We convert deterministic flow models to stochastic samplers.
problem Deterministic flow models are sensitive to errors and cannot condition on intermediate states.
method Transform ODEs into SDEs with the same marginal distributions.
result Empirically outperforms deterministic samplers and controls generation diversity.
Identifies most probable flows for Kunita SDEs in fluid dynamics.
problem Modeling stochastic processes with Eulerian noise and deterministic drifts.
method Equipping the domain with a Riemannian metric from the noise, solving the resulting PDEs.
result Most probable flows differ from deterministic flows, especially under noise.
sFML learns stochastic dynamical systems from data.
problem Learning unknown stochastic dynamical systems from measurement data.
method sFML extends FML for deterministic systems, using a stochastic flow map composed of deterministic and stochastic sub-maps.
result sFML constructs a stochastic evolution model approximating unknown stochastic systems.
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. Improves efficiency of simulators that fail to return.
problem Computational inefficiency in simulators that don't return for certain inputs.
method Trains a conditional normalizing flow to propose perturbations.
result Increased computational efficiency of simulators.
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.
Framework simulates market microstructure with stable Hawkes processes.
problem Reproduce realistic market order flow dynamics.
method Deterministic C++ LOB simulator with Hawkes-driven stochastic order flow.
result Derives stability and ergodicity proofs for Hawkes models.
RegFlow models future states with flexible probability distributions.
problem Predicting future states under complex, non-deterministic scenarios.
method Hypernetwork architecture and continuous normalizing flow model.
result RegFlow achieves state-of-the-art results on benchmark datasets.
Estimates CDF over complex regions using normalizing flows.
problem Challenges in estimating CDF over complex regions using traditional methods.
method Leverages diffeomorphic properties of normalizing flows and divergence theorem.
result Improves sample efficiency in estimating CDF over complex regions.
DDPM encoder matches optimal transport for natural images.
problem Understanding theoretical properties of DDPM latent space.
method Showed DDPM encoder matches optimal transport for common distributions.
result DDPM encoder map coincides with optimal transport map for natural images.
New bounds for model generalization under deterministic gradient descent.
problem Establishing generalization bounds for models trained with gradient descent methods.
method PAC-Bayesian bounds for deterministic optimisation algorithms.
result Fully computable bounds that depend on initial distribution and Hessian.
Bayesian inference for expensive likelihoods using Langevin Monte Carlo with NF.
problem Sampling from complex posterior distributions with expensive likelihoods.
method Deterministic Langevin equation with NF gradient, Metropolis-Hastings updates.
result Competitive performance compared to state-of-the-art methods.
Paper bounds PAC RL sample complexity in deterministic MDPs.
problem Identify ε-optimal policy with high probability.
method Proposes nearly matching upper and lower bounds on sample complexity, introduces deterministic return gap, uses graph-theoretical concepts and maximum-coverage exploration.
result First nearly matching upper and lower bounds on sample complexity for PAC RL in deterministic MDPs.
FM4PDE learns PDE solutions from sparse data.
problem Reconstructing PDE solutions from limited observations.
method Flow-matching generative framework that learns PDE coefficients and solutions.
result Error guarantees for guided procedures, including deterministic and stochastic samplers.
In a market of deterministic cash flows, given as an additive, symmetric relation of exchangeability on the finite signed Borel measures on the non-negative real time axis, it is shown that the only arbitrage-free price functional that fulfills some additional mild requirements is the integral of the unit zero-coupon b…
Hamiltonian dynamics-based algorithms achieve deterministic and accelerated convergence for convex optimization.
problem Accelerating convex optimization
method Hamiltonian dynamics
result Hamiltonian dynamics-based algorithms achieve deterministic and accelerated convergence for convex optimization.
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.
Develops new bounds for deterministic samplers in diffusion models.
problem Analyzing deterministic samplers in diffusion generative models.
method Operational interpretation of deterministic sampling; restoration and degradation steps.
result First polynomial convergence bounds for DDIM-type samplers.
SurVAE Flows combine VAEs and flows using surjective transformations.
problem Combining the strengths of VAEs and flows to model complex densities.
method Modular framework of composable deterministic and stochastic transformations.
result Exact likelihood computation and lower bound on likelihood.
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
Paper explores stability, regularization, and gradient flows for stochastic inverse problems.
problem Recovering random probability distributions from measurements.
method Direct inversion, variational formulation with regularization, and optimization via gradient flows.
result The choice of metric impacts stability and properties of the optimizer.
Deterministic training improves generative autoencoder performance.
problem Stochastic training limits generative autoencoder performance.
method Invertible layers for deterministic training.
result AEFs outperform VAEs in log-likelihood and sample quality.
Generative adversarial networks (GANs) were initially proposed to generate images by learning from a large number of samples. Recently, GANs have been used to emulate complex physical systems such as turbulent flows. However, a critical question must be answered before GANs can be considered trusted emulators for physi…
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.
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.
New game approximates mean curvature flow evolution.
problem Approximating geometric mean curvature flow evolution.
method Two-player zero-sum game with probabilistic elements.
result Value function approximates mean curvature flow.
Flow-based models use ODEs to generate complex data distributions.
problem Generating high-dimensional data with complex probability distributions.
method Flow-based models use invertible mappings governed by ODEs to capture these distributions.
result Flow-based models provide exact likelihood estimation and efficient sampling.
A new method for discrete data normalizing flows using latent transformations.
problem Challenges in parameterizing bijective transformations for discrete data.
method Predict a distribution over latent transformations to make the marginal likelihood differentiable.
result Discrete-data normalizing flows can be trained using gradient-based learning with unbiased score function estimation.
The study characterizes straight-line flows in dynamic measure transport.
problem Tackles the challenge of designing flows that are easy to integrate.
method Characterizes straight-line flows using a PDE and Reynolds tensor.
result Characterizes affine-in-time interpolants and necessary conditions for flow geometry.
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.
In this paper we propose a look at the capital risk problem inspired by deterministic, known from classical mechanics, problem of juggling. We propose capital equivalents to the Newton's laws of motion and on this basis we determine the most secure form of credit repayment with regard to maximisation of profit. Then we…
New Wasserstein divergence improves generative model robustness and structure preservation.
problem Improving generative model robustness and structure preservation.
method Introduces a novel Wasserstein-1 path-space divergence and a WUP theorem.
result Derives robustness and generalization bounds for flow-based models.
A training-free method for conditional sampling using flow matching.
problem Weight degeneracy in high-dimensional importance sampling.
method Sequential Monte Carlo with resampling and stochastic flow.
result Significantly outperforms existing methods on MNIST and CIFAR-10.
New method speeds up generative modeling without requiring diffusion steps.
problem Improving the speed and efficiency of generative modeling techniques.
method Probability flow ODE with a corrector step, achieving better dimension dependence.
result Better dimension dependence ( O ( d ) O(\sqrt{d}) O ( d ) vs. O ( d ) O(d) O ( d ) , assuming smoothness of the data distribution). In this paper, we formulate a general time-inconsistent stochastic linear--quadratic (LQ) control problem. The time-inconsistency arises from the presence of a quadratic term of the expected state as well as a state-dependent term in the objective functional. We define an equilibrium, instead of optimal, solution withi…
Improved sampling method using regularized Stein Variational Gradient Flow.
problem Improving the accuracy of sampling methods in machine learning.
method Proposed Regularized Stein Variational Gradient Flow to interpolate between SVGD and Wasserstein Gradient Flow.
result Established theoretical properties and provided preliminary numerical evidence of improved performance.
Diffusion models' sampling paths lie in a low-dimensional subspace, resembling boomerangs.
problem Understanding the geometric structure of diffusion-based generative models.
method Characterization of deterministic sampling trajectories using low-dimensional subspace and kernel-estimated data modeling.
result Sampling trajectories in diffusion models are confined to a low-dimensional subspace and exhibit a boomerang shape.
Muon dynamics study uses spectral Wasserstein flow for optimization stability.
problem Optimizing deep learning models with gradient normalization.
method Introduces Spectral Wasserstein distances for matrix flows, proving equivalence with Benamou--Brenier formulation.
result Gradient-flow interpretation of mean-field normalized training dynamics.
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.
New analysis improves convergence guarantees for diffusion-based samplers in Wasserstein distance.
problem Improving convergence guarantees for diffusion-based generative models.
method Simple framework to analyze discretization, initialization, and score estimation errors.
result First Wasserstein convergence bound for the Heun sampler and improved results for Euler sampler.
LFIS uses a time-dependent velocity field to sample from complex distributions.
problem Sampling from unnormalized density functions.
method LFIS learns a time-dependent velocity field to transport samples from a simple initial distribution to a complex target distribution.
result LFIS achieves state-of-the-art performance on various benchmark problems.
Bi-Lipschitz flows approximate a wide range of distributions.
problem Characterizing the expressivity of bi-Lipschitz normalizing flows.
method Linking score regularity to transport map bi-Lipschitzness via probability flow ODE.
result Gaussian pullbacks induced by bi-Lipschitz variance-preserving transport maps are L 1 L^1 L 1 -dense among all probability densities. StAD predicts divergence of diffusion and flow models without Jacobian computation.
problem Computing likelihood from diffusion and flow models is computationally expensive.
method Introduces StAD, a distillation method to predict divergence using Langevin-Stein operator.
result StAD predicts divergence with competitive variance and speed compared to existing methods.
A framework models order book dynamics using point processes and mass transport.
problem Capturing the complex dynamics of limit order books.
method Combines spatial point process for order flow and mass transport operator for market clearing.
result Provides insights into the interplay between order flow and price dynamics.
One-step diffusion samplers reduce sampling time and computational costs.
problem Efficient sampling from complex distributions.
method One-step diffusion, self-distillation, deterministic flow.
result Achieves competitive sample quality with fewer evaluations.
We study the problem of optimal portfolio selection in an illiquid market with discrete order flow. In this market, bids and offers are not available at any time but trading occurs more frequently near a terminal horizon. The investor can observe and trade the risky asset only at exogenous random times corresponding to…
Flow-based models generate data with improved theoretical guarantees.
problem Theoretical analysis of flow-based generative models.
method Proximal gradient descent in Wasserstein space for JKO flow model.
result KL guarantee of data generation by JKO flow model is O ( ε 2 ) O(\varepsilon^2) O ( ε 2 ) . MixFlows uses a mixture of flows for efficient variational inference.
problem Efficient and reliable variational inference for complex models.
method A new variational family of mixed flows with efficient algorithms and convergence guarantees.
result MixFlows provides more reliable posterior approximations and comparable sample quality to MCMC methods.