LFM learns a sequence of smaller models to generate data from noise.
problem Learning continuous, invertible flows between distributions.
method Stepwise Local Flow Matching (LFM) model, matching diffusion processes up to time-step size.
result LFM achieves competitive generative performance compared to Flow Matching.
Adapts flow matching for MCMC to improve sampling efficiency.
problem Improving sampling efficiency in MCMC for complex distributions.
method Combines Markov chain and CNFs to learn a path between distributions.
result Achieves similar performance to state-of-the-art methods but with lower computational cost.
EnFF uses flows to speed up DA in high dimensions.
problem Efficiently assimilating noisy data in high-dimensional systems.
method Flow Matching (FM) for training-free, scalable data assimilation.
result EnFF accelerates DA with improved cost-accuracy tradeoffs and scalability.
The best known finite-time local Ricci flow singularity is the neckpinch, in which a proper subset of the manifold becomes geometrically close to a portion of a shrinking cylinder. In this paper, we prove precise asymptotics for rotationally symmetric Ricci flow neckpinches. We then compare these rigorous results with …
New method uses normalizing flows to improve force fields for coarse-grained molecular dynamics.
problem Lack of reference atomistic forces makes force matching infeasible for MLCG force fields.
method Introduces noise-based kernels adapted to low-data regimes using normalizing flows.
result Flow-based kernels reduce local distortions while preserving global accuracy.
Flow Matching for count data improves sample quality and efficiency.
problem Mapping between count distributions across batches or time points in high-dimensional count data.
method count-FM, a flow-matching framework based on a continuous-time birth-death process with local unit jumps.
result count-FM achieves better sample quality than representative baselines while using fewer parameters.
Topological Flow Matching: A Generative Modeling Framework for Structured Spaces
problem Handling structured spaces in generative modeling
method Introducing topological flow matching
result Captures the structure of the underlying domain while preserving desirable properties
Rectified flows achieve optimal sample complexity for generating data.
problem Generating high-quality data samples efficiently.
method Rectified flows constrain transport trajectories to be linear, enabling efficient sampling.
result Achieve sample complexity of ildeO(ε−2), matching optimal rate for mean estimation. CDC-FM improves generative model quality-generalization tradeoff by regularizing with geometry-aware noise.
problem Tradeoff between high sample quality and memorization in deep generative models.
method Introduces Carré du champ flow matching (CDC-FM) that replaces homogeneous noise with anisotropic Gaussian noise capturing latent data manifold geometry.
result CDC-FM consistently offers better quality-generalization tradeoff across diverse datasets and architectures.
Flow matching KL divergence bound derived for smooth distributions.
problem Estimating smooth distributions efficiently.
method Deterministic upper bound on KL divergence derived from flow-matching loss.
result Flow matching achieves nearly minimax-optimal efficiency under TV distance.
Closed-form flow matching yields similar performance to stochastic version, improving model performance.
problem Understanding why flow matching models generalize well.
method Empirical analysis and comparison of stochastic and closed-form flow matching losses.
result Closed-form flow matching can improve model performance.
CatFlow uses variational flow matching for efficient graph generation.
problem Graph generation tasks, especially for categorical data.
method Variational flow matching for categorical data, computationally efficient.
result CatFlow achieves strong results on graph generation tasks.
Flow Matching improves statistical guarantees through kernel density estimation.
problem Improving statistical guarantees for generative models.
method Connecting Flow Matching to kernel density estimation and verifying optimal rates of convergence.
result Flow Matching achieves optimal rates up to logarithmic factors for large networks and on lower-dimensional manifolds.
Paper proves higher-order flow matching preserves optimality in generative modeling.
problem Theoretical guarantees for higher-order flow matching in generative modeling.
method Neural network approximations with controlled depth, width, and sparsity.
result Proves worst case optimality for second-order flow matching.
RFM improves CNFs by adding a boundary constraint term and matching velocity fields.
problem Flow matching on constrained domains leads to unnatural samples.
method RFM adds a boundary constraint term and matches velocity fields in a simulation-free manner.
result RFM achieves comparable or better results on standard image benchmarks and produces high-quality samples.
Improved sampling efficiency for molecular systems using path gradients after Flow Matching.
problem Improving sampling efficiency for complex molecular systems.
method Hybrid approach combining Flow Matching and path gradients.
result Up to a threefold increase in sampling efficiency for molecular systems.
The paper justifies time-dependent loss reweighting schemes for flow matching and diffusion models.
problem Theoretical justification for time-dependent loss reweighting schemes in flow matching and diffusion models.
method Clarifies that the loss can depend on both time and state, and shows theoretical justification for time-dependent loss weighting schemes.
result Time-dependent loss weighting schemes are theoretically justified for Generator Matching and Edit Flows.
Study of integral flows on Riemannian manifolds with focus on blow-up profiles and concentration-compactness.
problem Analyzing nonlinear integral flows on Riemannian manifolds with specific focus on blow-up profiles and concentration-compactness.
method Investigation of a family of nonlinear integral flows involving Riesz potentials, focusing on the Hardy-Littlewood-Sobolev (HLS) subcritical and critical regimes.
result Established convergence on unit spheres and certain locally conformally flat manifolds for the dual Yamabe flow.
This work interprets diffusion score matching using normalizing flows for better model training and evaluations.
problem Limitations of diffusion score matching when dealing with certain types of distributions.
method The approach involves interpreting the diffusion matrix using normalizing flows to provide better interpretation and usage of diffusion score matching.
result Diffusion score matching is equivalent to the original score matching evaluated in the transformed space defined by the normalizing flow.
The paper connects complex normalizing flows to Kähler-Ricci flows using geometric and statistical perspectives.
problem Understanding the relationship between complex normalizing flows and Kähler-Ricci flows.
method Develops connections between complex normalizing flows and Kähler-Ricci flows by relating the log determinant to Ricci curvature and using a Bayesian perspective.
result Reconciles the complex normalizing flow and Kähler-Ricci flow, showing they are related under certain conditions.
Flow Matching enables robust training of CNFs with various probability paths.
problem Training Continuous Normalizing Flows (CNFs) at large scales.
method Flow Matching (FM) is a simulation-free approach for training CNFs by regressing vector fields of conditional probability paths.
result Flow Matching with diffusion paths yields more robust and stable training compared to diffusion-based methods.
New error bounds for flow matching methods using deterministic sampling.
problem Improving the accuracy of flow matching methods for generating probability distributions.
method Derived error bounds for flow matching methods under deterministic sampling conditions.
result Presented error bounds for flow matching methods using L2 loss and regularity conditions. Flow matching adapts to manifold structures without diffusion.
problem Theoretical understanding of flow matching in manifold-supported settings.
method Flow matching with linear interpolation on smooth manifolds, analyzing velocity field and density estimator.
result Non-asymptotic convergence guarantee and statistical consistency of flow matching on manifolds.
Unified framework for continuous-state discrete flow matching models.
problem Discrete generative modeling with continuous probabilities.
method Introducing α-Flow, a family of CS-DFM models based on information geometry. result Optimal flow matching loss for α-flow minimizes generalized kinetic energy. DFM simplifies CNF training without interpolants.
problem Efficiently training CNFs with computationally expensive ODE solving.
method DFM optimizes dual vector fields for bijective transformations.
result DFM outperforms CNF trained with FM or ML objectives.
CFMI improves missing data imputation across various data types and dimensions.
problem Imputing missing data in complex, high-dimensional datasets.
method Combines normalising flows, flow-matching, and shared conditional modelling.
result Outperforms traditional and modern imputation methods across multiple metrics.
Generative model for condensed matter using Riemannian flow matching.
problem Sampling equilibrium distributions in condensed-phase systems.
method Riemannian flow matching to incorporate periodicity, using Hutchinson's trace estimator and cumulant expansion for bias correction.
result Highly accurate free energy estimates on monatomic ice without multistage estimators.
A new method learns straight trajectories in one step for optimal flow matching.
problem Learning flows with straight trajectories for fast inference.
method Optimal Flow Matching (OFM) approach using convex functions for vector fields.
result Recovering straight OT displacements in just one FM step for quadratic transport.
GLASS Flows improves flow and diffusion model performance by optimizing sampling efficiency.
problem Efficiency bottleneck in sampling Markov transitions for flow and diffusion models.
method Introduces GLASS Flows, a new sampling paradigm that simulates a 'flow matching model within a flow matching model' to sample Markov transitions efficiently.
result Eliminates the trade-off between stochastic evolution and efficiency in large-scale text-to-image models.
Abstract notes on generative modeling techniques.
problem Improving generative modeling techniques.
method Connections between optimal transport and Schrödinger bridge, flow matching.
result Showed connections between mathematical principles and generative modeling techniques.
Improved image generation through iterative flow matching to reduce hallucinations.
problem Hallucinations in image generation models.
method Iterative flow matching to refine and correct paths in generative models.
result Enhanced generative modeling with reduced unrealistic images.
Graphs model human mobility patterns, reducing errors in data matching.
problem Lack of high-quality data and computational resources for graph-based mobility analysis.
method Embedding graphs into a continuous space to address matching, modeling, and visualization challenges.
result Approx 40% decrease in error on average in matched graphs vs unmatched ones.
A new training method for efficient Boltzmann generators.
problem Training equivariant continuous normalizing flows (CNFs) is computationally expensive.
method Equivariant flow matching, based on optimal transport flow matching.
result Equivariant flow matching yields more efficient flows with shorter integration paths.
The paper matches features in images using centro-affine invariants and heat flow.
problem Feature matching in images with invariant algorithms.
method Developed an invariant algorithm using centro-affine invariants and heat flow.
result The algorithm compares favorably with existing feature matching methods.
Flow matching improves synthetic data generation for tabular data.
problem Generating synthetic tabular data while preserving privacy.
method Flow matching (FM) and Variational FM for tabular data synthesis.
result FM outperforms diffusion baselines in tabular data synthesis.
Given a subset S of vertices of an undirected graph G, the cut-improvement problem asks us to find a subset S that is similar to A but has smaller conductance. A very elegant algorithm for this problem has been given by Andersen and Lang [AL08] and requires solving a small number of single-commodity maximum flow comput…
CPFM integrates dimensionality reduction and reconstruction with flow networks.
problem Learning coupled continuous flows for data and embeddings.
method Coupled flow matching framework with Gromov-Wasserstein objective and dual-conditional flow network.
result CPFM preserves and recovers residual information in latent space.
Develops Hamiltonian Score Matching and Generative Flows for machine learning.
problem Estimating score functions and designing generative models.
method Introduces Hamiltonian velocity predictors (HVPs) for score matching and generative flows.
result Hamiltonian Generative Flows (HGFs) rival leading generative modeling techniques.
We extend rectified flow to infinite-dimensional Hilbert space.
problem Extending rectified flow to infinite-dimensional spaces.
method Established a rigorous functional formulation using the superposition principle for continuity equations.
result Demonstrated superior performance compared to existing models.
Improved flow matching using Gaussian processes for better sample quality.
problem Training continuous normalizing flows with reduced variance and flexibility.
method Extending conditional flow matching to streams modeled with Gaussian processes.
result Improved quality of generated samples with moderate computational cost.
RG-VFM extends VFM to curved manifolds for better material and protein design.
problem Designing materials and proteins on curved manifolds.
method Riemannian Gaussian Variational Flow Matching (RG-VFM) for generative modeling on manifolds.
result RG-VFM more effectively captures manifold structure and improves performance.
New method reduces discrete flow transitions, improving perplexity estimation.
problem Stochasticity in discrete paths makes rectification strategies ineffective.
method Dynamic-optimal-transport-like minimization objective with minibatch strategies.
result 32 times reduction in transitions for same perplexity.
New method improves generative modeling on convex domains using regularized mirror maps and Student-t priors.
problem Challenges in generative modeling on convex domains with heavy-tailed targets.
method Mirror Flow Matching with regularized mirror maps and Student-t priors.
result Empirically outperforms baselines and achieves competitive sample quality.
Paper studies flow on hyperbolic surfaces to match boundary lengths.
problem Matching boundary lengths of hyperbolic surfaces.
method Combinatorial Yamabe flow on hyperbolic bordered surfaces.
result Flow converges exponentially to a surface with equal boundary lengths.
New probability path model improves flow matching forecasting performance.
problem Impact of probability path model selection on flow matching forecasting performance.
method Proposed a novel probability path model designed to improve forecasting performance.
result Our model achieves faster convergence during training and improved predictive performance compared to existing models.
This research optimizes plate structures to reduce vibrations in vehicles and aircraft.
problem Minimizing structural vibrations in engineering systems for improved passenger comfort.
method Guided flow matching design optimization integrating generative flow matching and surrogate model.
result Generated plate designs with reduced vibrations compared to random search and other methods.
The paper explores rectified flows and their relation to optimal transport.
problem Understanding the connection between rectified flows and optimal transport.
method Investigates invariance properties, explicit constructions, and analysis of rectified flows in various settings.
result Rectified flows, when gradient constrained, do not generally solve optimal transport problems.
Branching Flows generates sequences of varying lengths using binary trees.
problem Generating sequences of unknown lengths or fixed elements.
method A generative modeling framework that evolves states over binary trees, controlling sequence length.
result Branching Flows can generate sequences of varying lengths and mix different types of state spaces.