Paper analyzes convergence of ODE samplers in Wasserstein distances.
problem Limited theoretical understanding of convergence properties of probability flow ODEs.
method Convergence analysis for general probability flow ODEs in 2-Wasserstein distance.
result First non-asymptotic convergence analysis for probability flow ODE samplers.
The paper improves the probability flow ODE sampler for faster sampling of natural images.
problem Improving the convergence rate of the probability flow ODE sampler.
method Adapting the probability flow ODE sampler to exploit intrinsic low-dimensional structures in natural image data.
result Achieves a dimension-free convergence rate of O ( k / T ) O(k/T) O ( k / T ) in total variation distance, improving upon existing results. A new method for sampling from complex distributions using Langevin samplers.
problem Sampling from unnormalized Boltzmann densities.
method Probability flow ODE derived from linear stochastic interpolants, employing Langevin samplers.
result Efficient simulation of the flow with non-asymptotic convergence rate.
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. Derives PF-ODE for infinite-dimensional functions, improving function generation tasks.
problem Efficient inference in infinite-dimensional diffusion models.
method Derives PF-ODE in infinite-dimensional function spaces.
result Reduces function evaluations while maintaining sample quality.
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.
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. 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). New bounds for generative models under weaker assumptions.
problem Establishing convergence guarantees for generative models under weak assumptions.
method Non-asymptotic 2-Wasserstein distance bounds for probability flow ODEs under weak log-concavity and Lipschitz continuity.
result Concrete convergence rates for generative models, including non-log-concave distributions.
New theory improves diffusion model convergence for generating data.
problem Improving convergence of diffusion models for data generation.
method Developed a non-asymptotic convergence theory for probability flow ODEs.
result Proves d / ε d/\varepsilon d / ε iterations suffice for approximating target distributions. SeqRF straightens generative model flows to speed up sampling.
problem High global truncation error in ODE-based solvers for generative models.
method SeqRF, a learning technique that straightens the probability flow.
result Significantly improved sampling speed and synthesis quality.
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.
Bayesian Gaussian Process ODEs enhanced with normalizing flows for improved flexibility and accuracy.
problem Limitations of standard Gaussian Process ODEs in modeling complex scenarios.
method Introducing normalizing flows to reparameterize the ODE vector field, developing a data-driven variational learning algorithm.
result Improved accuracy and uncertainty estimates for Bayesian Gaussian Process ODEs.
CTM improves diffusion model sampling quality with efficient ODE traversal.
problem Lack of natural trade-off between sample quality and speed in consistency models.
method CTM trains a neural network to output scores and traverse ODE trajectories efficiently.
result CTM achieves state-of-the-art FIDs and improves sample quality with increased computational budget.
Neural Manifold ODEs improve manifold data modeling.
problem Adapting deep generative models to non-Euclidean spaces.
method Introducing Neural Manifold ODEs for manifold generalization and continuous probability computation.
result Improves density estimation and downstream tasks on arbitrary manifolds.
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.
Improved analysis for diffusion models reduces KL divergence error dependence on data dimension and discretization step size.
problem Analyze the convergence of diffusion-based generative models under minimal assumptions.
method Model the generation process as a composition of reverse ODE and noising steps, leveraging Wasserstein-type error control and noise addition.
result Achieved a linear dependence on data dimension and improved dependence on discretization step size for KL divergence error.
This work establishes near-minimax optimal guarantees for ODE-based samplers under mild assumptions.
problem Develop rigorous statistical guarantees for ODE-based samplers in generative modeling.
method Proposes a smooth regularized score estimator and refined convergence analysis.
result Achieves minimax rate in total variation distance for ODE-based samplers under mild assumptions.
CNFs learn on manifolds using PPD, improving likelihood and sample quality.
problem Training CNFs on manifolds efficiently and accurately.
method Minimizing PPD, a novel divergence, to train CNFs on manifolds.
result CNFs trained with PPD achieve state-of-the-art results on manifold benchmarks.
JKO-iFlow uses neural ODEs to improve generative models with reduced memory and training complexity.
problem Efficiently training deep generative models in high dimensions with reduced memory and training complexity.
method JKO scheme inspired neural ODE flow network with adaptive time reparameterization.
result JKO-iFlow achieves competitive performance compared to existing models at reduced computational and memory cost.
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.
Riemannian flows model curved spaces better.
problem Normalizing flows misspecified on curved spaces.
method Riemannian continuous normalizing flows using ODE solutions.
result Improves modeling on spheres, torii, and hyperbolic spaces.
New method for estimating diffusion model densities without solving flows.
problem Estimating log densities from diffusion models efficiently.
method Monte Carlo path integral estimation, avoiding flow solving.
result Significantly more scalable and efficient density estimation.
OT-Flow uses optimal transport to improve CNFs for faster and more accurate density estimation.
problem Computational challenges in continuous normalizing flows.
method OT-Flow leverages optimal transport to regularize CNFs and uses exact trace computation.
result OT-Flow achieves competitive performance with one-fourth the number of weights and significant speedups.
The Normalizing Flow (NF) models a general probability density by estimating an invertible transformation applied on samples drawn from a known distribution. We introduce a new type of NF, called Deep Diffeomorphic Normalizing Flow (DDNF). A diffeomorphic flow is an invertible function where both the function and its i…
Generative model improved using Liouville PDE-based sliced-Wasserstein flow.
problem Improving generative models for fair regression.
method Transformed sliced-Wasserstein flow into Liouville PDE-based formalism, handling density estimation with normalizing flows of neural ODE.
result Outperforms in convergence and fairness with reduced variance.
A new method for normalizing flows using stochastic interpolants simplifies likelihood estimation and improves efficiency.
problem Efficient and scalable likelihood estimation for complex probability distributions.
method Inference of velocity field from time-dependent density interpolating between base and target densities.
result Simplified quadratic loss for velocity estimation, leading to faster and more efficient training.
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 paradigm for Neural ODEs stabilizes training and improves model performance.
problem Gradient vanishing-explosion problem in training deep neural networks.
method ODEtoODE: Nested system of flows with orthogonal group constraints.
result Strong convergence results and improved downstream models in reinforcement learning and supervised learning.
Develops a framework for distilling flow models from few steps.
problem Improving few-step sampling in diffusion models for better performance.
method Local approximation errors and dynamical amplification controlled through analytical tractability.
result Deep residual compositions efficiently approximate long-horizon transport with controlled global error.
CTRNNs improve blood glucose forecasting in ICU, outperforming traditional models.
problem Forecasting blood glucose in ICU with irregular measurements.
method Continuous time autoregressive recurrent neural networks (CTRNNs) using neural ODE or neural flow layers.
result CTRNNs generally outperform traditional autoregressive models in probabilistic forecasting of blood glucose.
Neural ODEs extended to manifolds for flexible sampling.
problem Sampling from complex multimodal distributions on non-trivial topologies.
method Extending Neural ODEs to smooth manifolds using vector fields.
result A general methodology for building normalizing flows on manifolds.
A new method for learning conditional distributions using ODEs and neural networks.
problem Learning conditional distributions efficiently and accurately.
method Conditional Föllmer Flow, discretized with Euler's method, using nonparametric velocity estimation.
result Effective approximation of target conditional distributions, with convergence results for Wasserstein-2 distance.
New method uses Fokker-Planck equation for sampling and inference.
problem Intractability of evaluating probability density in practical applications.
method Reformulates Fokker-Planck equation as a particle flow method, using velocity field.
result Turns intractable density evaluation into an advantage for variational inference, kernel mean embeddings, and sequential Monte Carlo.
The paper provides convergence guarantees for ODE-based generative models using transformers.
problem Theoretical guarantees for ODE-based generative models.
method A pre-trained autoencoder maps inputs to a latent space, and a transformer predicts the velocity field.
result The distribution of samples generated via estimated ODE flow converges to the target distribution in Wasserstein-2 distance.
OpFlow predicts robust OD flows by learning choice potentials conditioned on spatial exposures.
problem Deep models trained on raw counts are vulnerable to distribution shift.
method OpFlow learns row-centered choice potentials and reconstructs flows by combining them with a calibrated origin scale.
result OpFlow improves robustness under environment shifts, as shown by controlled synthetic shifts and a real-world experiment.
REGS samples from unnormalized distributions using gradient flow and neural networks.
problem Sampling from unnormalized distributions with high accuracy and efficiency.
method REGS is a particle method that iteratively transforms samples from a reference distribution to match an unnormalized target distribution using Wasserstein gradient flow and neural networks.
result REGS outperforms state-of-the-art methods in sampling from challenging multimodal distributions and real datasets.
The study focuses on estimating and predicting time-varying origin to destination (OD) trip tables for a dynamic traffic assignment (DTA) model. A bi-level optimisation problem is formulated and solved to estimate OD flows from pre-existent demand matrix and historical traffic flow counts. The estimated demand is then …
Deep residual networks implicitly converge to neural ODEs.
problem Link between discrete and continuous deep learning models.
method Establishing implicit regularization for residual networks towards neural ODEs.
result Deep residual networks initialized as discretizations of neural ODEs converge to such ODEs during training.
New method AM learns optimal vector fields for entire distribution sequences, matching OT.
problem Optimal Transport (OT) problem in generative modeling.
method Action Matching (AM) method learns optimal vector fields for a sequence of distributions.
result AM method achieves optimal transport by learning vector fields for entire distribution sequences.
In the vector space of algebraic curvature operators we study the reaction ODE $$\frac{dR}{dt} = R^2+R^{#}= Q(R)$$ which is associated to the evolution equation of the Riemann curvature oper- ator along the Ricci flow. More precisely, we analyze the stability of a special class of zeros of this ODE up to suitable norma…
Time series with non-uniform intervals occur in many applications, and are difficult to model using standard recurrent neural networks (RNNs). We generalize RNNs to have continuous-time hidden dynamics defined by ordinary differential equations (ODEs), a model we call ODE-RNNs. Furthermore, we use ODE-RNNs to replace t…
A two-phase algorithm identifies the best arm in sparse linear bandits with fixed budget.
problem Best arm identification in sparse linear bandits with limited budget.
method Lasso and Optimal-Design (Lasso-OD) based linear best-arm identification.
result Lasso-OD achieves significant performance improvement for sparse and high-dimensional linear bandits.
Neural ODEs' performance varies with numerical method, requiring adaptive step size control.
problem Neural ODEs' performance depends on the numerical method used during training.
method Proposes an adaptive step size control algorithm to ensure a valid ODE without increasing computational cost.
result Valid Neural ODEs require careful numerical method selection and step size adaptation.
This paper compares two methods for training neural ODEs in time-series regression and CNFs.
problem Training neural ODEs for time-series regression and CNFs efficiently.
method Discretize-Optimize (Disc-Opt) vs. Optimize-Discretize (Opt-Disc) approaches.
result Disc-Opt methods can achieve similar performance as Opt-Disc at inference with drastically reduced training costs.
We accelerate CNF by reducing ODE truncation errors with polynomial regularization.
problem High computation cost of CNF due to large truncation errors in solving ODEs.
method Add polynomial regularization to approximate ODE trajectories with polynomial functions.
result 42.3% to 71.3% reduction of NFE on density estimation, 19.3% to 32.1% on variational auto-encoder.
This work analyzes the statistical properties of neural ODEs for distribution learning.
problem Statistical properties of neural ODEs for distribution learning.
method General nonparametric statistical convergence analysis for distribution learning via neural ODE models.
result Established nearly minimax-optimal convergence rates for neural ODEs.
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.