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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

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Recent papers

All papers in Research

arXiv cs.LGOct 4
Hamiltonian Metric Learning and Energy-Based Training: A Dissipative Geometric Framework for Optimization
Sparsho Chakraborty, Mohammad Alamgir, Nishanth M, Akshit Nanda, Ram Prasad Padhy +1
Optimization in machine learning is usually expressed through iterative rules that update model parameters using information from the loss landscape. In this work, we study an alternative viewpoint in which parameter optimization is treated as the evolution of a dissipative dynamical system. The model parameters are regarded as generalized coordinates, the loss acts as a potential energy, and a positive-definite metric defines the local kinetic geometry of parameter space. Starting from a variational formulation, we derive the corresponding Hamiltonian dynamics, the geometric force generated by a position-dependent metric, and a metric-compatible Rayleigh dissipation law. The resulting continuous system satisfies a monotonic energy-dissipation relation, while its discrete form allows the influence of curvature on the optimization trajectory to be studied directly. We illustrate the framework using a controlled CIFAR-10 image-reconstruction problem for which the optimum is known analytically. With the image Hessian used as the metric, the curvature dependence of the quadratic modal dynamics is removed. We then reparameterize the same image as a matrix product state, producing a…
PDF arXiv
arXiv cs.LGOct 4
EDISCO: Equivariant DIScrete Diffusion for Euclidean Combinatorial Optimization
Ruogu Chen, Jie Han
Euclidean combinatorial optimization problems (ECOPs), such as the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP), possess inherent symmetries under the two-dimensional Euclidean group E(2), including rotations, reflections, and translations. Existing learning-based methods, including recent diffusion-based methods, rely on data augmentation or regularization to approximate E(2)-equivariance. This paper presents EDISCO, the first discrete diffusion model for ECOPs with exact E(2)-invariant generative distributions over node-index solutions. EDISCO introduces an E(2)-equivariant edge-score network coupled with a categorical continuous-time Markov chain over discrete edge variables, and exact posterior sampling provides efficient multi-step inference. This design gives EDISCO a local geometric inductive bias: edge neighborhoods with the same relative geometry and combinatorial context are represented consistently regardless of absolute position or orientation, making learning more efficient and inference more robust than non-equivariant methods. EDISCO outperforms previous learning-based state-of-the-art solvers on synthetic TSP from 100 to 10000…
PDF arXiv
arXiv cs.LGOct 4
TempoBridge: Source-Conditioned Flow Matching with Optimal Transport Couplings for Single-Cell Population Transitions
Bowen Han, Lingbei Meng, Shihuan Luo, Yupeng Zang, Wenlin LI +5
Destructive single-cell measurements provide unpaired population snapshots rather than observations of the same cells across conditions. Local cell states and transition requests may also be insufficient to distinguish responses across source populations. We introduce TempoBridge, a common source-conditioned transport formulation for temporal, genetic, and chemical population transitions. Source cells initialize latent transport and provide a fixed empirical population summary. The velocity field receives this summary alongside the evolving cell state, flow time, and a structured transition descriptor. Minibatch optimal transport (OT) supplies couplings only for conditional flow-matching training paths; inference requires neither target expression nor OT computation. On held-out donors, TempoBridge achieves an Energy distance of 0.129 versus 0.144 for scGen. Genetic mean-expression $L_2$ error is 2.261 versus 3.156 for scGPT-scratch under Seen 2/2. On held-out compounds, condition-averaged drug-effect correlation is 0.598 versus 0.561 for the CellFlow adapter. Temporal ablations show higher mean distributional error after removing source context, replacing optimal transport with…
PDF arXiv
arXiv cs.LGOct 4
A Graph-Based Inspection and Intervention Tool for Assessing Mechanistic Learning in PINNs
Adwait Patkhedkar, Alifaraz Lakhani, Prathmesh Mohite, Abhijeet Salunke
We ask whether physically meaningful correspondences discovered inside a trained scientific model remain meaningful outside the conditions under which they were discovered. We introduce GIIT (Graph-based Inspection and Intervention Tool), which represents governing physics as a computational physics dependency graph, maps graph nodes to internal network components via sensitivity- and trend-based discovery, and tests the resulting mapping under targeted intervention. Evaluating on temporal extrapolation out-of-distribution (OOD) regimes of increasing severity, we find that temporal extrapolation is associated with layer-wise correspondence drift and reduced functional correspondence. Specifically, while the model achieves low physics residual in-distribution (1.915 x 10-4 on full ID and 1.01 x 10-4 on an ID sub-window t in [0.5, 0.8]), the functional mapping changes even before leaving the training domain, and the shift continues as the evaluation window extends beyond the training domain: residual error increases from 2.81 x 10-2 on the boundary-crossing window (t in [0.5, 1.5]) to 3.30 x 10-1 on severe OOD (t in [1, 2]), accompanied by a systematic leftward shift of internal…
PDF arXiv
arXiv cs.CEOct 3
Latent-Lagrangian Neural Networks for Reduced Order Modeling of Non-autonomous Nonlinear Dynamical Systems
Anand Kumar Agrawal, Anders Thorin
This work proposes a latent Lagrangian-based framework for reduced-order modelling of forced nonlinear dynamical systems. In contrast with conventional Lagrangian or Hamiltonian neural networks, our approach learns a set of latent coordinates sufficient to capture the dynamics conjointly with two neural networks for the latent kinetic and latent potential energies, and leverages force supervision to eliminate the need for an ODE solver during training. Consistency of physical laws in the latent space is ensured through the principle of virtual work. Results show that the model effectively learns the subtle dynamics induced by the system's nonlinearity and non-convex potential energy, and generalizes well to unseen forces and initial conditions. These observations confirm the physical relevance of the proposed approach, and its interest for model reduction.
PDF arXiv
arXiv cs.LGOct 3
Localized Operator Learning with Adaptive Partition-of-Unity Mixture-of-Expert Networks
Madison Cooley, Ramansh Sharma, Shandian Zhe, Robert M. Kirby, Varun Shankar
Operator learning methods such as DeepONets and FNOs often struggle with PDE families featuring sharp interfaces, heterogeneous coefficients, and localized multiscale structures. We introduce a partition-of-unity (POU) mixture-of-experts framework for localized operator learning, in which geometry-aware gating networks produce smooth spatial partitions which blend the contributions of local expert networks. Our main contribution is HiRefPOU, a residual-style hierarchical POU architecture for DeepONets that organizes localized representations through nested parent-child partitions while preserving global continuity. We also show that the same POU principle can be incorporated into Fourier Neural Operators to introduce spatial adaptivity without modifying the underlying spectral layers. On heterogeneous Darcy and reaction-diffusion benchmarks, HiRefPOU achieves substantially lower error than global DeepONet and static POU-MoE baselines, while the broader operator-learning experiments show that the benefits of localization depend on the PDE structure and the chosen neural-operator backbone. The learned partitions are interpretable and align with interfaces and regions of rapid…
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

Recent papers

All papers in Research

arXiv cs.LGOct 4
Hamiltonian Metric Learning and Energy-Based Training: A Dissipative Geometric Framework for Optimization
Sparsho Chakraborty, Mohammad Alamgir, Nishanth M, Akshit Nanda, Ram Prasad Padhy +1
Optimization in machine learning is usually expressed through iterative rules that update model parameters using information from the loss landscape. In this work, we study an alternative viewpoint in which parameter optimization is treated as the evolution of a dissipative dynamical system. The model parameters are regarded as generalized coordinates, the loss acts as a potential energy, and a positive-definite metric defines the local kinetic geometry of parameter space. Starting from a variational formulation, we derive the corresponding Hamiltonian dynamics, the geometric force generated by a position-dependent metric, and a metric-compatible Rayleigh dissipation law. The resulting continuous system satisfies a monotonic energy-dissipation relation, while its discrete form allows the influence of curvature on the optimization trajectory to be studied directly. We illustrate the framework using a controlled CIFAR-10 image-reconstruction problem for which the optimum is known analytically. With the image Hessian used as the metric, the curvature dependence of the quadratic modal dynamics is removed. We then reparameterize the same image as a matrix product state, producing a…
PDF arXiv
arXiv cs.LGOct 4
EDISCO: Equivariant DIScrete Diffusion for Euclidean Combinatorial Optimization
Ruogu Chen, Jie Han
Euclidean combinatorial optimization problems (ECOPs), such as the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP), possess inherent symmetries under the two-dimensional Euclidean group E(2), including rotations, reflections, and translations. Existing learning-based methods, including recent diffusion-based methods, rely on data augmentation or regularization to approximate E(2)-equivariance. This paper presents EDISCO, the first discrete diffusion model for ECOPs with exact E(2)-invariant generative distributions over node-index solutions. EDISCO introduces an E(2)-equivariant edge-score network coupled with a categorical continuous-time Markov chain over discrete edge variables, and exact posterior sampling provides efficient multi-step inference. This design gives EDISCO a local geometric inductive bias: edge neighborhoods with the same relative geometry and combinatorial context are represented consistently regardless of absolute position or orientation, making learning more efficient and inference more robust than non-equivariant methods. EDISCO outperforms previous learning-based state-of-the-art solvers on synthetic TSP from 100 to 10000…
PDF arXiv
arXiv cs.LGOct 4
TempoBridge: Source-Conditioned Flow Matching with Optimal Transport Couplings for Single-Cell Population Transitions
Bowen Han, Lingbei Meng, Shihuan Luo, Yupeng Zang, Wenlin LI +5
Destructive single-cell measurements provide unpaired population snapshots rather than observations of the same cells across conditions. Local cell states and transition requests may also be insufficient to distinguish responses across source populations. We introduce TempoBridge, a common source-conditioned transport formulation for temporal, genetic, and chemical population transitions. Source cells initialize latent transport and provide a fixed empirical population summary. The velocity field receives this summary alongside the evolving cell state, flow time, and a structured transition descriptor. Minibatch optimal transport (OT) supplies couplings only for conditional flow-matching training paths; inference requires neither target expression nor OT computation. On held-out donors, TempoBridge achieves an Energy distance of 0.129 versus 0.144 for scGen. Genetic mean-expression $L_2$ error is 2.261 versus 3.156 for scGPT-scratch under Seen 2/2. On held-out compounds, condition-averaged drug-effect correlation is 0.598 versus 0.561 for the CellFlow adapter. Temporal ablations show higher mean distributional error after removing source context, replacing optimal transport with…
PDF arXiv
arXiv cs.LGOct 4
A Graph-Based Inspection and Intervention Tool for Assessing Mechanistic Learning in PINNs
Adwait Patkhedkar, Alifaraz Lakhani, Prathmesh Mohite, Abhijeet Salunke
We ask whether physically meaningful correspondences discovered inside a trained scientific model remain meaningful outside the conditions under which they were discovered. We introduce GIIT (Graph-based Inspection and Intervention Tool), which represents governing physics as a computational physics dependency graph, maps graph nodes to internal network components via sensitivity- and trend-based discovery, and tests the resulting mapping under targeted intervention. Evaluating on temporal extrapolation out-of-distribution (OOD) regimes of increasing severity, we find that temporal extrapolation is associated with layer-wise correspondence drift and reduced functional correspondence. Specifically, while the model achieves low physics residual in-distribution (1.915 x 10-4 on full ID and 1.01 x 10-4 on an ID sub-window t in [0.5, 0.8]), the functional mapping changes even before leaving the training domain, and the shift continues as the evaluation window extends beyond the training domain: residual error increases from 2.81 x 10-2 on the boundary-crossing window (t in [0.5, 1.5]) to 3.30 x 10-1 on severe OOD (t in [1, 2]), accompanied by a systematic leftward shift of internal…
PDF arXiv
arXiv cs.CEOct 3
Latent-Lagrangian Neural Networks for Reduced Order Modeling of Non-autonomous Nonlinear Dynamical Systems
Anand Kumar Agrawal, Anders Thorin
This work proposes a latent Lagrangian-based framework for reduced-order modelling of forced nonlinear dynamical systems. In contrast with conventional Lagrangian or Hamiltonian neural networks, our approach learns a set of latent coordinates sufficient to capture the dynamics conjointly with two neural networks for the latent kinetic and latent potential energies, and leverages force supervision to eliminate the need for an ODE solver during training. Consistency of physical laws in the latent space is ensured through the principle of virtual work. Results show that the model effectively learns the subtle dynamics induced by the system's nonlinearity and non-convex potential energy, and generalizes well to unseen forces and initial conditions. These observations confirm the physical relevance of the proposed approach, and its interest for model reduction.
PDF arXiv
arXiv cs.LGOct 3
Localized Operator Learning with Adaptive Partition-of-Unity Mixture-of-Expert Networks
Madison Cooley, Ramansh Sharma, Shandian Zhe, Robert M. Kirby, Varun Shankar
Operator learning methods such as DeepONets and FNOs often struggle with PDE families featuring sharp interfaces, heterogeneous coefficients, and localized multiscale structures. We introduce a partition-of-unity (POU) mixture-of-experts framework for localized operator learning, in which geometry-aware gating networks produce smooth spatial partitions which blend the contributions of local expert networks. Our main contribution is HiRefPOU, a residual-style hierarchical POU architecture for DeepONets that organizes localized representations through nested parent-child partitions while preserving global continuity. We also show that the same POU principle can be incorporated into Fourier Neural Operators to introduce spatial adaptivity without modifying the underlying spectral layers. On heterogeneous Darcy and reaction-diffusion benchmarks, HiRefPOU achieves substantially lower error than global DeepONet and static POU-MoE baselines, while the broader operator-learning experiments show that the benefits of localization depend on the PDE structure and the chosen neural-operator backbone. The learned partitions are interpretable and align with interfaces and regions of rapid…
PDF arXiv

Activity · 12 weeks

Fields · AI · updated 1h ago

Flow matching

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

69papers this week−56.3% vs last week

All papers · 656 With code · 3

Newest Most relevant

620 papers this month

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.