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Open problems in Flow matching

Scalable and stable training for flow matching1 paper raises it · 1 addresses it
Large-scale flow models struggle with training stability and integration error due to stochastic source-target pairing.
- Scaling Online Optimal Transport Minibatches for Flow Matchingraises · addresses
Efficient few-step generation without fixed discretization1 paper raises it · 1 addresses it
Few-step generation often requires heuristic timestep discretization, limiting flexibility and performance.
- Few-Step Generation via Data-Space Iterationraises · addresses
Data-free and simulation-free distillation for diffusion/flow models1 paper raises it · 1 addresses it
Distillation often relies on curated datasets or costly teacher rollouts, complicating training and scaling.
- Consistent Distribution Matching for Data-Free Diffusion Distillationraises · addresses
Dynamics-aligned latent representations for PDEs1 paper raises it · 1 addresses it
Reconstruction-based learning for PDEs often fails to capture the evolution of physical fields accurately.
- PDE-JEPA: Predictive Representation Learning of Latent Dynamics Modeling for Parametric PDEsraises · addresses
Detecting memorization in diffusion models1 paper raises it · 1 addresses it
Memorization in diffusion models can lead to failure in proper distributional learning.
- Detection of Memorization in Diffusion Models Through Thermodynamic Singularityraises · addresses

Named by an AI from these papers' abstracts.

Open problems

Recently funded

Topics in this field

flow matching · flow · generative modeling292 papers30 this week
physics informed neural · neural operators · informed neural networks291 papers25 this week
diffusion priors · posterior sampling · diffusion posterior73 papers14 this week

Topics in this field

Active contributors · 90 days

Anima AnandkumarNeural Operator Splitting for Fluid Dynamics in Complex Geometry5
Stefan T. RadevConditional Mean Flows: Few-Step Densities for Simulation-Based Inference5
Taiji SuzukiFinite-Sample Approximation of Hessian-Guided Perturbed Wasserstein Gradient Flows5
Jing XuSame Target, Different Origins: Aligning Latent Rollout for Consistent PDE Emulation4
Jun ZhangEqual Path Cost, Unequal Output Effects: Understanding Perturbation Propagation in Diffusion Models4
Alexander KorotinDiscrete Action Matching: Learning Stochastic Dynamics from Samples via State Graphs4

Active contributors

Activity · 12 weeks

Coming with more sources: repos

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Recent papers

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arXiv math.NAOct 5
IGA-KAN: Isogeometric Analysis with Physics-Informed Closed-Form Kolmogorov-Arnold Networks for Forward and Inverse PDEs
Sima Naraghi, Kourosh Parand, Amirhossein Sadr, Dara Rahmati
Isogeometric analysis (IGA) solves partial differential equations accurately on exact NURBS geometry, whereas neural solvers are mesh-free but often orders of magnitude less accurate and typically trained by non-convex optimization without error control. We propose IGA-KAN, which uses local Kolmogorov-Arnold networks, fitted in closed form, to improve the IGA solution instead of replacing it. An IGA Galerkin solve produces u_h; on every knot-vertex patch a Kolmogorov-Arnold ridge model is fitted to the strong form of the equation, the exact boundary data and u_h, and the models are blended by IGA hat functions. With fixed inner functions the fit is one batched linear least-squares problem, without optimizer, learning rate or initialization. An a posteriori safeguard, motivated by a maximum-principle bound, decides where local models are used, keeping the IGA solution elsewhere. On eight benchmarks with exact solutions, five from the literature and one also posed on a domain fitted to a brain slice from MRI, the method reduces the error of IGA, at an unchanged number of Galerkin unknowns, by factors of 4.2 to 90 in L^2 and 4.1 to 220 in H^1 on the reference meshes, and its L^2…
PDF arXiv
arXiv cs.CVOct 5
SPIN: Image Immunization Against Diffusion Editing via Single-Step Projection in Stochastic Neighborhoods
Fengming Gu, Jie Zhang, Zhongqi Wang, Qiankun Li, Shiguang Shan +1
Diffusion models have greatly advanced instruction-guided image editing, while also raising concerns about unauthorized image manipulation. Image immunization addresses this risk by adding imperceptible perturbations to an input image to disrupt subsequent edits. Since editing requests are unknown at image release, protection should remain effective beyond the instruction used to construct the perturbation. Existing immunization methods either require costly full-trajectory backpropagation or use intermediate objectives whose effects may be weakened by subsequent denoising. Meanwhile, a single inference path provides limited feedback about alternative denoising continuations. To address these challenges, we propose \textsc{SPIN}, a framework for image immunization via one-step projection over local stochastic trajectory neighborhoods. Starting from an early denoising state, \textsc{SPIN} generates stochastic neighboring states under the same instruction and predicts their clean latents through one-step projection without full unrolling. We then optimize a bounded input perturbation to maximize the average deviation of these predictions from a clean-edit reference, encouraging the…
PDF arXiv
arXiv cs.LGOct 5
OCL-PDE: A Generative Framework for PDE Inverse Problems with Observation-Complementary Latents
Ding Yang, Chuqi Chen, Chang Ma, Yang Xiang
Partial differential equation (PDE) inverse problems are often ill-posed, making fine-scale details difficult to recover. We address this problem by introducing a learned observation-complementary latent representation that preserves reconstruction-relevant information and is combined with the observation to reconstruct the unknown field. Building on this representation, we propose OCL-PDE, a generative framework that encourages the observation to guide large-scale structure and the latent to supply complementary fine-scale details. OCL-PDE is built on a physics-aware autoencoder (AE) and conditional Flow Matching, supporting inverse reconstruction as well as forward PDE prediction. Experiments demonstrate improved reconstruction accuracy and fine-detail recovery compared with the evaluated baselines.
PDF arXiv
arXiv cs.LGOct 5
Parameter Estimation in Machining Dynamics with Regenerative Delay and Nonsmooth Friction using Physics-Informed Neural Networks
Meiyazhagan Jaganathan, Vikram Pakrashi, Aasifa Rounak
A multi-domain eXtended Physics-Informed Neural Network (XPINN) framework is developed for nonsmooth Delay Differential Equations (DDEs). This is the first implementation to demonstrate the efficacy of partitioning the temporal domain into subdomains of integer multiples of the characteristic time delay and progressively training the associated subnetworks while freezing previously learned parameters. The efficacy of the proposed framework is demonstrated using a machining dynamics model that incorporates both regenerative and nonsmooth frictional effects. Results demonstrate that the proposed multi-domain XPINN framework leads to better solution reconstruction in DDEs and improved parameter estimation compared to a generic PINN (SPINN) formulation. The proposed method works particularly well for extended temporal domains and non-constant history functions. The robustness of inverse XPINN (I-XPINN) is also assessed using reference data contaminated with Gaussian measurement noise. Results indicate that I-XPINN remains resilient to measurement noise and the physics-informed constraints guide the network toward accurately recovering the underlying dynamics. This demonstrates, for…
PDF arXiv
arXiv cs.CVOct 5
Frequency-Decoupled Diffusion Guidance for Non-Blind Image Deblurring
Sihan Wang, Jinshu Huang, Haibin Su, Yunhua Xue
Pretrained diffusion models provide powerful image priors for training-free posterior sampling in image restoration. To guide this sampling process, frequency-aware methods progressively incorporate measurement information across frequency bands, facilitating coarse-to-fine reconstruction. However, existing methods typically do not explicitly separate frequency activation from degradation-induced attenuation, leaving attenuation differences among inactive frequencies insufficiently modeled. In this work, we propose frequency-decoupled posterior guidance to separate frequency activation from attenuation-aware spectral regularization. Specifically, a progressive low-to-high frequency schedule determines the active measurement band, while a kernel-derived attenuation map defines a selective spectral prior over inactive components. To stabilize the sampling process, we also introduce a local trajectory regularizer that suppresses spatially irregular state-to-clean deviations. For a fixed endpoint energy, we provide a KL-regularized path-space interpretation. In practice, we construct time-dependent guidance through local energy corrections using a Tweedie plug-in approximation.…
PDF arXiv
arXiv cs.LGOct 5
Transmission Factors for Lossy Compression of PDE Training Data: Measuring What Reaches a Trained Operator
Huy Hoang Le
Operator-learning benchmarks ship as full-precision arrays, and they have grown to terabyte scale. A curator who wants to distribute one has to decide how coarsely to store it. That decision is usually made by fixing a tolerance on the reconstruction error of the stored field. We show that this quantity is measured in the wrong place. It compares the stored field with the original, before any model is trained. What the curator is buying is the accuracy of a model trained on the compressed copy, and the two can disagree: two PDEBench families stored to identical field error differ threefold downstream. A solution operator smooths, so only part of the codec error ever reaches the model's output. That part can be measured. Push a compressed field through a model already trained at full precision, and compare its output against the output on the clean field. The measurement costs forward passes and no training on compressed data. It spans more than two orders of magnitude across six PDE families, and it orders downstream cost where field error does not, inverting 12 of 104 cross-dataset comparisons against field error's 36. Read as a budget, the same curve nominates a storage rate…
PDF arXiv

Papers

Topics in this field

flow matching · flow · generative modeling292 papers30 this week
physics informed neural · neural operators · informed neural networks291 papers25 this week
diffusion priors · posterior sampling · diffusion posterior73 papers14 this week

Active contributors · 90 days

Anima AnandkumarNeural Operator Splitting for Fluid Dynamics in Complex Geometry5
Stefan T. RadevConditional Mean Flows: Few-Step Densities for Simulation-Based Inference5
Taiji SuzukiFinite-Sample Approximation of Hessian-Guided Perturbed Wasserstein Gradient Flows5
Jing XuSame Target, Different Origins: Aligning Latent Rollout for Consistent PDE Emulation4
Jun ZhangEqual Path Cost, Unequal Output Effects: Understanding Perturbation Propagation in Diffusion Models4
Alexander KorotinDiscrete Action Matching: Learning Stochastic Dynamics from Samples via State Graphs4

Activity · 12 weeks

Coming with more sources: repos

Open problems in Flow matching

Scalable and stable training for flow matching1 paper raises it · 1 addresses it
Large-scale flow models struggle with training stability and integration error due to stochastic source-target pairing.
- Scaling Online Optimal Transport Minibatches for Flow Matchingraises · addresses
Efficient few-step generation without fixed discretization1 paper raises it · 1 addresses it
Few-step generation often requires heuristic timestep discretization, limiting flexibility and performance.
- Few-Step Generation via Data-Space Iterationraises · addresses
Data-free and simulation-free distillation for diffusion/flow models1 paper raises it · 1 addresses it
Distillation often relies on curated datasets or costly teacher rollouts, complicating training and scaling.
- Consistent Distribution Matching for Data-Free Diffusion Distillationraises · addresses
Dynamics-aligned latent representations for PDEs1 paper raises it · 1 addresses it
Reconstruction-based learning for PDEs often fails to capture the evolution of physical fields accurately.
- PDE-JEPA: Predictive Representation Learning of Latent Dynamics Modeling for Parametric PDEsraises · addresses
Detecting memorization in diffusion models1 paper raises it · 1 addresses it
Memorization in diffusion models can lead to failure in proper distributional learning.
- Detection of Memorization in Diffusion Models Through Thermodynamic Singularityraises · addresses

Named by an AI from these papers' abstracts.

Recent papers

All in Research →

arXiv math.NAOct 5
IGA-KAN: Isogeometric Analysis with Physics-Informed Closed-Form Kolmogorov-Arnold Networks for Forward and Inverse PDEs
Sima Naraghi, Kourosh Parand, Amirhossein Sadr, Dara Rahmati
Isogeometric analysis (IGA) solves partial differential equations accurately on exact NURBS geometry, whereas neural solvers are mesh-free but often orders of magnitude less accurate and typically trained by non-convex optimization without error control. We propose IGA-KAN, which uses local Kolmogorov-Arnold networks, fitted in closed form, to improve the IGA solution instead of replacing it. An IGA Galerkin solve produces u_h; on every knot-vertex patch a Kolmogorov-Arnold ridge model is fitted to the strong form of the equation, the exact boundary data and u_h, and the models are blended by IGA hat functions. With fixed inner functions the fit is one batched linear least-squares problem, without optimizer, learning rate or initialization. An a posteriori safeguard, motivated by a maximum-principle bound, decides where local models are used, keeping the IGA solution elsewhere. On eight benchmarks with exact solutions, five from the literature and one also posed on a domain fitted to a brain slice from MRI, the method reduces the error of IGA, at an unchanged number of Galerkin unknowns, by factors of 4.2 to 90 in L^2 and 4.1 to 220 in H^1 on the reference meshes, and its L^2…
PDF arXiv
arXiv cs.CVOct 5
SPIN: Image Immunization Against Diffusion Editing via Single-Step Projection in Stochastic Neighborhoods
Fengming Gu, Jie Zhang, Zhongqi Wang, Qiankun Li, Shiguang Shan +1
Diffusion models have greatly advanced instruction-guided image editing, while also raising concerns about unauthorized image manipulation. Image immunization addresses this risk by adding imperceptible perturbations to an input image to disrupt subsequent edits. Since editing requests are unknown at image release, protection should remain effective beyond the instruction used to construct the perturbation. Existing immunization methods either require costly full-trajectory backpropagation or use intermediate objectives whose effects may be weakened by subsequent denoising. Meanwhile, a single inference path provides limited feedback about alternative denoising continuations. To address these challenges, we propose \textsc{SPIN}, a framework for image immunization via one-step projection over local stochastic trajectory neighborhoods. Starting from an early denoising state, \textsc{SPIN} generates stochastic neighboring states under the same instruction and predicts their clean latents through one-step projection without full unrolling. We then optimize a bounded input perturbation to maximize the average deviation of these predictions from a clean-edit reference, encouraging the…
PDF arXiv
arXiv cs.LGOct 5
OCL-PDE: A Generative Framework for PDE Inverse Problems with Observation-Complementary Latents
Ding Yang, Chuqi Chen, Chang Ma, Yang Xiang
Partial differential equation (PDE) inverse problems are often ill-posed, making fine-scale details difficult to recover. We address this problem by introducing a learned observation-complementary latent representation that preserves reconstruction-relevant information and is combined with the observation to reconstruct the unknown field. Building on this representation, we propose OCL-PDE, a generative framework that encourages the observation to guide large-scale structure and the latent to supply complementary fine-scale details. OCL-PDE is built on a physics-aware autoencoder (AE) and conditional Flow Matching, supporting inverse reconstruction as well as forward PDE prediction. Experiments demonstrate improved reconstruction accuracy and fine-detail recovery compared with the evaluated baselines.
PDF arXiv
arXiv cs.LGOct 5
Parameter Estimation in Machining Dynamics with Regenerative Delay and Nonsmooth Friction using Physics-Informed Neural Networks
Meiyazhagan Jaganathan, Vikram Pakrashi, Aasifa Rounak
A multi-domain eXtended Physics-Informed Neural Network (XPINN) framework is developed for nonsmooth Delay Differential Equations (DDEs). This is the first implementation to demonstrate the efficacy of partitioning the temporal domain into subdomains of integer multiples of the characteristic time delay and progressively training the associated subnetworks while freezing previously learned parameters. The efficacy of the proposed framework is demonstrated using a machining dynamics model that incorporates both regenerative and nonsmooth frictional effects. Results demonstrate that the proposed multi-domain XPINN framework leads to better solution reconstruction in DDEs and improved parameter estimation compared to a generic PINN (SPINN) formulation. The proposed method works particularly well for extended temporal domains and non-constant history functions. The robustness of inverse XPINN (I-XPINN) is also assessed using reference data contaminated with Gaussian measurement noise. Results indicate that I-XPINN remains resilient to measurement noise and the physics-informed constraints guide the network toward accurately recovering the underlying dynamics. This demonstrates, for…
PDF arXiv
arXiv cs.CVOct 5
Frequency-Decoupled Diffusion Guidance for Non-Blind Image Deblurring
Sihan Wang, Jinshu Huang, Haibin Su, Yunhua Xue
Pretrained diffusion models provide powerful image priors for training-free posterior sampling in image restoration. To guide this sampling process, frequency-aware methods progressively incorporate measurement information across frequency bands, facilitating coarse-to-fine reconstruction. However, existing methods typically do not explicitly separate frequency activation from degradation-induced attenuation, leaving attenuation differences among inactive frequencies insufficiently modeled. In this work, we propose frequency-decoupled posterior guidance to separate frequency activation from attenuation-aware spectral regularization. Specifically, a progressive low-to-high frequency schedule determines the active measurement band, while a kernel-derived attenuation map defines a selective spectral prior over inactive components. To stabilize the sampling process, we also introduce a local trajectory regularizer that suppresses spatially irregular state-to-clean deviations. For a fixed endpoint energy, we provide a KL-regularized path-space interpretation. In practice, we construct time-dependent guidance through local energy corrections using a Tweedie plug-in approximation.…
PDF arXiv
arXiv cs.LGOct 5
Transmission Factors for Lossy Compression of PDE Training Data: Measuring What Reaches a Trained Operator
Huy Hoang Le
Operator-learning benchmarks ship as full-precision arrays, and they have grown to terabyte scale. A curator who wants to distribute one has to decide how coarsely to store it. That decision is usually made by fixing a tolerance on the reconstruction error of the stored field. We show that this quantity is measured in the wrong place. It compares the stored field with the original, before any model is trained. What the curator is buying is the accuracy of a model trained on the compressed copy, and the two can disagree: two PDEBench families stored to identical field error differ threefold downstream. A solution operator smooths, so only part of the codec error ever reaches the model's output. That part can be measured. Push a compressed field through a model already trained at full precision, and compare its output against the output on the clean field. The measurement costs forward passes and no training on compressed data. It spans more than two orders of magnitude across six PDE families, and it orders downstream cost where field error does not, inverting 12 of 104 cross-dataset comparisons against field error's 36. Read as a budget, the same curve nominates a storage rate…
PDF arXiv

Fields · AI · updated 1h ago

Flow matching

Found by the topic model: flow matching, physics informed neural, diffusion priors.

69papers this week−56.6% vs last week

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