New method efficiently simulates fluid flows across various conditions.
problem High computational cost in simulating fluid flows.
method Parameter-conditioned sequential generative modeling of neural networks.
result Trained models simulate fluid flows at orders of magnitude faster than traditional methods.
Study proves mean curvature flow in GRW spacetimes with perpendicular boundary condition.
problem Longtime existence of mean curvature flow in GRW spacetimes.
method Proved longtime existence using perpendicular Neumann boundary condition and null convergence condition.
result Metric of solution is conformal to GRW leaf's metric in asymptotic time.
Guided Flows enhance sample quality in conditional image generation and text-to-speech.
problem Improving sample quality in conditional generative models.
method Integrating classifier-free guidance into Flow Matching (FM) models for Continuous Normalizing Flows (CNFs).
result Guided Flows significantly improve sample quality in conditional image generation and text-to-speech synthesis.
Diverging Flows detects extrapolations in flow models, ensuring reliable predictions.
problem Flow models extrapolate into invalid data, leading to silent failures.
method Structurally enforce inefficient transport for off-manifold inputs.
result Effective detection of extrapolations without compromising predictive fidelity or inference latency.
Generative model for set-valued data using permutation invariant flows.
problem Modeling set-valued data with conditional generative models.
method Conditional generative probabilistic model using continuous normalizing flows with permutation equivariant dynamics.
result Significantly outperforms non-permutation invariant baselines in log likelihood and domain-specific metrics.
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.
ContextFlow++ improves generative models by conditioning on mixed-variable contexts.
problem Lack of effective methods for context conditioning in flow-based generative models.
method Proposes ContextFlow++ with additive conditioning and mixed-variable architecture.
result ContextFlow++ achieves higher performance metrics and faster training.
MAGIC-Flow generates and classifies medical images with interpretability.
problem Challenges in generative modeling for medical imaging.
method Conditional multiscale normalizing flow architecture.
result MAGIC-Flow creates realistic, diverse samples and improves classification.
We derive general Novikov-Morse type inequalities in a Conley type framework for flows carrying cocycles, therefore generalizing our results in [FJ2] derived for integral cocycle. The condition of carrying a cocycle expresses the nontriviality of integrals of that cocycle on flow lines. Gradient-like flows are distingu…
AC-Flow models yield arbitrary conditional distributions for imputation.
problem Intractable conditional distributions of arbitrary subsets of features.
method Novel extension of flow models for arbitrary conditioning.
result State-of-the-art performance in imputation across various datasets.
CCVFM uses coreset to improve generative models by refining residual flows.
problem Generating multimodal distributions from scratch is challenging.
method Augments hierarchical rectified flow with a data-informed source distribution using a coreset.
result CCVFM achieves competitive few-step generation without a learned noise-to-data map.
Study of Kähler-Ricci flow on toric Fano varieties with preserved symplectic condition.
problem Analyzing the generalized Kähler-Ricci flow on toric Fano varieties.
method Establishing global existence, deriving entropy and energy functionals.
result Convergence of nonsingular solutions at infinity and weak convergence of the flow.
VFMs use noise adapters to conditionally generate images in one step.
problem Conditional image generation with iterative models is slow and requires explicit sampling paths.
method Developed a variational flow map framework that learns noise distributions for conditional sampling.
result VFMs achieve well-calibrated conditional samples in a single forward pass.
Study shows how to preserve Lagrangian condition in mean curvature flow on Kim-McCann metrics.
problem Preserving Lagrangian condition in mean curvature flow on Kim-McCann metrics.
method Expressed mean curvature flow within generalized mean curvature flow framework.
result Lagrangian condition is preserved along the flow.
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.
Proposes a new method for posterior sampling using MMD with negative distance kernel.
problem Posterior sampling and conditional generative modeling.
method Approximates joint distribution using discrete Wasserstein gradient flows of MMD with negative distance kernel.
result Establishes an error bound for posterior distributions and proves the method is a Wasserstein gradient flow.
Generative model uses neural flows for next-frame video generation conditioned on labels.
problem Blurriness and instability in video generation models.
method Proposes using Glow, a neural flow model, for next-frame video generation conditioned on labels.
result Glow model produces clearer and more stable videos compared to GANs.
New theorem using Ricci flow for Gromov almost flat manifolds.
problem Conditions for Gromov almost flat manifolds.
method Employing Ricci flow to derive a new theorem.
result New theorem with weaker condition than Gromov--Ruh Theorem.
Study of t-Gauduchon Ricci-flat condition under Chern-Ricci flow on non-Kähler manifolds.
problem Investigating the t-Gauduchon Ricci-flat condition on non-Kähler manifolds. method Chern-Ricci flow approach, examples of non-Kähler Calabi-Yau manifolds, and geometric flow analysis.
result Examples of Chern-Ricci flow on non-Kähler Calabi-Yau manifolds that do not preserve the t-Gauduchon Ricci-flat condition. We construct maximal hypersurfaces with a Neumann boundary condition in Minkowski space via mean curvature flow. In doing this we give general conditions for long time existence of the flow with boundary conditions with assumptions on the curvature of a the Lorentz boundary manifold.
The paper proves uniqueness of evolving graphs by mean curvature flow under specific conditions.
problem Proving uniqueness of entire graphs evolving by mean curvature flow.
method Analyzes graphs of locally Lipschitz functions and rotationally symmetric solutions, proving uniqueness under uniform lower bounds and proper graphs.
result Uniqueness of entire graphs evolving by mean curvature flow under specified conditions.
We prove a gradient estimate for graphical spacelike mean curvature flow with a general Neumann boundary condition in dimension n=2. This then implies that the mean curvature flow exists for all time and converges to a translating solution.
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.
This work introduces a new model for complex stochastic processes.
problem Difficulties in representing non-stationary distributions with conventional models.
method Recurrent Autoregressive Flows using normalizing flows with recurrent neural connections.
result Demonstrates the effectiveness of the proposed model through experiments.
New formulations for Ricci flows without smoothness.
problem Characterize Ricci flows without smooth solutions.
method Weak formulations of super Ricci flows with saturation condition.
result Generalized formulations for singular settings.
Paper introduces c-Glow for efficient structured output learning.
problem Intractable computation of conditional likelihood in structured prediction models.
method Conditional Glow (c-Glow) - a conditional generative flow that computes p(y|x) exactly and efficiently.
result c-Glow outperforms state-of-the-art baselines in structured prediction tasks.
Improves conditional distribution modeling with simpler training.
problem Analyzing inverse problems with invertible neural networks.
method Uses normalizing flows to maximize posterior likelihood, incorporating conditioning.
result Easier training and natural framework for conditional generation.
HCNAF models complex conditional distributions for probabilistic occupancy forecasting.
problem Modeling complex conditional probability density functions for occupancy forecasting.
method Hyper-Conditioned Neural Autoregressive Flow (HCNAF) combining AF and hyper-network.
result HCNAF achieves state-of-the-art performance in self-driving datasets.
CSI method learns conditional distributions by estimating flow equations.
problem Learning conditional distributions in generative models.
method Estimates probability flow equations to transport reference to target distribution.
result Derives explicit expressions for conditional drift and score functions.
Paper proves stability of flow in cotangent bundle for special Lagrangian submanifolds.
problem Stability of generalized Lagrangian mean curvature flow in cotangent bundle.
method New derivative estimates to weaken initial conditions and remove curvature constraints.
result Stability of flow near special Lagrangian submanifolds in cotangent bundle.
Generalizes Ricci flow starting from small curvature concentration with a Morrey-type condition.
problem Ricci flow starting from manifolds with unbounded curvature.
method Replaces bounded curvature with a Morrey-type condition on the gradient of the metric relative to a complete bounded curvature metric.
result Long-time existence of Ricci flow with curvature decay estimates and diffeomorphic manifold.
Proposes a method to apply conformal prediction to probabilistic time series forecasting models.
problem Obtaining accurate prediction regions for multi-step time series forecasting with probabilistic models.
method Conformalises conditional normalising flows to generate potentially disjoint prediction regions.
result Improves predictive efficiency in time series forecasting with multimodal distributions.
The study finds sufficient conditions for Reeb flows to have genus zero global surfaces of section.
problem Finding conditions for Reeb flows to have genus zero global surfaces of section.
method Analyzes linking assumptions on periodic orbits and ambient contact geometry.
result Reveals sufficient conditions for Reeb flows to have genus zero global surfaces of section.
We address representational challenges in normalizing flows, particularly depth and conditioning issues.
problem Challenges in training normalizing flows, including vanishing/exploding gradients and poor conditioning.
method Analyzes representational aspects of depth and conditioning in normalizing flows, proving theoretical bounds and investigating phenomena.
result Proves that shallow affine coupling networks are universal approximators in Wasserstein distance if ill-conditioning is allowed.
The paper improves heat equation estimates under weaker Ricci curvature conditions.
problem Improving heat equation estimates under weaker Ricci curvature conditions.
method Establishing Li-Yau-type and Hamilton-type estimates for positive solutions of the heat equation under generalized Ricci flow.
result Deriving Harnack-type inequalities and monotonicity of parabolic frequency.
CAFLOW uses auto-regressive flows to translate images efficiently.
problem Image-to-image translation tasks.
method Transforms conditioning image into latent encodings using normalizing flows, models conditional distribution with auto-regressive distributions.
result Outperforms former conditional flow designs.
Unified approach to analysis on Ricci nonnegative manifolds and flows using optimal transport.
problem Generalizing Perelman's functionals to super Ricci flows.
method Optimal transport, Bochner inequality, gradient estimates, EVI.
result Unified condition equivalent to Ricci nonnegativity for smooth evolutions of Riemannian manifolds.
We show that the pluriclosed flow preserves generalized Kähler structures with the extra condition [J+,J−]=0, a condition referred to as "split tangent bundle." Moreover, we show that in this in this case the flow reduces to a nonconvex fully nonlinear parabolic flow of a scalar potential function. We prove a num…
In this note we generalize an extension theorem in [5] and [9] of the mean curvature flow to the H^{k} mean curvature flow under some extra conditions. The main difficult problem in proving the extension theorem is to find a suitable version of Michael-Simon inequality for the H^{k} mean curvature flow, and to do a sui…
PL-MCMC samples from normalizing flows' conditional distributions.
problem Sampling from complex conditional distributions learned by normalizing flows.
method Metropolis-Hastings implementation of PL-MCMC.
result PL-MCMC asymptotically samples from exact conditional distributions.
The paper constructs optimal confidence bands for kernel gradient flow estimators.
problem Estimating generalization error and constructing confidence bands for kernel gradient flows.
method Established convergence rates and constructed optimal confidence bands under capacity-source condition.
result Optimal confidence bands for kernel gradient flows have shrinkage rates close to minimax optimal rates.
MFGs explain and enhance generative models, revealing new model types.
problem Understanding and improving generative models.
method Mean-field games (MFGs) as a framework to explain and enhance generative models.
result Established connections between MFGs and generative flows, diffusions, and gradient flows.
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.
Flow approach solves Toda system equations.
problem Solving the Toda system equations.
method Introducing Toda flow to study the system.
result Global existence and convergence conditions established.
New framework explains normalizing flows' power and limitations.
problem Understanding the expressive power and limitations of normalizing flows.
method Theoretical framework for well-conditioned coupling-based normalizing flows and volume-preserving flows.
result RealNVP is distributionally universal, but volume-preserving flows are not.
Paper introduces new flows to find circle packings with specific curvature.
problem Finding circle packings with prescribed total geodesic curvatures.
method Introduces combinatorial Calabi flow, fractional combinatorial Calabi flow, and combinatorial p-th Calabi flow.
result Establishes conditions for the longtime behaviors of these flows.
We study curvature pinching estimates of Ricci flow on complete 3- dimensional manifolds without bounded curvature assumption. We will derive some general curvature conditions which are preserved on any complete solution of 3-dim Ricci flow, these conditions include nonnegative Ricci curvature and sectional curvature a…
B List has proposed a geometric flow whose fixed points correspond to solutions of the static Einstein equations of general relativity. This flow is now known to be a certain Hamilton-DeTurck flow (the pullback of a Ricci flow by an evolving diffeomorphism) on RxM^n. We study the SO(n) rotationally symmetric case of Li…