driven density transport dynamics on Wasserstein space, differing only by initial condition, which yields a finite stopping criterion for Langevin sampling and additive composition rules that keep
OGPO is a sample-efficient off-policy method for full finetuning of generative control policies that reaches SOTA on robotic manipulation tasks and can recover from poor behavior-cloning initializations without expert data.
CARD uses radix decomposition to enable autoregressive modeling of molecular coordinates as a zero-free-energy reference distribution, delivering classical accuracy for absolute free energy on unseen systems at ~40x speedup.
citing papers explorer
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Divergence is Uncertainty: A Closed-Form Posterior Covariance for Flow Matching
In flow matching, the uncertainty of the clean data given the current state is exactly the divergence of the velocity field (up to a known scalar).
-
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.
-
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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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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Is Monotonic Sampling Necessary in Diffusion Models?
Non-monotonic sampling schedules never improve upon monotonic baselines in diffusion models, with performance gaps ranging from substantial to negligible depending on the denoiser.
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TMPO: Trajectory Matching Policy Optimization for Diverse and Efficient Diffusion Alignment
TMPO uses Softmax Trajectory Balance to match policy probabilities over multiple trajectories to a Boltzmann reward distribution, improving diversity by 9.1% in diffusion alignment tasks.
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FLUX: Geometry-Aware Longitudinal Flow Matching with Mixture of Experts
FLUX reconstructs longitudinal transport and recovers interpretable regime structure from unpaired biological snapshots by combining geometry-aware flow matching with mixture-of-experts velocity decomposition.
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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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Bayesian Rain Field Reconstruction using Commercial Microwave Links and Diffusion Model Priors
Diffusion model priors enable training-free Bayesian sampling for more accurate rain field reconstruction from path-integrated commercial microwave link measurements than Gaussian process baselines.
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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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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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How to Guide Your Flow: Few-Step Alignment via Flow Map Reward Guidance
FMRG is a training-free, single-trajectory guidance method for flow models derived from optimal control that achieves strong reward alignment with only 3 NFEs.
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Annealed Langevin Monte Carlo for Flow ODE Sampling
ALMC-ODE uses annealed Langevin Monte Carlo with Jarzynski reweighting to produce a low-variance velocity estimator for flow ODE sampling, with an O(1/n) MSE bound and superior performance on multimodal benchmarks.
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ScoRe-Flow: Complete Distributional Control via Score-Based Reinforcement Learning for Flow Matching
ScoRe-Flow achieves decoupled mean-variance control in stochastic flow matching by deriving a closed-form score for drift modulation plus learned variance, yielding faster RL convergence and higher success rates on locomotion and manipulation 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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MixGRPO: Unlocking Flow-based GRPO Efficiency with Mixed ODE-SDE
MixGRPO speeds up GRPO for flow-based image generators by restricting SDE sampling and optimization to a sliding window while using ODE elsewhere, cutting training time by up to 71% with better alignment performance.
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The two clocks and the innovation window: When and how generative models learn rules
Generative models learn rules before memorizing data, creating an innovation window whose width depends on dataset size and rule complexity, observed in both diffusion and autoregressive architectures.
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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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Flow Matching with Arbitrary Auxiliary Paths
AuxPath-FM extends flow matching to arbitrary auxiliary distributions while preserving the continuity equation and marginal training objective.
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Physical Fidelity Reconstruction via Improved Consistency-Distilled Flow Matching for Dynamical Systems
Distilled one-step consistency model from optimal-transport flow-matching teacher reconstructs high-fidelity dynamical system flows from low-fidelity data with 12x speedup, half the parameters, and 23.1% better SSIM than scratch-trained baselines.
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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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Energy Generative Modeling: A Lyapunov-based Energy Matching Perspective
Training and sampling in static scalar energy generative models are two instances of the same Lyapunov-driven density transport dynamics on Wasserstein space, differing only by initial condition, which yields a finite stopping criterion for Langevin sampling and additive composition rules that keep
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OGPO: Sample Efficient Full-Finetuning of Generative Control Policies
OGPO is a sample-efficient off-policy method for full finetuning of generative control policies that reaches SOTA on robotic manipulation tasks and can recover from poor behavior-cloning initializations without expert data.
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CARD: Coarse-to-fine Autoregressive Modeling with Radix-based Decomposition for Transferable Free Energy Estimation
CARD uses radix decomposition to enable autoregressive modeling of molecular coordinates as a zero-free-energy reference distribution, delivering classical accuracy for absolute free energy on unseen systems at ~40x speedup.
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Uncertainty-Aware Spatiotemporal Super-Resolution Data Assimilation with Diffusion Models
DiffSRDA uses denoising diffusion models to perform uncertainty-aware spatiotemporal super-resolution data assimilation, achieving EnKF-like quality from low-resolution forecasts on an ocean jet testbed.
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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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Denoising, Fast and Slow: Difficulty-Aware Adaptive Sampling for Image Generation
Patch Forcing enables diffusion models to denoise image patches at varying rates based on predicted difficulty, advancing easier regions first to improve context and achieve better generation quality on ImageNet while scaling to text-to-image tasks.
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Perron-Frobenius Contractive Operator Matching for Data-Driven Reachable Fault Identification and Recovery
A framework learns fault-indexed Perron-Frobenius operators from trajectory data to provide certifiable 2-Wasserstein bounds for detecting actuator faults and enabling recovery via density propagation in nonlinear control-affine systems.
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MENO: MeanFlow-Enhanced Neural Operators for Dynamical Systems
MENO enhances neural operators with MeanFlow to restore multi-scale accuracy in dynamical system predictions while keeping inference costs low, achieving up to 2x better power spectrum accuracy and 12x faster inference than diffusion-enhanced baselines on phase-field, Kolmogorov flow, and active-m<f
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Improving Controllable Generation: Faster Training and Better Performance via $x_0$-Supervision
x0-supervision or equivalent loss re-weighting accelerates convergence in controllable diffusion models while improving visual quality and conditioning accuracy.
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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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Uncertainty Quantification for Distribution-to-Distribution Flow Matching in Scientific Imaging
Bayesian Stochastic Flow Matching augments flow models with stochastic diffusion for better generalization and uses Monte Carlo Dropout with antithetic sampling to disentangle uncertainties and detect out-of-distribution cases in scientific imaging.
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World Action Models are Zero-shot Policies
DreamZero uses a 14B video diffusion model as a World Action Model to achieve over 2x better zero-shot generalization on real robots than state-of-the-art VLAs, real-time 7Hz closed-loop control, and cross-embodiment transfer with 10-30 minutes of data.
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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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Representation Alignment for Generation: Training Diffusion Transformers Is Easier Than You Think
Aligning noisy hidden states in diffusion transformers to clean features from pretrained visual encoders speeds up training over 17x and reaches FID 1.42.
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Sharpen Your Flow: Sharpness-Aware Sampling for Flow Matching
SharpEuler estimates a sharpness profile via finite differences on calibration trajectories, smooths it, and applies a quantile transform to generate adaptive timestep grids that improve Euler sampling quality in flow matching models at fixed budgets.
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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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PRiMeFlow: Capturing Complex Expression Heterogeneity in Perturbation Response Modelling
PRiMeFlow applies flow matching in gene expression space with a U-Net velocity field and pretraining-finetuning to model perturbation-induced heterogeneity, showing strong benchmark performance on PerturBench and the ARC Virtual Cell Challenge.
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Energy-oriented Diffusion Bridge for Image Restoration with Foundational Diffusion Models
E-Bridge approximates low-cost geodesic trajectories in diffusion bridges for image restoration by using shorter time horizons, entropy-regularized starts mixing degraded images with noise, and consistency-model single-step mapping, achieving SOTA results with one or few steps.
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A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models
Diffusion, score-based, and flow matching models are unified as instances of learning time-dependent vector fields inducing marginal distributions governed by continuity and Fokker-Planck equations.
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Generative models for decision-making under distributional shift
Generative models via pushforward maps, Fokker-Planck equations, and Wasserstein geometry enable learning nominal uncertainty, stressed distributions for robustness, and conditional posteriors under distributional shift.
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Machine Learning Techniques for Astrophysics and Cosmology: Simulation-Based Inference
Simulation-based inference uses neural networks trained on simulations to enable parameter inference in cosmology and astrophysics where traditional likelihood calculations are intractable.
- Quotient-Space Diffusion Models