Derives closed-form posterior covariance for flow matching from divergence of velocity field, enabling post-hoc uncertainty on pre-trained models including one-step generators.
super hub Mixed citations
Stochastic Interpolants: A Unifying Framework for Flows and Diffusions
Mixed citation behavior. Most common role is background (69%).
103
Pith papers citing it
Background
69% of classified citations
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.
hub tools
citation-role summary
background 11
method 5
citation-polarity summary
claims ledger
- 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
authors
co-cited works
representative citing papers
FMRG reformulates guidance as deterministic optimal control, deriving a single-trajectory method using the flow map that matches or exceeds baselines on reward-guided generation and inverse problems with 3 NFEs at text-to-image scale.
Quotient-space diffusion models generate correct symmetric distributions by removing redundancy on the quotient space, simplifying learning and improving results on small molecules and proteins under SE(3) symmetry.
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.
Introduces VICIS task and training framework for inferring visual concepts from image sets, with experiments showing better accuracy, diversity, and generalization than standard VLMs on synthetic and ImageNet data.
A transformer-based diffusion model learns the joint distribution of convergence maps and cosmology from log-normal weak lensing simulations and generates calibrated posterior samples matching MCMC results.
Flow models reach 99.2% Sudoku accuracy in 7 passes and 96.1% on out-of-distribution Sudoku-Extreme by selecting dynamically stable candidates and training with self-conditioning plus DPO to avoid failed outputs.
Defines generative probability paths as self-consistent when they form random fixed points of admissible variational transport operators and derives associated existence, attraction, and residual bounds.
Naive samplers beat published diffusion and flow models on gen-PPL with incoherent output, proving the metric unsound and motivating distributional evaluation suites.
DiSI disentangles stochastic interpolants into separate generation and regression paths, allowing controllable transitions between regression and generative image restoration with a unified few-step sampler.
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.
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.
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.
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.
Flow matching on time series targets a closed-form nonparametric velocity field that is a similarity-weighted mixture of observed transition velocities, making neural models approximations to an ideal memory-augmented dynamical system sampler.
citing papers explorer
-
Divergence is Uncertainty: A Closed-Form Posterior Covariance for Flow Matching
Derives closed-form posterior covariance for flow matching from divergence of velocity field, enabling post-hoc uncertainty on pre-trained models including one-step generators.
-
How to Guide Your Flow: Few-Step Alignment via Flow Map Reward Guidance
FMRG reformulates guidance as deterministic optimal control, deriving a single-trajectory method using the flow map that matches or exceeds baselines on reward-guided generation and inverse problems with 3 NFEs at text-to-image scale.
-
Quotient-Space Diffusion Models
Quotient-space diffusion models generate correct symmetric distributions by removing redundancy on the quotient space, simplifying learning and improving results on small molecules and proteins under SE(3) symmetry.
-
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.
-
Show Me Examples: Inferring Visual Concepts from Image Sets
Introduces VICIS task and training framework for inferring visual concepts from image sets, with experiments showing better accuracy, diversity, and generalization than standard VLMs on synthetic and ImageNet data.
-
Joint inference of weak lensing convergence map and cosmology with diffusion models
A transformer-based diffusion model learns the joint distribution of convergence maps and cosmology from log-normal weak lensing simulations and generates calibrated posterior samples matching MCMC results.
-
Self-Consistent Generative Paths via Admissible Random Variational Transport
Defines generative probability paths as self-consistent when they form random fixed points of admissible variational transport operators and derives associated existence, attraction, and residual bounds.
-
Disentangling Generation and Regression in Stochastic Interpolants for Controllable Image Restoration
DiSI disentangles stochastic interpolants into separate generation and regression paths, allowing controllable transitions between regression and generative image restoration with a unified few-step sampler.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
Is Flow Matching Just Trajectory Replay for Sequential Data?
Flow matching on time series targets a closed-form nonparametric velocity field that is a similarity-weighted mixture of observed transition velocities, making neural models approximations to an ideal memory-augmented dynamical system sampler.
-
Generative Modeling of Discrete Data Using Geometric Latent Subspaces
A geometric latent-subspace model on Riemannian manifolds of categorical distributions enables low-dimensional generative modeling of discrete data via isometries and geometric PCA for flow matching.
-
On The Hidden Biases of Flow Matching Samplers
Empirical flow matching introduces coupled biases from plug-in estimation, including altered statistical targets, non-gradient minimizers, and non-unique dynamics via flux-null fields, with base distribution controlling kinetic energy tails.
-
Generative Modeling from Black-box Corruptions via Self-Consistent Stochastic Interpolants
SCSI iteratively refines a self-consistent transport map to invert black-box corruptions and enable generative modeling of clean data.
-
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.
-
Lipschitz-Guided Design of Interpolation Schedules in Generative Models
Minimizing averaged squared Lipschitzness of the drift produces interpolation schedules that improve numerical accuracy and mitigate mode collapse in generative models, with closed-form optima for Gaussians and validation on stochastic PDEs.
-
Constraint-Aware Flow Matching via Randomized Exploration
The paper introduces penalty-based and randomized-exploration adaptations to flow matching for improved constraint satisfaction in generative models while matching target distributions.
-
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.
-
UniEdit-Flow: Unleashing Inversion and Editing in the Era of Flow Models
UniEdit-Flow presents tuning-free Uni-Inv and Uni-Edit methods for inversion and editing in flow models that achieve accurate reconstruction and robust region-preserving edits across generative models.
-
Interpretation-Oriented Cloud Removal via Observation-Anchored Residual Flow with Geo-Contextual Alignment
GACR reformulates cloud removal as an observation-anchored residual inversion process with geo-contextual prior alignment to preserve semantic structures for improved downstream interpretation tasks.
-
TerraDiT-$\Omega$: Unified Spatial Control for Satellite Image Synthesis with Any Geospatial Primitive
TerraDiT-Ω generates satellite imagery from native geospatial primitives via Geometry-Aware Local Attention and outperforms dense and sparse control baselines while boosting downstream GeoAI tasks.
-
Streamlining Analysis and Design of Two-Dimensional Electronic Spectroscopy using Machine Learning
A Gaussian mixture model is used to learn spectral densities from 2DES experiments, enabling extraction of vibronic couplings, spectral extrapolation, and optimized experiment selection across simulated and experimental systems.
-
HYDRA-X: Native Unified Multimodal Models with Holistic Visual Tokenizers
HYDRA-X presents the first unified multimodal model using a single ViT for holistic image-video tokenization, with ablations on attention and compression plus a latent-level editing improvement.
-
Double Preconditioning (DoPr): Optimization for Test-Time Performance, not Validation Loss
Double preconditioning (DoPr) improves downstream task performance in test-time feedback settings without consistent gains in validation loss.
-
Scalable Inference-Time Annealing with Surrogate Likelihood Estimators
SITA performs scalable inference-time annealing of flow-based models on molecular systems by substituting energy-based surrogate likelihoods for divergence-based importance weights.
-
GenSBI: Generative Methods for Simulation-Based Inference in JAX
GenSBI delivers JAX-native implementations of generative SBI methods with transformer backbones and reports near-ideal calibration scores on standard benchmarks.
-
AdvantageFlow: Advantage-Weighted Least Squares for RL in Flow Models
AdvantageFlow proposes an advantage-weighted forward-process least-squares loss for RL in rectified flow models, stabilized by rollout policy regularization, and reports better image generation performance than Flow-GRPO on Stable Diffusion 3.5.
-
PrismFlow: Residual Dynamics for Flow Matching in Time-Series Generation
PrismFlow augments flow matching with residual dynamical experts and a winner-take-all objective to reduce spectral distortion and improve mode coverage in time-series generation.
-
StreamEdit: Training-Free Video Editing via Few-Step Streaming Video Generation
StreamEdit enables high-quality training-free video editing by adapting streaming video generation models with dual-branch fast sampling, self-attention bridge, cross-attention grounding, source-oriented guidance, and visual prompting, outperforming prior methods in few-step regimes.
-
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.
-
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.
-
Flow Matching with Arbitrary Auxiliary Paths
AuxPath-FM extends flow matching to arbitrary auxiliary distributions while preserving the continuity equation and marginal training objective.
-
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.
-
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.
-
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
-
OGPO: Sample Efficient Full-Finetuning of Generative Control Policies
OGPO enables sample-efficient full-finetuning of generative control policies via off-policy critics and modified PPO, achieving SOTA on robot manipulation tasks while rescuing poorly initialized behavior cloning policies without expert data.
-
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.
-
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.
-
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.