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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

Activity

Recent papers

All papers in Research

arXiv cs.LGOct 4
Universality and Convergence of Generative Flows
Leo Brunswic
Generative flows sample from an unnormalized target by training a flow to be balanced, and the training loss is the signal a practitioner watches. We ask what that signal is worth: whether a small loss certifies an accurate sampler, whether the loss can be driven to zero, and how fast gradient descent does so. The loss decides the first. Losses that compare the two sides of the balance by their difference bound, in total variation, the error of the sampler the flow implies, with explicit constants that do not involve the policy; flow-matching losses that compare them through a ratio admit no such bound, already on a single cycle, whenever their generator is continuous at balance. On graphs, the backward policy decides the other two. Once it is frozen, balance becomes invariance under the backward chain, so that existence is free on finite graphs, and one constant --- the norm of that chain's Green operator, which plays the role of an inverse spectral gap --- fixes the order of the curvature of the loss around the balanced flow, from above and below, and sets a floor under the rate at which training converges near it. The mechanism is that gradient descent diffuses the flow along…
PDF arXiv
arXiv cs.LGOct 4
Shaping the Wind: Nested Potentials for Kinematically Admissible Urban Wind Prediction
Yidi Wang, Yunhe Zhang, Jiawei Gu, Ziyue Qiao, Pengyang Wang
Predicting transient urban winds is fundamental to understanding urban microclimates and designing climate-resilient cities. Building-resolving large-eddy simulation produces detailed incompressible urban wind fields at substantial computational cost for each layout. Neural surrogates offer a faster alternative by learning to predict the evolution of velocity fields. However, minimizing velocity prediction error does not guarantee local mass conservation and wall impermeability, which together define kinematic admissibility. This limitation stems from an unconstrained output representation: geometry conditioning guides predictions but does not restrict them to admissible velocity fields. Correcting boundary violations in these outputs changes the flux balance in adjacent fluid cells and may consequently compromise local mass conservation. To address the challenge, we propose Sculpt, a nested potential framework that builds the coupled, geometry-dependent constraints directly into its parameterization. This nested parameterization generates divergence-free velocity updates through the discrete curl of a volume vector potential on the native three-dimensional staggered grid. A…
PDF arXiv
arXiv cs.AIOct 4
Learning Field Reconstruction from Incomplete Data by Globally Correcting Local Estimates
Renhao Zhong, Zihan Zhou, Chiyuan Ma, Tianshu Yu
Reconstructing physical fields from training samples that are always incomplete requires learning spatial structure from fragmented observations. Existing context--query work establishes how held-out observations provide valid training targets, but this does not make the complete-field distribution identifiable when every training field is incomplete. With finite data, weak evidence of sharp transitions and localized variations can further favor averaged predictions that attenuate local detail. A structural prior is therefore needed to favor plausible completions; local spatial relationships offer one grounded in the observations. We propose a locally constructed, globally revisable estimator that explicitly learns local field estimates and subsequently corrects them using full-domain observations. A shared coordinate-conditioned predictor learns from incomplete patches, allowing relatively well-observed neighborhoods to provide direct supervision of local structure. Its overlapping predictions are reconciled into an observation-conditioned consensus field. A full-domain estimator retains the original observations and learns a residual correction around this frozen field…
PDF arXiv
arXiv cs.LGOct 4
Robust Ensemble Guidance for Scientific Inverse Problems
Zixiang Li, Wei Wang, Yunchao Wei, Yao Zhao, Yue Song
Ensemble guidance combines pretrained diffusion priors with black-box forward models to solve inverse problems without differentiating through the physical simulator. However, observation coordinates with large predictive spread or extreme residuals can dominate the ensemble correction, degrading reconstruction accuracy. We show that two simple modifications, weighting and clipping, substantially improve this correction. Our method, Robust Ensemble Guidance (REG), uses ensemble predictive spread to balance observation scales and adaptively clips standardized residuals to limit the influence of extreme discrepancies. Both operations reuse existing particles and forward predictions, requiring no additional denoiser or forward-model evaluations. Under a local linear Gaussian model, we derive conditions for reduced one-step estimation risk, bound the influence of individual observation coordinates, and characterize when these benefits persist with finite ensembles. Experiments on Navier-Stokes inversion, black-hole imaging, and acoustic full-waveform inversion demonstrate improved reconstruction over the underlying ensemble solver. In particular, REG increases black-hole…
PDF arXiv
arXiv cs.LGOct 4
Green-Routed Neural Operators: Physics Determines Where the Network Reads
Chenhao Si, Ming Yan
We identify a mismatch between the physical role of transport fields in many PDEs and their usual role in neural operators: PDEs use them to select read coordinates, whereas neural operators typically treat them only as input values. We address this mismatch with the Green-Routed Neural Operator (GRNO), which uses the governing equation to determine where latent features are sampled. A parameter-free equation adapter evaluates the diagnostic relation and constructs a departure map whose values are the read coordinates. A multiscale encoder-decoder combines centered and routed reads of latent features to learn the complete finite-time update. Across five two- and three-dimensional PDE systems, GRNO achieves the lowest mean final relative $L^2$ error on four under 40-step autoregressive evaluation and remains competitive on Keller-Segel. Fixed-weight route interventions reveal strong dependence on direction and spatial alignment in four systems, with weak dependence in Keller-Segel. In independently trained ablations, GRNO achieves lower mean errors than variants that supply the transport field only as an input feature, substitute a learned displacement for the equation-specified…
PDF arXiv
arXiv cs.LGOct 4
Cross-Time Directional Selection in Diffusion Sampling
Dhia naouali
How strongly do the remaining diffusion-sampling steps amplify a perturbation at a late latent state? Standard measurements answer this question with newly sampled isotropic noise, even though perturbations encountered during sampling have already been transformed by earlier steps. We compare these two cases directly. For each trajectory, we transport a centered perturbation from an earlier step to a late state, then replay its direction at the same magnitude as a newly sampled isotropic perturbation; both then undergo the same remaining updates. Across the samplers we study, median paired shaped-to-fresh angular-gain ratios range from $1.14$ to $2.35$. Shaped angular gain exceeds its matched fresh counterpart in every trajectory in the original main cohorts. The same pattern appears when endpoint change is measured by latent RMS. The effect also appears in perceptual feature representations: earlier-sampling directions cause larger feature changes at the endpoint, even when the corresponding pixel-space change is comparable. Permuting shaped directions across trajectories weakens the effect, including within class, indicating that the advantage depends on alignment with the…
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

Recent papers

All papers in Research

arXiv cs.LGOct 4
Universality and Convergence of Generative Flows
Leo Brunswic
Generative flows sample from an unnormalized target by training a flow to be balanced, and the training loss is the signal a practitioner watches. We ask what that signal is worth: whether a small loss certifies an accurate sampler, whether the loss can be driven to zero, and how fast gradient descent does so. The loss decides the first. Losses that compare the two sides of the balance by their difference bound, in total variation, the error of the sampler the flow implies, with explicit constants that do not involve the policy; flow-matching losses that compare them through a ratio admit no such bound, already on a single cycle, whenever their generator is continuous at balance. On graphs, the backward policy decides the other two. Once it is frozen, balance becomes invariance under the backward chain, so that existence is free on finite graphs, and one constant --- the norm of that chain's Green operator, which plays the role of an inverse spectral gap --- fixes the order of the curvature of the loss around the balanced flow, from above and below, and sets a floor under the rate at which training converges near it. The mechanism is that gradient descent diffuses the flow along…
PDF arXiv
arXiv cs.LGOct 4
Shaping the Wind: Nested Potentials for Kinematically Admissible Urban Wind Prediction
Yidi Wang, Yunhe Zhang, Jiawei Gu, Ziyue Qiao, Pengyang Wang
Predicting transient urban winds is fundamental to understanding urban microclimates and designing climate-resilient cities. Building-resolving large-eddy simulation produces detailed incompressible urban wind fields at substantial computational cost for each layout. Neural surrogates offer a faster alternative by learning to predict the evolution of velocity fields. However, minimizing velocity prediction error does not guarantee local mass conservation and wall impermeability, which together define kinematic admissibility. This limitation stems from an unconstrained output representation: geometry conditioning guides predictions but does not restrict them to admissible velocity fields. Correcting boundary violations in these outputs changes the flux balance in adjacent fluid cells and may consequently compromise local mass conservation. To address the challenge, we propose Sculpt, a nested potential framework that builds the coupled, geometry-dependent constraints directly into its parameterization. This nested parameterization generates divergence-free velocity updates through the discrete curl of a volume vector potential on the native three-dimensional staggered grid. A…
PDF arXiv
arXiv cs.AIOct 4
Learning Field Reconstruction from Incomplete Data by Globally Correcting Local Estimates
Renhao Zhong, Zihan Zhou, Chiyuan Ma, Tianshu Yu
Reconstructing physical fields from training samples that are always incomplete requires learning spatial structure from fragmented observations. Existing context--query work establishes how held-out observations provide valid training targets, but this does not make the complete-field distribution identifiable when every training field is incomplete. With finite data, weak evidence of sharp transitions and localized variations can further favor averaged predictions that attenuate local detail. A structural prior is therefore needed to favor plausible completions; local spatial relationships offer one grounded in the observations. We propose a locally constructed, globally revisable estimator that explicitly learns local field estimates and subsequently corrects them using full-domain observations. A shared coordinate-conditioned predictor learns from incomplete patches, allowing relatively well-observed neighborhoods to provide direct supervision of local structure. Its overlapping predictions are reconciled into an observation-conditioned consensus field. A full-domain estimator retains the original observations and learns a residual correction around this frozen field…
PDF arXiv
arXiv cs.LGOct 4
Robust Ensemble Guidance for Scientific Inverse Problems
Zixiang Li, Wei Wang, Yunchao Wei, Yao Zhao, Yue Song
Ensemble guidance combines pretrained diffusion priors with black-box forward models to solve inverse problems without differentiating through the physical simulator. However, observation coordinates with large predictive spread or extreme residuals can dominate the ensemble correction, degrading reconstruction accuracy. We show that two simple modifications, weighting and clipping, substantially improve this correction. Our method, Robust Ensemble Guidance (REG), uses ensemble predictive spread to balance observation scales and adaptively clips standardized residuals to limit the influence of extreme discrepancies. Both operations reuse existing particles and forward predictions, requiring no additional denoiser or forward-model evaluations. Under a local linear Gaussian model, we derive conditions for reduced one-step estimation risk, bound the influence of individual observation coordinates, and characterize when these benefits persist with finite ensembles. Experiments on Navier-Stokes inversion, black-hole imaging, and acoustic full-waveform inversion demonstrate improved reconstruction over the underlying ensemble solver. In particular, REG increases black-hole…
PDF arXiv
arXiv cs.LGOct 4
Green-Routed Neural Operators: Physics Determines Where the Network Reads
Chenhao Si, Ming Yan
We identify a mismatch between the physical role of transport fields in many PDEs and their usual role in neural operators: PDEs use them to select read coordinates, whereas neural operators typically treat them only as input values. We address this mismatch with the Green-Routed Neural Operator (GRNO), which uses the governing equation to determine where latent features are sampled. A parameter-free equation adapter evaluates the diagnostic relation and constructs a departure map whose values are the read coordinates. A multiscale encoder-decoder combines centered and routed reads of latent features to learn the complete finite-time update. Across five two- and three-dimensional PDE systems, GRNO achieves the lowest mean final relative $L^2$ error on four under 40-step autoregressive evaluation and remains competitive on Keller-Segel. Fixed-weight route interventions reveal strong dependence on direction and spatial alignment in four systems, with weak dependence in Keller-Segel. In independently trained ablations, GRNO achieves lower mean errors than variants that supply the transport field only as an input feature, substitute a learned displacement for the equation-specified…
PDF arXiv
arXiv cs.LGOct 4
Cross-Time Directional Selection in Diffusion Sampling
Dhia naouali
How strongly do the remaining diffusion-sampling steps amplify a perturbation at a late latent state? Standard measurements answer this question with newly sampled isotropic noise, even though perturbations encountered during sampling have already been transformed by earlier steps. We compare these two cases directly. For each trajectory, we transport a centered perturbation from an earlier step to a late state, then replay its direction at the same magnitude as a newly sampled isotropic perturbation; both then undergo the same remaining updates. Across the samplers we study, median paired shaped-to-fresh angular-gain ratios range from $1.14$ to $2.35$. Shaped angular gain exceeds its matched fresh counterpart in every trajectory in the original main cohorts. The same pattern appears when endpoint change is measured by latent RMS. The effect also appears in perceptual feature representations: earlier-sampling directions cause larger feature changes at the endpoint, even when the corresponding pixel-space change is comparable. Permuting shaped directions across trajectories weakens the effect, including within class, indicating that the advantage depends on alignment with the…
PDF arXiv

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.

Fields · AI · updated 43m ago

Flow matching

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

69papers this week−56.3% vs last week

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