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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 modeling301 papers33 this week
physics informed neural · neural operators · informed neural networks295 papers27 this week
diffusion priors · posterior sampling · diffusion posterior75 papers16 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
Alexander TongImproved Training of Strong Stochastic Flow Maps4
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

Active contributors

Activity · 12 weeks

Activity

Recent papers

All papers in Research

arXiv cs.LGSep 26
Staying on the Attractor: Supervising Neural Surrogates of 3D Turbulence Where They Leave It
Yilong Dai, Shaswata Mitra, Raj Patel, Yiming Sun, Shengyu Chen +5
Neural surrogates are trained to predict 3D turbulent flows in place of direct numerical simulation (DNS). For chaotic flows, the goal is short-term pointwise accuracy followed by long-term physical and statistical fidelity. However, small prediction errors can carry a surrogate away from the flow's attractor. Off-attractor states are poorly represented in training data, leaving their evolution weakly constrained. The learned dynamics can then amplify deviations and lead to blow-up, freezing, or statistical drift. We propose off-attractor supervision (OAS) to supervise neural surrogates where they leave the attractor. OAS teaches the model how the true Navier-Stokes dynamics would evolve from these states. Each selected state is paired with its own future computed by DNS. Three generators select a few hundred states for relabeling. The first collects states from the surrogate's own rollouts. The second uses surrogate attacks to target freezing, excessive amplification, and violations of incompressibility and energy balance. The third perturbs training states along an amplified direction and a strongly damped random direction of the dynamics. All attacks run on the surrogate…
PDF arXiv
arXiv cs.LGSep 26
HamiFormer: Dual-Expert Diffusion Fields with Affine Symplectic Maps
Haoxiang Huang, Xiang Liu, Shuwei Wang, Jingheng Ma, Sen Cui
Predicting smooth dynamics and collisions requires modeling continuous evolution and abrupt state changes. We introduce HamiFormer, a dual-expert diffusion field combining whole-window denoising with residual-corrected Hamiltonian propagation. Their mixed-state feedback attenuates the direct contribution of inherited autoregressive error: each mixed state guides subsequent propagation within the jointly refined window. Parallel Local Affine Scan (PLAS) amortizes iterative refinement across rectified-flow steps and evaluates derivatives in parallel across physical time. PLAS's affine symplectic maps achieve lower solver error and runtime than sequential explicit Euler in our evaluation. A Regime Model Tree specializes residuals and routing to balance typical-state accuracy against large tail errors. Our analysis gives conditions for physically consistent refinement and warm-start tracking, and finite-window error bounds under diffusion feedback. In 192-step evaluations, HamiFormer reduces normalized phase-space MSE by 26.3% against PhysiFormer on HamiBalls-1 and 21.4% against DiT on HamiBalls-2, with comparable model capacities. Disjoint-interval comparisons show the lowest…
PDF arXiv
arXiv cs.LGSep 26
Retimed Bellman Flows: Escaping the Impossible Triangle of Velocity Bootstrapping
Boyang Xu, Shengzhe Chen, Hao Yan
Flow critics learn return distributions by transporting Gaussian noise to Bellman endpoints via continuous velocity fields. While velocity bootstrapping stabilizes training by querying a successor teacher, existing methods face a structural dilemma: on straight paths, no residual-free same-time affine mapping can preserve Gaussian initial noise while maintaining an unbiased target. To overcome this limitation, we introduce Retimed Bellman Flows (ReBF). ReBF queries the teacher critic at a dynamically shifted earlier flow time, aligning intermediate student and teacher trajectories. By combining this retimed clock with fresh, decoupled noise generation, ReBF constructs a provably conditionally unbiased velocity target that preserves the Bellman fixed point and contracts under Wasserstein distances. Empirically, ReBF reduces $W_1$ distance to ground-truth return distributions by up to $7.7\times$ on synthetic MRPs and outperforms existing flow critics across 38 challenging OGBench and D4RL offline reinforcement learning tasks.
PDF arXiv
arXiv cs.CVSep 26
Unlocking Geodesic Gromov-Wasserstein Distances for 3D Modeling
Krzysztof Marcin Choromanski, Derek Long, Ananya Parashar, Dwaipayan Saha
\textit{Gromov-Wasserstein Distances} (GWDs) provide quantitative ways of comparing probabilistic distributions defined on different metric spaces by applying techniques from the optimal transport theory. As such, GWD can be potentially useful in a large variety of applications ranging from graph matching problems to 3D object detection. However its practical use at scale is significantly limited by cubic time complexity computations involving dense intra-space distance matrices. Even though in the Euclidean metric spaces several techniques (e.g. involving scalable kernel methods) were proposed to address it, to the best of our knowledge, analogous techniques for general geodesic distances on manifolds, or shortest-path distance on graphs in their discretized variants, were not developed. In this paper, we present \textbf{E}fficient \textbf{G}eodesic \textbf{Gro}mov-\textbf{W}asserstein methods (EGGroW), a new class of efficient algorithms designed to calculate geodesic Gromov-Wasserstein distances with entropic Sinkhorn-like approaches, leveraging recently introduced \textit{GenusSink} methods \citep{genussink} and the theory of random features. We provide important downstream…
PDF arXiv
arXiv cs.LGSep 26
Derivative-Informed Training of Neural Operators On-the-Fly via Sketched Tangent Consistency
Xinhan Yang, Lu Lu, Shancong Mou
Derivative-informed training improves neural operators by directly supervising their input-output sensitivities, which is crucial when neural operators are used as differentiable surrogates for inverse problems, PDE-constrained optimization, design, and control. However, existing methods rely on offline-generated derivative labels, making data generation slow, storage-intensive, and difficult to adapt across datasets, resolutions, or perturbation bases. We propose sketched tangent consistency loss (sTCL), an on-the-fly derivative-informed training objective that, for PDEs with a known and differentiable residual, enforces sensitivity consistency directly from the governing equation without offline tangent labels or neural-operator architecture changes. sTCL uses randomly sketched input perturbations to provide a lightweight derivative-level physics constraint during training. However, raw forward-sensitivity residual penalties can fail for stiff, ill-conditioned, indefinite, or coupled saddle-point tangent operators. To address this, we introduce lightweight operator-aware loss-conditioning mechanisms selected by a simple tangent-operator decision rule. Across Helmholtz,…
PDF arXiv
arXiv cs.LGSep 26
Beyond Gaussian Assumptions: Distribution-Aware Channel Capacity for Effective Connectivity
Jianan Jian, Jacob Kang, Nurahmed Multezem, Benjamin Li, Nan Xu
Effective-connectivity estimation from brain signals often relies on Gaussian residual modeling, which enables tractable estimation but can discard informative distributional structure and distort inferred directed interactions when empirical residuals are non-Gaussian. We show across multiple modalities, species, and experimental conditions that both brain signals and fitted channel residuals frequently deviate from Gaussianity. We therefore introduce a distribution-aware, information-theoretic measure of effective connectivity based on channel capacity under general residual distributions. To estimate the resulting capacity from empirical, potentially non-Gaussian residuals, we develop a dual-flow min-max estimator based on normalizing flows, in which a generator searches over admissible input distributions under a power constraint while an observer estimates output entropy. We provide a theoretical characterization of the estimator, showing that the observer objective recovers differential entropy up to a KL approximation term, that the formulation reduces to classical Gaussian capacity as a special case, and that residual entropy can alter achievable information rates beyond…
PDF arXiv

Papers

Topics in this field

flow matching · flow · generative modeling301 papers33 this week
physics informed neural · neural operators · informed neural networks295 papers27 this week
diffusion priors · posterior sampling · diffusion posterior75 papers16 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
Alexander TongImproved Training of Strong Stochastic Flow Maps4
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

Recent papers

All papers in Research

arXiv cs.LGSep 26
Staying on the Attractor: Supervising Neural Surrogates of 3D Turbulence Where They Leave It
Yilong Dai, Shaswata Mitra, Raj Patel, Yiming Sun, Shengyu Chen +5
Neural surrogates are trained to predict 3D turbulent flows in place of direct numerical simulation (DNS). For chaotic flows, the goal is short-term pointwise accuracy followed by long-term physical and statistical fidelity. However, small prediction errors can carry a surrogate away from the flow's attractor. Off-attractor states are poorly represented in training data, leaving their evolution weakly constrained. The learned dynamics can then amplify deviations and lead to blow-up, freezing, or statistical drift. We propose off-attractor supervision (OAS) to supervise neural surrogates where they leave the attractor. OAS teaches the model how the true Navier-Stokes dynamics would evolve from these states. Each selected state is paired with its own future computed by DNS. Three generators select a few hundred states for relabeling. The first collects states from the surrogate's own rollouts. The second uses surrogate attacks to target freezing, excessive amplification, and violations of incompressibility and energy balance. The third perturbs training states along an amplified direction and a strongly damped random direction of the dynamics. All attacks run on the surrogate…
PDF arXiv
arXiv cs.LGSep 26
HamiFormer: Dual-Expert Diffusion Fields with Affine Symplectic Maps
Haoxiang Huang, Xiang Liu, Shuwei Wang, Jingheng Ma, Sen Cui
Predicting smooth dynamics and collisions requires modeling continuous evolution and abrupt state changes. We introduce HamiFormer, a dual-expert diffusion field combining whole-window denoising with residual-corrected Hamiltonian propagation. Their mixed-state feedback attenuates the direct contribution of inherited autoregressive error: each mixed state guides subsequent propagation within the jointly refined window. Parallel Local Affine Scan (PLAS) amortizes iterative refinement across rectified-flow steps and evaluates derivatives in parallel across physical time. PLAS's affine symplectic maps achieve lower solver error and runtime than sequential explicit Euler in our evaluation. A Regime Model Tree specializes residuals and routing to balance typical-state accuracy against large tail errors. Our analysis gives conditions for physically consistent refinement and warm-start tracking, and finite-window error bounds under diffusion feedback. In 192-step evaluations, HamiFormer reduces normalized phase-space MSE by 26.3% against PhysiFormer on HamiBalls-1 and 21.4% against DiT on HamiBalls-2, with comparable model capacities. Disjoint-interval comparisons show the lowest…
PDF arXiv
arXiv cs.LGSep 26
Retimed Bellman Flows: Escaping the Impossible Triangle of Velocity Bootstrapping
Boyang Xu, Shengzhe Chen, Hao Yan
Flow critics learn return distributions by transporting Gaussian noise to Bellman endpoints via continuous velocity fields. While velocity bootstrapping stabilizes training by querying a successor teacher, existing methods face a structural dilemma: on straight paths, no residual-free same-time affine mapping can preserve Gaussian initial noise while maintaining an unbiased target. To overcome this limitation, we introduce Retimed Bellman Flows (ReBF). ReBF queries the teacher critic at a dynamically shifted earlier flow time, aligning intermediate student and teacher trajectories. By combining this retimed clock with fresh, decoupled noise generation, ReBF constructs a provably conditionally unbiased velocity target that preserves the Bellman fixed point and contracts under Wasserstein distances. Empirically, ReBF reduces $W_1$ distance to ground-truth return distributions by up to $7.7\times$ on synthetic MRPs and outperforms existing flow critics across 38 challenging OGBench and D4RL offline reinforcement learning tasks.
PDF arXiv
arXiv cs.CVSep 26
Unlocking Geodesic Gromov-Wasserstein Distances for 3D Modeling
Krzysztof Marcin Choromanski, Derek Long, Ananya Parashar, Dwaipayan Saha
\textit{Gromov-Wasserstein Distances} (GWDs) provide quantitative ways of comparing probabilistic distributions defined on different metric spaces by applying techniques from the optimal transport theory. As such, GWD can be potentially useful in a large variety of applications ranging from graph matching problems to 3D object detection. However its practical use at scale is significantly limited by cubic time complexity computations involving dense intra-space distance matrices. Even though in the Euclidean metric spaces several techniques (e.g. involving scalable kernel methods) were proposed to address it, to the best of our knowledge, analogous techniques for general geodesic distances on manifolds, or shortest-path distance on graphs in their discretized variants, were not developed. In this paper, we present \textbf{E}fficient \textbf{G}eodesic \textbf{Gro}mov-\textbf{W}asserstein methods (EGGroW), a new class of efficient algorithms designed to calculate geodesic Gromov-Wasserstein distances with entropic Sinkhorn-like approaches, leveraging recently introduced \textit{GenusSink} methods \citep{genussink} and the theory of random features. We provide important downstream…
PDF arXiv
arXiv cs.LGSep 26
Derivative-Informed Training of Neural Operators On-the-Fly via Sketched Tangent Consistency
Xinhan Yang, Lu Lu, Shancong Mou
Derivative-informed training improves neural operators by directly supervising their input-output sensitivities, which is crucial when neural operators are used as differentiable surrogates for inverse problems, PDE-constrained optimization, design, and control. However, existing methods rely on offline-generated derivative labels, making data generation slow, storage-intensive, and difficult to adapt across datasets, resolutions, or perturbation bases. We propose sketched tangent consistency loss (sTCL), an on-the-fly derivative-informed training objective that, for PDEs with a known and differentiable residual, enforces sensitivity consistency directly from the governing equation without offline tangent labels or neural-operator architecture changes. sTCL uses randomly sketched input perturbations to provide a lightweight derivative-level physics constraint during training. However, raw forward-sensitivity residual penalties can fail for stiff, ill-conditioned, indefinite, or coupled saddle-point tangent operators. To address this, we introduce lightweight operator-aware loss-conditioning mechanisms selected by a simple tangent-operator decision rule. Across Helmholtz,…
PDF arXiv
arXiv cs.LGSep 26
Beyond Gaussian Assumptions: Distribution-Aware Channel Capacity for Effective Connectivity
Jianan Jian, Jacob Kang, Nurahmed Multezem, Benjamin Li, Nan Xu
Effective-connectivity estimation from brain signals often relies on Gaussian residual modeling, which enables tractable estimation but can discard informative distributional structure and distort inferred directed interactions when empirical residuals are non-Gaussian. We show across multiple modalities, species, and experimental conditions that both brain signals and fitted channel residuals frequently deviate from Gaussianity. We therefore introduce a distribution-aware, information-theoretic measure of effective connectivity based on channel capacity under general residual distributions. To estimate the resulting capacity from empirical, potentially non-Gaussian residuals, we develop a dual-flow min-max estimator based on normalizing flows, in which a generator searches over admissible input distributions under a power constraint while an observer estimates output entropy. We provide a theoretical characterization of the estimator, showing that the observer objective recovers differential entropy up to a KL approximation term, that the formulation reduces to classical Gaussian capacity as a special case, and that residual entropy can alter achievable information rates beyond…
PDF arXiv

Activity · 12 weeks

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.

Fields · AI · updated 2h ago

Flow matching

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

76papers this week−51.0% vs last week

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