Multi-Fidelity Flow Matching: Cascaded Refinement of PDE Solutions

• URL: http://arxiv.org/abs/2605.16118v1
• Date: Fri, 15 May 2026 16:02:18 GMT
• Title: Multi-Fidelity Flow Matching: Cascaded Refinement of PDE Solutions
• Abstract summary: Multi-Fidelity Flow Matching is a cascade refinement framework for PDE solutions.<n>We exploit this in Multi-Fidelity Flow Matching (MFFM), a cascade refinement framework for PDE solutions.<n>MFFM is a learned analog of multigrid refinement that reaches the finest grid in $L$ deterministic network evaluations per query.
• Score: 6.144605787421899
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The source distribution in conditional flow matching is a design parameter that can be calibrated to data, not a default isotropic prior. We exploit this in Multi-Fidelity Flow Matching (MFFM), a cascade refinement framework for parametric PDE solutions: the source is calibrated to the empirical low-to-high-fidelity residual scale with local Gaussian-blur correlation, and the velocity network is conditioned on the low-fidelity solution. Conditioning makes the residual refinement problem substantially easier than unconditional field generation, while residual-calibrated source noise improves the flow-matching training geometry. A multi-resolution cascade applies the same construction independently between adjacent fidelities. After level-wise flow-matching pretraining, we fine-tune the composed cascade end-to-end with a deterministic one-step rollout, which makes one velocity evaluation per cascade level the optimized operating point at inference. The result is a learned analog of multigrid refinement that reaches the finest grid in $L$ deterministic network evaluations per query. We validate MFFM on eight benchmarks: two super-resolution problems and six spatiotemporal forecasting tasks from PDEBench, The Well, and the FNO Navier--Stokes dataset.

Related papers

• FMOPF: Latent Flow Matching with Constraint-Aware Interaction Priors for AC Optimal Power Flow [4.037525873726113]
  AC optimal power flow determines the minimum-cost generation dispatch under nonlinear power balance constraints.<n>This paper presents FMOPF, a framework that resolves the conflation of two tasks within a single model.<n>Experiments on four IEEE test systems demonstrate that FMOPF provides the most effective Newton-Raphson warm starts.
  arXiv  Detail & Related papers  (2026-07-24T12:49:09Z)
• From Atoms to Entropy: Optimal Noise Allocation for Diffusion Training in the Convex Regime [52.459513910242485]
  We develop a general statistical framework for studying optimal noise-level allocation in diffusion training.<n>We show that the optimized training schedule admits an atomic minimizer, concentrated on finitely many noise levels.<n>We then evaluate the entropic schedule in larger-scale experiments, where full schedule optimization is currently intractable.
  arXiv  Detail & Related papers  (2026-07-10T20:59:06Z)
• RBE-Flow: Recurrent Bayesian Estimation on Feature Manifolds for Cross-Modal Registration [14.194086645453767]
  Cross-pixel image registration is challenging due to severe non-linear radiometric and uncertainty.<n>In this paper we propose a novel framework that reformulates dense-modal flow estimation.
  arXiv  Detail & Related papers  (2026-06-29T15:58:25Z)
• Closed-Form Spectral Regularization for Multi-Task Model Merging [96.82449201305234]
  Model merging combines several independently fine-tuned experts into a single multi-task model without any training data.<n>State-of-the-art merging methods formulate merging as a layer-wise interference problem.<n>We propose SWUDI, a closed-form method that combines a soft exponential filter, which matches the gradient-flow trajectory of iterative descent.
  arXiv  Detail & Related papers  (2026-06-05T14:00:47Z)
• Precise: SDE-Consistent Stochastic Sampling for RL Post-Training of Flow-Matching Models [56.67321805551389]
  Reinforcement learning (RL) has become an effective way to improve prompt alignment and perceptual quality in diffusion and flow-matching generators.<n>The sampler, controlling the exploration behavior and denoising dynamics, is thus part of the policy.<n>We propose a new sampler that balances effective exploration with stability.
  arXiv  Detail & Related papers  (2026-05-22T11:37:22Z)
• Efficient Adjoint Matching for Fine-tuning Diffusion Models [29.082214342696858]
  We propose EAM, which substantially improves training efficiency by reformulating the SOC problem with a textit base drift and a textitterminal cost.<n>EAM converges up to 4x faster than AM and matches or surpasses it across various metrics including PickScore, ImageReward, HPSv2.1, CLIPScore and Aesthetics.
  arXiv  Detail & Related papers  (2026-05-12T03:55:12Z)
• Training-Free Refinement of Flow Matching with Divergence-based Sampling [17.850801452423074]
  Flow Divergence Sampler (FDS) is a training-free framework that refines intermediate states before each solver step.<n>FDS exploits this signal to steer states toward less ambiguous regions.<n>As a plug-and-play framework compatible with standard solvers and off-the-shelf flow backbones, FDS consistently improves fidelity across various generation tasks.
  arXiv  Detail & Related papers  (2026-04-06T12:54:58Z)
• 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)
• Diversity-Aware Adaptive Collocation for Physics-Informed Neural Networks via Sparse QUBO Optimization and Hybrid Coresets [0.0]
  PINNs enforce governing equations by penalizing PDE residuals at interior collocation points.<n>Standard collocation strategies can oversample smooth regions, produce highly correlated point sets, and incur unnecessary training cost.<n>We propose a sparse graph-based BQM built on a kNN similarity graph and an efficient repair procedure that enforces an exact collocation budget.
  arXiv  Detail & Related papers  (2026-03-06T14:26:34Z)
• Temporal Pair Consistency for Variance-Reduced Flow Matching [13.328987133593154]
  Temporal Pair Consistency (TPC) is a lightweight variance-reduction principle that couples velocity predictions at paired timesteps along the same probability path.<n>Instantiated within flow matching, TPC improves sample quality and efficiency across CIFAR-10 and ImageNet at multiple resolutions.
  arXiv  Detail & Related papers  (2026-02-04T00:05:21Z)
• Environment-Aware Indoor LoRaWAN Path Loss: Parametric Regression Comparisons, Shadow Fading, and Calibrated Fade Margins [3.776919981139063]
  Indoor LoRaWAN propagation is shaped by structural and time-varying context factors.<n>We present an environment-aware, statistically disciplined path loss framework evaluated using leakage-safe cross-validation.
  arXiv  Detail & Related papers  (2025-10-05T20:14:48Z)
• Decentralized Nonconvex Composite Federated Learning with Gradient Tracking and Momentum [78.27945336558987]
  Decentralized server (DFL) eliminates reliance on client-client architecture.<n>Non-smooth regularization is often incorporated into machine learning tasks.<n>We propose a novel novel DNCFL algorithm to solve these problems.
  arXiv  Detail & Related papers  (2025-04-17T08:32:25Z)
• Consistency Flow Matching: Defining Straight Flows with Velocity Consistency [97.28511135503176]
  We introduce Consistency Flow Matching (Consistency-FM), a novel FM method that explicitly enforces self-consistency in the velocity field. Preliminary experiments demonstrate that our Consistency-FM significantly improves training efficiency by converging 4.4x faster than consistency models.
  arXiv  Detail & Related papers  (2024-07-02T16:15:37Z)
• Green, Quantized Federated Learning over Wireless Networks: An Energy-Efficient Design [68.86220939532373]
  The finite precision level is captured through the use of quantized neural networks (QNNs) that quantize weights and activations in fixed-precision format. The proposed FL framework can reduce energy consumption until convergence by up to 70% compared to a baseline FL algorithm.
  arXiv  Detail & Related papers  (2022-07-19T16:37:24Z)
• FPCR-Net: Feature Pyramidal Correlation and Residual Reconstruction for Optical Flow Estimation [72.41370576242116]
  We propose a semi-supervised Feature Pyramidal Correlation and Residual Reconstruction Network (FPCR-Net) for optical flow estimation from frame pairs. It consists of two main modules: pyramid correlation mapping and residual reconstruction. Experiment results show that the proposed scheme achieves the state-of-the-art performance, with improvement by 0.80, 1.15 and 0.10 in terms of average end-point error (AEE) against competing baseline methods.
  arXiv  Detail & Related papers  (2020-01-17T07:13:51Z)

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.