SplineFlow: Flow Matching for Dynamical Systems with B-Spline Interpolants

• URL: http://arxiv.org/abs/2601.23072v1
• Date: Fri, 30 Jan 2026 15:19:48 GMT
• Title: SplineFlow: Flow Matching for Dynamical Systems with B-Spline Interpolants
• Abstract summary: SplineFlow is a theoretically grounded flow matching algorithm that jointly models conditional paths across observations via B-spline.<n>We show how SplineFlow exploits the smoothness and stability of B-spline bases learn the complex underlying dynamics while ensuring the multi-marginal requirements are met.
• Score: 14.711575625163045
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Flow matching is a scalable generative framework for characterizing continuous normalizing flows with wide-range applications. However, current state-of-the-art methods are not well-suited for modeling dynamical systems, as they construct conditional paths using linear interpolants that may not capture the underlying state evolution, especially when learning higher-order dynamics from irregular sampled observations. Constructing unified paths that satisfy multi-marginal constraints across observations is challenging, since naïve higher-order polynomials tend to be unstable and oscillatory. We introduce SplineFlow, a theoretically grounded flow matching algorithm that jointly models conditional paths across observations via B-spline interpolation. Specifically, SplineFlow exploits the smoothness and stability of B-spline bases to learn the complex underlying dynamics in a structured manner while ensuring the multi-marginal requirements are met. Comprehensive experiments across various deterministic and stochastic dynamical systems of varying complexity, as well as on cellular trajectory inference tasks, demonstrate the strong improvement of SplineFlow over existing baselines. Our code is available at: https://github.com/santanurathod/SplineFlow.

Related papers

• TracingFlow: A Simulation-Free Trajectory Inference Framework Based on Second-Order Dynamics [7.088148340428723]
  Inferring continuous system evolution from sparse temporal snapshots is a key challenge in generative modeling and single-cell omics.<n>Here, we introduce TracingFlow, a simulation-free Flow Matching framework generalizing to second-order dynamics.<n>By using neural networks to regress the acceleration field, TracingFlow provides an exact, efficient solution to the Dynamical Optimal Acceleration Transport (DOAT) problem.
  arXiv  Detail & Related papers  (2026-08-21T13:11:29Z)
• P-Flow: Proxy-gradient Flows for Linear Inverse Problems [28.438072266272954]
  P-Flow is a framework that stabilizes the reconstruction process by leveraging a proxy gradient to update the source point.<n>Experiments across diverse restoration tasks demonstrate that P-Flow delivers competitive performance.
  arXiv  Detail & Related papers  (2026-05-08T17:07:36Z)
• Chain of Modality: From Static Fusion to Dynamic Orchestration in Omni-MLLMs [84.3271821505699]
  Chain of Modality (CoM) is an agentic framework that transitions multimodal fusion from passive concatenation to dynamic orchestration.<n> operating in either a training-free or a data-efficient SFT setting, CoM achieves robust and consistent generalization across diverse benchmarks.
  arXiv  Detail & Related papers  (2026-04-16T01:21:14Z)
• Equivariant Efficient Joint Discrete and Continuous MeanFlow for Molecular Graph Generation [10.729712481687628]
  Graph-structured data jointly contain discrete topology and continuous geometry.<n>Existing flow-matching approaches for graph generation typically decouple structure from geometry.<n>We propose Equivariant MeanFlow (EQUIMF), a unified SE(3)-equivariant generative framework.
  arXiv  Detail & Related papers  (2026-04-09T12:42:01Z)
• FluidFlow: a flow-matching generative model for fluid dynamics surrogates on unstructured meshes [2.7455202504794642]
  We introduce FluidFlow, a generative model based on conditional flow-matching.<n> FluidFlow is specifically designed to operate directly on CFD data defined on both structured and unstructured meshes.
  arXiv  Detail & Related papers  (2026-03-30T10:08:20Z)
• Riemannian MeanFlow for One-Step Generation on Manifolds [54.09734511705173]
  Flow Matching enables simulation-free training of generative models.<n>MeanFlow can be extended to manifold-valued generation where velocities lie in location-dependent tangent spaces.<n>Experiments on spheres, tori, and SO(3) demonstrate competitive one-step sampling with improved quality-efficiency trade-offs and substantially reduced sampling cost.
  arXiv  Detail & Related papers  (2026-03-11T12:41:46Z)
• GeodesicNVS: Probability Density Geodesic Flow Matching for Novel View Synthesis [54.39598154430305]
  We propose a Data-to-Data Flow Matching framework that learns deterministic transformations directly between paired views.<n>PDG-FM constrains flow trajectories using geodesic interpolants derived from probability density metrics of pretrained diffusion models.<n>These results highlight the advantages of incorporating data-dependent geometric regularization into deterministic flow matching for consistent novel view generation.
  arXiv  Detail & Related papers  (2026-03-01T09:30:11Z)
• Variational Bayesian Flow Network for Graph Generation [54.94088904387278]
  We propose Variational Bayesian Flow Network (VBFN) for graph generation.<n>VBFN performs variational lifting to a tractable joint Gaussian variational belief family governed by structured precisions.<n>On synthetic and molecular graph datasets, VBFN improves fidelity and diversity, and surpasses baseline methods.
  arXiv  Detail & Related papers  (2026-01-30T03:59:38Z)
• MixFlow: Mixture-Conditioned Flow Matching for Out-of-Distribution Generalization [31.579433319908485]
  We introduce MixFlow, a conditional flow-matching framework for descriptor-controlled generation.<n>MixFlow enables smooth and extrapolation to unseen conditions, leading to substantially improved out-of-distribution generalization.<n>We empirically demonstrate its effectiveness across multiple domains, including prediction of responses to unseen perturbations in single-cell transcriptomic data and high-content microscopy-based drug screening tasks.
  arXiv  Detail & Related papers  (2026-01-16T23:13:21Z)
• WAM-Flow: Parallel Coarse-to-Fine Motion Planning via Discrete Flow Matching for Autonomous Driving [9.719456684859606]
  We introduce WAM-Flow, a vision--action (VLA) model that casts ego-trajectory planning as discrete flow matching over a structured token space.<n>WAM-Flow performs fully parallel, bidirectional denoising, enabling coarse-to-fine refinement with a tunable compute-accuracy trade-off.<n>These results establish discrete flow matching as a new promising paradigm for end-to-end autonomous driving.
  arXiv  Detail & Related papers  (2025-12-05T19:36:46Z)
• FlowPath: Learning Data-Driven Manifolds with Invertible Flows for Robust Irregularly-sampled Time Series Classification [14.643457217551484]
  We propose FlowPath, a novel approach that learns the geometry of the control path via an invertible neural flow.<n>We show that FlowPath consistently achieves statistically significant improvements in classification accuracy over baselines using fixed interpolants or non-invertible architectures.
  arXiv  Detail & Related papers  (2025-11-13T22:59:26Z)
• Longitudinal Flow Matching for Trajectory Modeling [7.063657100587108]
  We propose Interpolative Multi-Marginal Flow Matching (IMMFM), a framework that learns continuous dynamics jointly consistent with multiple observed time points.<n>IMMFM captures intrinsicity, handles irregular sparse sampling, and yields subject-specific trajectories.<n> Experiments on synthetic benchmarks and real-world longitudinal datasets show that IMMFM outperforms existing methods in both forecasting accuracy and further downstream tasks.
  arXiv  Detail & Related papers  (2025-10-03T23:33:50Z)
• CurveFlow: Curvature-Guided Flow Matching for Image Generation [11.836900973675297]
  Existing rectified flow models are based on linear trajectories between data and noise distributions.<n>This linearity enforces zero curvature, which can inadvertently force the image generation process through low-probability regions of the data manifold.<n>We introduce CurveFlow, a novel flow matching framework designed to learn smooth, non-linear trajectories by incorporating curvature guidance into the flow path.
  arXiv  Detail & Related papers  (2025-08-20T22:06:13Z)
• Stochastic Generative Flow Networks [89.34644133901647]
  Generative Flow Networks (or GFlowNets) learn to sample complex structures through the lens of "inference as control" Existing GFlowNets can be applied only to deterministic environments, and fail in more general tasks with dynamics. This paper introduces GFlowNets, a new algorithm that extends GFlowNets to environments.
  arXiv  Detail & Related papers  (2023-02-19T03:19:40Z)
• Manifold Interpolating Optimal-Transport Flows for Trajectory Inference [64.94020639760026]
  We present a method called Manifold Interpolating Optimal-Transport Flow (MIOFlow) MIOFlow learns, continuous population dynamics from static snapshot samples taken at sporadic timepoints. We evaluate our method on simulated data with bifurcations and merges, as well as scRNA-seq data from embryoid body differentiation, and acute myeloid leukemia treatment.
  arXiv  Detail & Related papers  (2022-06-29T22:19:03Z)
• Value Iteration in Continuous Actions, States and Time [99.00362538261972]
  We propose a continuous fitted value iteration (cFVI) algorithm for continuous states and actions. The optimal policy can be derived for non-linear control-affine dynamics. Videos of the physical system are available at urlhttps://sites.google.com/view/value-iteration.
  arXiv  Detail & Related papers  (2021-05-10T21:40:56Z)
• Learning Likelihoods with Conditional Normalizing Flows [54.60456010771409]
  Conditional normalizing flows (CNFs) are efficient in sampling and inference. We present a study of CNFs where the base density to output space mapping is conditioned on an input x, to model conditional densities p(y|x)
  arXiv  Detail & Related papers  (2019-11-29T19:17:58Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.