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Open problems in Flow matching

Stable and scalable source-target coupling in flow matching1 paper raises it · 1 addresses it
Independent random pairing introduces high stochasticity, harming training stability and integration accuracy, especially 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 few-step flow matching is heuristic, expensive to tune, and may not adapt to 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
Lifelong adaptation without trajectory simulation errors1 paper raises it · 1 addresses it
Generative replay in continual learning accumulates discretization errors, degrading historical distribution quality.
- Trajectory Replay: Continuous-Time Mixture Transport for Lifelong Generative Modelsraises · addresses
Dynamics-aligned latent spaces for PDE flow matching1 paper raises it · 1 addresses it
Predictive representations capture physical information but do not guarantee accurate field evolution without explicit alignment.
- 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 modeling290 papers39 this week
physics informed neural · neural operators · informed neural networks282 papers25 this week
diffusion priors · posterior sampling · diffusion posterior68 papers12 this week

Topics in this field

Active contributors · 90 days

Stefan T. RadevConditional Mean Flows: Few-Step Densities for Simulation-Based Inference5
Taiji SuzukiFinite-Sample Approximation of Hessian-Guided Perturbed Wasserstein Gradient Flows5
Anima AnandkumarLearnable Splines for Unstructured Neural Operators4
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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arXiv cs.AIOct 18
LowNet: Looped Wavelet Neural Networks with 24 Learnable Parameters for Solving Poisson Equations
Yuanhao Gong
Poisson equations frequently appear in various fields, such as mathematics, physics and informatics. Solving Poisson equation, however, is challenging. Traditional methods are not data-specific, although have high certainty. They require a large number of iterations due to the CFL numerical stability. In contrast, deep learning methods are data-driven and more efficient, but require accurate training data and suffer from heavy computation. To tackle these issues, we propose a wavelet-inspired Poisson solver with 24 trainable scalars. The proposed network has several advantages. First, it is compact. It has four independent $5\times5$ kernels, each represented by six parameters, leading to 24 scalars in total. Such compact format can be deployed on most devices. Second, thanks to the loop design, it achieves higher accuracy than previous methods. A residual loop reuses the wavelet block without increasing its parameters. Numerical experiments confirm that such loop indeed improves the solving accuracy. On 10000 images, one, two, and three loops of the wavelet block lead to PSNRs of $47.27$, $74.14$, and $100.74$ dB, respectively. Third, the proposed method is computationally fast.…
PDF arXiv
arXiv stat.MLOct 17
Martingale Posterior Cox Processes
Joshua Rooijakkers, Edwin Fong
Cox processes provide a principled Bayesian nonparametric framework for modeling event-based data through an underlying intensity function. However, existing inference methods for estimating the intensity typically rely on computationally expensive Markov chain Monte Carlo sampling or approximate inference techniques. In addition, to ensure tractability, these methods often define priors over indirect latent structures, making them challenging to interpret. In this paper, we introduce the Martingale Posterior Cox Process (MPCP), which recasts Bayesian intensity estimation as inference over unobserved events given the observed event history. This perspective avoids the need to define complex priors while retaining the flexibility of nonparametric modeling. We propose a scalable, GPU-friendly copula-based predictive update, and provide strong theoretical guarantees for the convergence of the predictive resampling algorithm. Empirically, we show that MPCP provides excellent performance in both simulations and real data at a fraction of the computational cost of competing Bayesian approaches.
PDF arXiv
arXiv physics.plasm-phOct 17
Reconstruction of Unobserved Core Electron Density in Tokamak Plasmas with a Neural Operator Transport Surrogate and Uncertainty Quantification
D. Sorokin, A. Granovskiy, M. Stokolesov, E. Adishchev, M. Nurgaliev +1
Real-time control of tokamak plasmas requires the electron density profile. However, in a reactor-relevant device, diagnostic port access is limited and the profile can be observed only partially. In the present work we reconstruct the density profile by inferring the coefficients of a physics-based one-dimensional particle transport equation, using a Fourier Neural Operator (FNO) surrogate of the transport solver as a fast differentiable forward model. The surrogate enables realtime-compatible gradient-based reconstruction and uncertainty quantification from the reflectometry and interferometry measurements. We compare four uncertainty quantification methods - multi-seed ensembles, the Laplace approximation, Metropolis-Hastings, and a Gaussian method independent of the reconstruction fit. The resulting uncertainty is scored with CRPS and coverage calibration, separately on the observed and unobserved regions. We further demonstrate advantage of our approach over standard analytical function fit on synthetic and experimental DIII-D discharges.
PDF arXiv
arXiv stat.MLOct 17
Denoising Implicit Variational Inference
Zitong Wang, Zekun Wu, Longlin Yu, Cheng Zhang
Semi-implicit variational inference (SIVI) expands the representational capacity of variational families, but optimizing the Evidence Lower Bound (ELBO) remains challenging because the marginal score of the semi-implicit distribution is generally intractable. Unbiased Implicit Variational Inference (UIVI) and related methods address this difficulty through reparameterized ELBO gradients, but existing approaches estimate the required score indirectly through reverse-conditional sampling or approximation, which can be computationally costly and unstable. We propose Denoising Implicit Variational Inference (DIVI), which learns the marginal score directly via denoising score matching. The learned score is used as a plug-in estimator in the pathwise ELBO gradient, replacing inner reverse-conditional sampling with a score-network evaluation. We analyze DIVI as inexact stochastic gradient ascent and show, under stated assumptions, that the averaged stationarity measure is controlled by the usual optimization term and the average score-matching error. Empirically, we evaluate DIVI on both synthetic distributions and a variety of real-data Bayesian inference tasks. The results show that…
PDF arXiv
arXiv cs.CVOct 17
Unifying Amplitude-Phase Coupling and Reliable Endogenous Priors for Low-Light Image Enhancement
Tongshun Zhang, Zixuan Zhong, Pingping Liu, Jin Kuang, Yubing Lu +2
Frequency-domain methods have shown strong potential for low-light image enhancement (LLIE) because they can effectively regulate global illumination. However, most existing methods assume that amplitude and phase can be restored independently, while overlooking their inherent spectral coupling. This artificial decoupling often leads to information inconsistency and structural distortions. To address this issue, we propose a frequency-spatial framework that jointly models spectral interaction and reliable prior guidance. We first empirically analyze the coupling between amplitude and phase and develop an Amplitude-Phase Adaptive Compensation Fusion (APACF) module. Instead of enforcing a hard separation between the two components, APACF enables their bidirectional interaction, resulting in spectrally coherent restoration. In addition, directly extracting priors from raw low-light inputs is unreliable, since severe noise and underexposure destroy critical visual content. To alleviate this problem, we introduce an Endogenous Reliability Prior (ERP). Specifically, we treat an intermediate result, preliminarily restored in the frequency domain and already close to the ground-truth…
PDF arXiv
arXiv cs.LGOct 16
Latent State Utilization in Probabilistic Circuits
Zilei Shao, Anji Liu
Probabilistic circuits (PCs) are generative models that support efficient probabilistic inference. Adding latent states to a PC increases its representational capacity, but yields diminishing gains in likelihood. We use mutual information to examine how the dependence represented by a trained PC changes with latent size. Experiments with Hidden Chow-Liu Trees (HCLTs) on ImageNet32 show that learned dependence grows slowly and remains well below both the latent-state upper bound and estimates of dependence in the data. To understand how learning uses these states, we examine how strongly each sample favors particular latent states and how broadly states are used across the dataset. Tracking these measurements during HCLT training distinguishes rapid early posterior concentration from the more gradual stabilization of sample-dependent state preferences. Early measurements also guide initialization selection in HCLTs and hidden Markov models (HMMs), as well as tree selection in HCLTs. The resulting choices improve the ultimate performance across the tested latent sizes, providing a practical benefit from our study of latent-state utilization.
PDF arXiv

Papers

Topics in this field

flow matching · flow · generative modeling290 papers39 this week
physics informed neural · neural operators · informed neural networks282 papers25 this week
diffusion priors · posterior sampling · diffusion posterior68 papers12 this week

Active contributors · 90 days

Stefan T. RadevConditional Mean Flows: Few-Step Densities for Simulation-Based Inference5
Taiji SuzukiFinite-Sample Approximation of Hessian-Guided Perturbed Wasserstein Gradient Flows5
Anima AnandkumarLearnable Splines for Unstructured Neural Operators4
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

Stable and scalable source-target coupling in flow matching1 paper raises it · 1 addresses it
Independent random pairing introduces high stochasticity, harming training stability and integration accuracy, especially 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 few-step flow matching is heuristic, expensive to tune, and may not adapt to 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
Lifelong adaptation without trajectory simulation errors1 paper raises it · 1 addresses it
Generative replay in continual learning accumulates discretization errors, degrading historical distribution quality.
- Trajectory Replay: Continuous-Time Mixture Transport for Lifelong Generative Modelsraises · addresses
Dynamics-aligned latent spaces for PDE flow matching1 paper raises it · 1 addresses it
Predictive representations capture physical information but do not guarantee accurate field evolution without explicit alignment.
- PDE-JEPA: Predictive Representation Learning of Latent Dynamics Modeling for Parametric PDEsraises · addresses

Named by an AI from these papers' abstracts.

Fields · AI · updated 52m ago

Flow matching

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

76papers this week−54.2% vs last week

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Recent papers

All in Research →

arXiv cs.AIOct 18
LowNet: Looped Wavelet Neural Networks with 24 Learnable Parameters for Solving Poisson Equations
Yuanhao Gong
Poisson equations frequently appear in various fields, such as mathematics, physics and informatics. Solving Poisson equation, however, is challenging. Traditional methods are not data-specific, although have high certainty. They require a large number of iterations due to the CFL numerical stability. In contrast, deep learning methods are data-driven and more efficient, but require accurate training data and suffer from heavy computation. To tackle these issues, we propose a wavelet-inspired Poisson solver with 24 trainable scalars. The proposed network has several advantages. First, it is compact. It has four independent $5\times5$ kernels, each represented by six parameters, leading to 24 scalars in total. Such compact format can be deployed on most devices. Second, thanks to the loop design, it achieves higher accuracy than previous methods. A residual loop reuses the wavelet block without increasing its parameters. Numerical experiments confirm that such loop indeed improves the solving accuracy. On 10000 images, one, two, and three loops of the wavelet block lead to PSNRs of $47.27$, $74.14$, and $100.74$ dB, respectively. Third, the proposed method is computationally fast.…
PDF arXiv
arXiv stat.MLOct 17
Martingale Posterior Cox Processes
Joshua Rooijakkers, Edwin Fong
Cox processes provide a principled Bayesian nonparametric framework for modeling event-based data through an underlying intensity function. However, existing inference methods for estimating the intensity typically rely on computationally expensive Markov chain Monte Carlo sampling or approximate inference techniques. In addition, to ensure tractability, these methods often define priors over indirect latent structures, making them challenging to interpret. In this paper, we introduce the Martingale Posterior Cox Process (MPCP), which recasts Bayesian intensity estimation as inference over unobserved events given the observed event history. This perspective avoids the need to define complex priors while retaining the flexibility of nonparametric modeling. We propose a scalable, GPU-friendly copula-based predictive update, and provide strong theoretical guarantees for the convergence of the predictive resampling algorithm. Empirically, we show that MPCP provides excellent performance in both simulations and real data at a fraction of the computational cost of competing Bayesian approaches.
PDF arXiv
arXiv physics.plasm-phOct 17
Reconstruction of Unobserved Core Electron Density in Tokamak Plasmas with a Neural Operator Transport Surrogate and Uncertainty Quantification
D. Sorokin, A. Granovskiy, M. Stokolesov, E. Adishchev, M. Nurgaliev +1
Real-time control of tokamak plasmas requires the electron density profile. However, in a reactor-relevant device, diagnostic port access is limited and the profile can be observed only partially. In the present work we reconstruct the density profile by inferring the coefficients of a physics-based one-dimensional particle transport equation, using a Fourier Neural Operator (FNO) surrogate of the transport solver as a fast differentiable forward model. The surrogate enables realtime-compatible gradient-based reconstruction and uncertainty quantification from the reflectometry and interferometry measurements. We compare four uncertainty quantification methods - multi-seed ensembles, the Laplace approximation, Metropolis-Hastings, and a Gaussian method independent of the reconstruction fit. The resulting uncertainty is scored with CRPS and coverage calibration, separately on the observed and unobserved regions. We further demonstrate advantage of our approach over standard analytical function fit on synthetic and experimental DIII-D discharges.
PDF arXiv
arXiv stat.MLOct 17
Denoising Implicit Variational Inference
Zitong Wang, Zekun Wu, Longlin Yu, Cheng Zhang
Semi-implicit variational inference (SIVI) expands the representational capacity of variational families, but optimizing the Evidence Lower Bound (ELBO) remains challenging because the marginal score of the semi-implicit distribution is generally intractable. Unbiased Implicit Variational Inference (UIVI) and related methods address this difficulty through reparameterized ELBO gradients, but existing approaches estimate the required score indirectly through reverse-conditional sampling or approximation, which can be computationally costly and unstable. We propose Denoising Implicit Variational Inference (DIVI), which learns the marginal score directly via denoising score matching. The learned score is used as a plug-in estimator in the pathwise ELBO gradient, replacing inner reverse-conditional sampling with a score-network evaluation. We analyze DIVI as inexact stochastic gradient ascent and show, under stated assumptions, that the averaged stationarity measure is controlled by the usual optimization term and the average score-matching error. Empirically, we evaluate DIVI on both synthetic distributions and a variety of real-data Bayesian inference tasks. The results show that…
PDF arXiv
arXiv cs.CVOct 17
Unifying Amplitude-Phase Coupling and Reliable Endogenous Priors for Low-Light Image Enhancement
Tongshun Zhang, Zixuan Zhong, Pingping Liu, Jin Kuang, Yubing Lu +2
Frequency-domain methods have shown strong potential for low-light image enhancement (LLIE) because they can effectively regulate global illumination. However, most existing methods assume that amplitude and phase can be restored independently, while overlooking their inherent spectral coupling. This artificial decoupling often leads to information inconsistency and structural distortions. To address this issue, we propose a frequency-spatial framework that jointly models spectral interaction and reliable prior guidance. We first empirically analyze the coupling between amplitude and phase and develop an Amplitude-Phase Adaptive Compensation Fusion (APACF) module. Instead of enforcing a hard separation between the two components, APACF enables their bidirectional interaction, resulting in spectrally coherent restoration. In addition, directly extracting priors from raw low-light inputs is unreliable, since severe noise and underexposure destroy critical visual content. To alleviate this problem, we introduce an Endogenous Reliability Prior (ERP). Specifically, we treat an intermediate result, preliminarily restored in the frequency domain and already close to the ground-truth…
PDF arXiv
arXiv cs.LGOct 16
Latent State Utilization in Probabilistic Circuits
Zilei Shao, Anji Liu
Probabilistic circuits (PCs) are generative models that support efficient probabilistic inference. Adding latent states to a PC increases its representational capacity, but yields diminishing gains in likelihood. We use mutual information to examine how the dependence represented by a trained PC changes with latent size. Experiments with Hidden Chow-Liu Trees (HCLTs) on ImageNet32 show that learned dependence grows slowly and remains well below both the latent-state upper bound and estimates of dependence in the data. To understand how learning uses these states, we examine how strongly each sample favors particular latent states and how broadly states are used across the dataset. Tracking these measurements during HCLT training distinguishes rapid early posterior concentration from the more gradual stabilization of sample-dependent state preferences. Early measurements also guide initialization selection in HCLTs and hidden Markov models (HMMs), as well as tree selection in HCLTs. The resulting choices improve the ultimate performance across the tested latent sizes, providing a practical benefit from our study of latent-state utilization.
PDF arXiv