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Open problems in Flow matching

Stable and scalable source-target pairing for flow matching1 paper raises it · 1 addresses it
Unstable or random pairing degrades training and integration, limiting model performance at scale.
- Scaling Online Optimal Transport Minibatches for Flow Matchingraises · addresses
Efficient few-step generation without fixed discretization1 paper raises it · 1 addresses it
Fixed timestep discretization in flow matching is heuristic, expensive to tune, and restrictive for varying sample difficulty.
- Few-Step Generation via Data-Space Iterationraises · addresses
Data-free and simulation-free distillation for flow/diffusion models1 paper raises it · 1 addresses it
Existing distillation methods rely on curated datasets, costly teacher rollouts, or auxiliary networks, complicating training and scaling.
- Consistent Distribution Matching for Data-Free Diffusion Distillationraises · addresses
Accelerating numerical integration for neuro-spectral PDE solvers1 paper raises it · 1 addresses it
Sequential time-stepping in neuro-spectral architectures limits temporal parallelism and slows training/inference.
- PaPi: Parallel Picard-Duhamel Integration for Fast Neuro-Spectral Architecturesraises · addresses
Dynamics-aligned latent spaces for PDE representation learning1 paper raises it · 1 addresses it
Reconstruction-based objectives fail to capture evolution geometry, limiting accurate field prediction.
- PDE-JEPA: Predictive Representation Learning of Latent Dynamics Modeling for Parametric PDEsraises · addresses

Named by an AI from these papers' abstracts.

Open problems

Recently funded

Topics in this field

flow matching · flow · generative modeling299 papers32 this week
physics informed neural · neural operators · informed neural networks295 papers27 this week
diffusion priors · posterior sampling · diffusion posterior74 papers15 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

Activity

Recent papers

All papers in Research

arXiv cs.LGSep 28
KernelOnet: An Interpretable Neural Operator Based on Kernel Functions
Yuan Guo, Hanshu Chen, Qiang Xi, Timon Rabczuk, Zhuojia Fu
This paper proposes an interpretable neural operator framework, the Kernel Operator Network (KernelOnet), which incorporates kernel functions explicitly into the neural operator architecture, so that the operator structure matches the kernel-expansion form used in boundary-type kernel-expansion methods. Unlike traditional neural operators such as DeepONet, which learn basis functions implicitly through deep networks, KernelOnet replaces the trunk network with explicit kernels and offers three complementary kernels: a data-driven learnable kernel, in which a neural network parameterizes a radial basis function learned from data, and which for constant-coefficient linear problems can be regarded as a non-singular fundamental solution; a physics-informed kernel, which embeds physical information such as analytic fundamental solutions into the network structure, so that the expansion satisfies the governing equation automatically and can be trained without supervision on boundary conditions alone, with no interior solution data; and a hybrid kernel, which splits the solution, according to the linear principal part of the governing equation, into a homogeneous part spanned by analytic…
PDF arXiv
arXiv cs.LGSep 28
Weighting Schedules Govern What and When Score-Based Generative Models Learn from Multimodal Data
Jérémie Klinger, Raphaël Urfin, Giulio Biroli, Marylou Gabrié
Score-based generative models generate new samples by integrating a time-dependent drift that carries Gaussian noise onto the target distribution. In practice this drift is modeled by a neural network, trained on a loss integrated over time $t$ with a weighting schedule $w(t)$. Along the backward dynamics, and for multi-modal distributions, trajectories commit to modes of the target within a narrow time window, the \textit{speciation time}. In this work, focusing on high-dimensional data, we decompose the integrated loss into its single-time contributions and analyze each at fixed signal-to-noise ratio $Λ(t)$: we show that $Λ(t)$ sets the rate at which each feature of a multimodal target - the mode directions and their relative weights - is acquired during training. Crucially, at high $Λ(t)$ all mode directions are acquired together, on a single timescale insensitive to their amplitudes, while the relative weights are not learned at all. Only near the speciation time, where $Λ(t)$ becomes of order one, do all features become learnable, each on its own timescale: the weights are acquired jointly with the directions, and the directions at rates set by their relative amplitudes. For…
PDF arXiv
arXiv eess.ASSep 28
Simulation-Based Inference for Plate Reverb System Identification
Dylan Sechet, Marc Evrard, Matthieu Kowalski
We address Task A of the 1st DAFx Parameter Estimation Challenge, which aims to retrieve the physical parameters of a plate model from an impulse response. To do so, we use the Simulation-Based Inference (SBI) framework, in which we train a neural network to estimate a density over plate parameters given an impulse response, using a dataset generated by the simulator. Inference for a new impulse response then requires only a forward pass through the network, without involving the simulator. For each test observation, we fine-tune a specific network: additional simulation rounds are performed by sampling parameters from the current estimated distribution, simulating the corresponding impulse responses, and fine-tuning to produce the specialized network.
PDF arXiv
arXiv math.NASep 28
GAC-PINN: Geometry-Adaptive and Constraint-Enhanced Physics-Informed Neural Networks
Yanxin Zhang, Yong Zhang, Houbiao Li
For systems with steep gradients, sharp interfaces, or severe spatio-temporal coupling, Physics-informed neural networks (PINNs) suffer from spectral bias, geometric inflexibility, and boundary constraint conflicts, which undermine accuracy and convergence. To overcome these issues, we propose a geometry-adaptive and constraint-enhanced PINN (GAC-PINN). The framework comprises four components: a gradient-driven adaptive grid mapping (AGM) for diffeomorphic point concentration with Jacobian regularization, an adaptive bandwidth hard-constraint ansatz with spatially-varying boundary transition widths, a Gaussian Fourier feature mapping as a spectral preconditioner to further enhance high-wavenumber representation, and an operator-aware router that automatically selects the appropriate hard-constraint construction based on whether the governing PDE contains temporal derivatives. An AGM callback mechanism and a three-stage training strategy ensure stable coordination. Benchmarks including the viscous Burgers equation, a sharp-peaked 2D Poisson problem, and the Allen-Cahn phase-transition equation show that GAC-PINN attains relative (L^2) errors of ((1.747\pm 0.450)\times 10^{-4}),…
PDF arXiv
arXiv cs.LGSep 28
DRIFT: Disentangled Responsive-Invariant Flow Transport for Single-Cell Perturbation Prediction
Mustapha Bounoua, Giulio Franzese, Pietro Michiardi
Predicting cellular responses to perturbations is a central problem in cellular biology, with broad applications in systems biology and drug discovery. This task is challenging because cellular responses can be complex and cell-state dependent, intrinsic cell-to-cell variability can be confounded with perturbation effects, and destructive single-cell RNA sequencing precludes paired measurements of the same cell before and after treatment. Flow matching transports control cells to perturbed states flexibly, but acting on the full cell state can confound perturbation effects with pre-existing cell-to-cell variability. Disentangled approaches separate responsive from invariant components, but model perturbations through prescribed mechanisms, such as latent shifts or graph edits, limiting their flexibility. We address both limitations in a unified framework. A variational encoder disentangles each cell into an invariant block, capturing state unaffected by the perturbation, and a responsive block, capturing state it changes, through conditional priors and an information-theoretic invariance constraint. Conditional flow matching transports only the responsive block, conditioned on…
PDF arXiv
arXiv cs.LGSep 28
Beyond Gradient Flow: Identifiability and Recovery from Distribution Snapshots
Nam D. Nguyen, Valeriya Malysheva
Inferring dynamics from snapshots of evolving distributions is fundamentally underdetermined: the Fokker-Planck equation constrains the drift $F$ only through its score-weighted divergence $\nabla\cdot F+F\cdot\nabla\logρ$, leaving a $ρ$-solenoidal gauge invisible to any single-time constraint. Time-indexed transport formulations cannot resolve this ambiguity: every admissible marginal path admits a curl-free explanation, minimum-action reconstruction selects it, and marginal fit alone cannot distinguish dynamically inequivalent explanations. Requiring one autonomous field to explain several marginals instead makes part of the hidden circulation visible as $\nabla\logρ$ changes across marginals. Separating instantaneous Fokker-Planck source constraints from the snapshot experiment, we show that the source constraints identify the field modulo the kernel of a stacked score-weighted divergence operator. For generic Gaussian shape variation, source constraints at $K\ge m$ time points in intrinsic dimension $m$ eliminate every polynomial gauge direction, whereas finitely many density snapshots alone admit aliasing; we give the obstruction explicitly. At a Gaussian anchor, for Sobolev…
PDF arXiv

Papers

Topics in this field

flow matching · flow · generative modeling299 papers32 this week
physics informed neural · neural operators · informed neural networks295 papers27 this week
diffusion priors · posterior sampling · diffusion posterior74 papers15 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

Recent papers

All papers in Research

arXiv cs.LGSep 28
KernelOnet: An Interpretable Neural Operator Based on Kernel Functions
Yuan Guo, Hanshu Chen, Qiang Xi, Timon Rabczuk, Zhuojia Fu
This paper proposes an interpretable neural operator framework, the Kernel Operator Network (KernelOnet), which incorporates kernel functions explicitly into the neural operator architecture, so that the operator structure matches the kernel-expansion form used in boundary-type kernel-expansion methods. Unlike traditional neural operators such as DeepONet, which learn basis functions implicitly through deep networks, KernelOnet replaces the trunk network with explicit kernels and offers three complementary kernels: a data-driven learnable kernel, in which a neural network parameterizes a radial basis function learned from data, and which for constant-coefficient linear problems can be regarded as a non-singular fundamental solution; a physics-informed kernel, which embeds physical information such as analytic fundamental solutions into the network structure, so that the expansion satisfies the governing equation automatically and can be trained without supervision on boundary conditions alone, with no interior solution data; and a hybrid kernel, which splits the solution, according to the linear principal part of the governing equation, into a homogeneous part spanned by analytic…
PDF arXiv
arXiv cs.LGSep 28
Weighting Schedules Govern What and When Score-Based Generative Models Learn from Multimodal Data
Jérémie Klinger, Raphaël Urfin, Giulio Biroli, Marylou Gabrié
Score-based generative models generate new samples by integrating a time-dependent drift that carries Gaussian noise onto the target distribution. In practice this drift is modeled by a neural network, trained on a loss integrated over time $t$ with a weighting schedule $w(t)$. Along the backward dynamics, and for multi-modal distributions, trajectories commit to modes of the target within a narrow time window, the \textit{speciation time}. In this work, focusing on high-dimensional data, we decompose the integrated loss into its single-time contributions and analyze each at fixed signal-to-noise ratio $Λ(t)$: we show that $Λ(t)$ sets the rate at which each feature of a multimodal target - the mode directions and their relative weights - is acquired during training. Crucially, at high $Λ(t)$ all mode directions are acquired together, on a single timescale insensitive to their amplitudes, while the relative weights are not learned at all. Only near the speciation time, where $Λ(t)$ becomes of order one, do all features become learnable, each on its own timescale: the weights are acquired jointly with the directions, and the directions at rates set by their relative amplitudes. For…
PDF arXiv
arXiv eess.ASSep 28
Simulation-Based Inference for Plate Reverb System Identification
Dylan Sechet, Marc Evrard, Matthieu Kowalski
We address Task A of the 1st DAFx Parameter Estimation Challenge, which aims to retrieve the physical parameters of a plate model from an impulse response. To do so, we use the Simulation-Based Inference (SBI) framework, in which we train a neural network to estimate a density over plate parameters given an impulse response, using a dataset generated by the simulator. Inference for a new impulse response then requires only a forward pass through the network, without involving the simulator. For each test observation, we fine-tune a specific network: additional simulation rounds are performed by sampling parameters from the current estimated distribution, simulating the corresponding impulse responses, and fine-tuning to produce the specialized network.
PDF arXiv
arXiv math.NASep 28
GAC-PINN: Geometry-Adaptive and Constraint-Enhanced Physics-Informed Neural Networks
Yanxin Zhang, Yong Zhang, Houbiao Li
For systems with steep gradients, sharp interfaces, or severe spatio-temporal coupling, Physics-informed neural networks (PINNs) suffer from spectral bias, geometric inflexibility, and boundary constraint conflicts, which undermine accuracy and convergence. To overcome these issues, we propose a geometry-adaptive and constraint-enhanced PINN (GAC-PINN). The framework comprises four components: a gradient-driven adaptive grid mapping (AGM) for diffeomorphic point concentration with Jacobian regularization, an adaptive bandwidth hard-constraint ansatz with spatially-varying boundary transition widths, a Gaussian Fourier feature mapping as a spectral preconditioner to further enhance high-wavenumber representation, and an operator-aware router that automatically selects the appropriate hard-constraint construction based on whether the governing PDE contains temporal derivatives. An AGM callback mechanism and a three-stage training strategy ensure stable coordination. Benchmarks including the viscous Burgers equation, a sharp-peaked 2D Poisson problem, and the Allen-Cahn phase-transition equation show that GAC-PINN attains relative (L^2) errors of ((1.747\pm 0.450)\times 10^{-4}),…
PDF arXiv
arXiv cs.LGSep 28
DRIFT: Disentangled Responsive-Invariant Flow Transport for Single-Cell Perturbation Prediction
Mustapha Bounoua, Giulio Franzese, Pietro Michiardi
Predicting cellular responses to perturbations is a central problem in cellular biology, with broad applications in systems biology and drug discovery. This task is challenging because cellular responses can be complex and cell-state dependent, intrinsic cell-to-cell variability can be confounded with perturbation effects, and destructive single-cell RNA sequencing precludes paired measurements of the same cell before and after treatment. Flow matching transports control cells to perturbed states flexibly, but acting on the full cell state can confound perturbation effects with pre-existing cell-to-cell variability. Disentangled approaches separate responsive from invariant components, but model perturbations through prescribed mechanisms, such as latent shifts or graph edits, limiting their flexibility. We address both limitations in a unified framework. A variational encoder disentangles each cell into an invariant block, capturing state unaffected by the perturbation, and a responsive block, capturing state it changes, through conditional priors and an information-theoretic invariance constraint. Conditional flow matching transports only the responsive block, conditioned on…
PDF arXiv
arXiv cs.LGSep 28
Beyond Gradient Flow: Identifiability and Recovery from Distribution Snapshots
Nam D. Nguyen, Valeriya Malysheva
Inferring dynamics from snapshots of evolving distributions is fundamentally underdetermined: the Fokker-Planck equation constrains the drift $F$ only through its score-weighted divergence $\nabla\cdot F+F\cdot\nabla\logρ$, leaving a $ρ$-solenoidal gauge invisible to any single-time constraint. Time-indexed transport formulations cannot resolve this ambiguity: every admissible marginal path admits a curl-free explanation, minimum-action reconstruction selects it, and marginal fit alone cannot distinguish dynamically inequivalent explanations. Requiring one autonomous field to explain several marginals instead makes part of the hidden circulation visible as $\nabla\logρ$ changes across marginals. Separating instantaneous Fokker-Planck source constraints from the snapshot experiment, we show that the source constraints identify the field modulo the kernel of a stacked score-weighted divergence operator. For generic Gaussian shape variation, source constraints at $K\ge m$ time points in intrinsic dimension $m$ eliminate every polynomial gauge direction, whereas finitely many density snapshots alone admit aliasing; we give the obstruction explicitly. At a Gaussian anchor, for Sobolev…
PDF arXiv

Activity · 12 weeks

Fields · AI · updated 2m ago

Flow matching

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

74papers this week−52.6% vs last week

All papers · 668 With code · 3

Newest Most relevant

630 papers this month

Open problems in Flow matching

Stable and scalable source-target pairing for flow matching1 paper raises it · 1 addresses it
Unstable or random pairing degrades training and integration, limiting model performance at scale.
- Scaling Online Optimal Transport Minibatches for Flow Matchingraises · addresses
Efficient few-step generation without fixed discretization1 paper raises it · 1 addresses it
Fixed timestep discretization in flow matching is heuristic, expensive to tune, and restrictive for varying sample difficulty.
- Few-Step Generation via Data-Space Iterationraises · addresses
Data-free and simulation-free distillation for flow/diffusion models1 paper raises it · 1 addresses it
Existing distillation methods rely on curated datasets, costly teacher rollouts, or auxiliary networks, complicating training and scaling.
- Consistent Distribution Matching for Data-Free Diffusion Distillationraises · addresses
Accelerating numerical integration for neuro-spectral PDE solvers1 paper raises it · 1 addresses it
Sequential time-stepping in neuro-spectral architectures limits temporal parallelism and slows training/inference.
- PaPi: Parallel Picard-Duhamel Integration for Fast Neuro-Spectral Architecturesraises · addresses
Dynamics-aligned latent spaces for PDE representation learning1 paper raises it · 1 addresses it
Reconstruction-based objectives fail to capture evolution geometry, limiting accurate field prediction.
- PDE-JEPA: Predictive Representation Learning of Latent Dynamics Modeling for Parametric PDEsraises · addresses

Named by an AI from these papers' abstracts.