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.
TSFlow uses Gaussian processes to match priors for better time series forecasting.
problem Difficulties in aligning generative models' priors with time series data.
method Conditional flow matching (CFM) with Gaussian processes, optimal transport, and data-dependent priors.
result TSFlow produces high-quality unconditional samples and competitive forecasting results.
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.
CW-Gen models improve probabilistic time series forecasting by incorporating prior information.
problem Challenges in probabilistic forecasting of multivariate time series due to non-stationarity, inter-variable dependencies, and distribution shifts.
method CW-Gen framework that incorporates prior information through conditional whitening. JMCE learns conditional mean and covariance, improving sample quality.
result CW-Gen consistently enhances predictive performance, capturing non-stationary dynamics and inter-variable correlations more effectively than prior-free approaches.
Flow Matching models help generative models stay within the subspace of real data.
problem How do generative models stay within the subspace of real data?
method Flow Matching models using a learned velocity field to transform a simple prior into a complex target distribution.
result Generated samples memorize real data points and represent the sample data subspace exactly.
FMCPE improves SBI accuracy by correcting posterior estimators with flow matching.
problem Model misspecification in SBI leads to biased or overconfident posteriors.
method Flow Matching Corrected Posterior Estimation (FMCPE) trains a posterior approximator and corrects it using calibration samples.
result FMCPE consistently mitigates misspecification effects, improving inference accuracy and uncertainty quantification.
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.
Framework solves physics-constrained inverse problems with limited data.
problem Physics-constrained inverse problems with scarce training data.
method Conditional flow matching for Bayesian inverse problems.
result Conditional flow matching mitigates degeneracy in finite training data.
Flow Annealing Posterior Sampling unifies stochastic-process regression and PDE inverse problems.
problem Function-space posterior sampling for stochastic processes and inverse problems.
method Flow Annealing Posterior Sampling (FAPS) using pretrained function-space flow-matching priors.
result Coherent posterior samples with accurate uncertainty quantification.
Improved KL bounds and Wasserstein guarantees for diffusion flow matching under minimal conditions.
problem Theoretical convergence properties of Brownian motion based diffusion flow matching.
method Refined analysis under Kullback-Leibler and 2-Wasserstein distances.
result State-of-the-art scaling in KL convergence bounds under minimal conditions.
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
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.
Energy Matching unifies flow matching and energy-based models for generative modeling.
problem Inability of flow-based models to integrate partial observations and priors.
method Energy Matching framework that integrates flow matching and energy-based models.
result Substantially outperforms existing EBMs on CIFAR-10 and ImageNet generation.
WSD uses a deterministic model to accelerate diffusion-based sampling.
problem Slow refinement process in diffusion models.
method Warm-start model that predicts an informed prior conditioned on input context.
result Significantly reduces the number of diffusion steps required for realistic samples.
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.
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.
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.
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.
SFM matches flows on statistical manifolds for better discrete generation.
problem Discrete generation on statistical manifolds with strong prior assumptions.
method Statistical Flow Matching (SFM) on manifold of categorical distributions using Fisher information metric.
result SFM achieves higher sampling quality and likelihood than other models.
DeepWeightFlow generates diverse neural network weights efficiently.
problem Generating complete neural network weights efficiently and accurately.
method Flow Matching in weight space with Git Re-Basin and TransFusion.
result DeepWeightFlow generates high-accuracy neural networks without fine-tuning.
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.
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.
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 L 2 L^2 L 2 loss and regularity conditions. 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.
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.
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.
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.
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.
Unified framework for continuous-state discrete flow matching models.
problem Discrete generative modeling with continuous probabilities.
method Introducing α α α -Flow, a family of CS-DFM models based on information geometry. result Optimal flow matching loss for α α α -flow minimizes generalized kinetic energy. 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.
Framework learns continuous dynamics from sparse trajectories.
problem Learning dynamics from sparsely sampled and high-dimensional trajectories.
method Interpolative Multi-Marginal Flow Matching (IMMFM) framework.
result IMMFM outperforms existing methods in forecasting and downstream tasks.
Novel alignment framework for text-to-image generation using diffusion models and flow matching.
problem Improving text-to-image generation with minimal computational resources.
method Proposes a novel alignment framework that decomposes the score function into pre-trained score plus a conditional expectation of the reward.
result Achieves comparable performance to finetuning-based models with reduced computational cost.
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.
Sharp Lipschitz bounds for flow-matching and diffusion models with optimal sampling rates.
problem Establishing optimal Lipschitz regularity for flow-matching and diffusion models.
method Sharp Lipschitz regularity theory for flow-matching vector fields and diffusion-model scores.
result Achieves optimal sampling rate of d / N \sqrt{d}/N d / N for Euler-type samplers in dimension d d d . 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.
A new method reformulates Optimal Transport Conditional Flow Matching using proximal operators.
problem Optimal Transport Conditional Flow Matching (OT-CFM) for generating models.
method Reformulate OT-CFM using proximal operators and extended Brenier potential.
result OT-CFM dynamics are terminally normally hyperbolic for manifold-supported targets.
Flow Matching improves Wasserstein 1 distance convergence in high dimensions.
problem Improving Wasserstein 1 distance estimation for unbounded distributions.
method Flow Matching approach based on ODEs, controlling Lipschitz constant.
result Derives a convergence rate for Wasserstein 1 distance, improving previous results.
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.
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.
A new method improves flow matching by dynamically weighting density estimates.
problem High-dimensional integration inefficiency in flow matching.
method Density-weighted Dynamic Stein operators.
result Significant improvement in vector field smoothness and sampling efficiency.
SFM resolves small-scale physics challenges in weather data.
problem Challenges in super-resolving small-scale details in physical sciences like weather.
method Encoding inputs to a latent base distribution, flow matching for stochastic details, adaptive noise scaling.
result SFM framework significantly outperforms existing methods.
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.
RFM simplifies generative modeling on complex geometries without simulation.
problem Training generative models on non-Euclidean geometries is challenging.
method Riemannian Flow Matching (RFM) constructs a premetric for efficient vector field computation.
result RFM achieves state-of-the-art performance on various non-Euclidean datasets.
This paper provides guarantees for DFM models using KL divergence.
problem Ensuring generative models match target distributions efficiently.
method Using KL divergence and Brownian motion bridge for generative models.
result Non-asymptotic guarantees for DFM models under specific conditions.