Latent Transport

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9 papers in the last four weeks, up 200% on the four weeks before. 0.1% of all new papers.

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Latest papers 50

Oct 1, 2026stat.ML

Wasserstein Gradient Flows and Forward-Only Diffusion Are Not Enough for Multimodal Sampling

There has been a proliferation of sampling algorithms based on Wasserstein gradient flows (WGF) and forward-only diffusion processes (FODP), often accompanied by theoretical guarantees of exponentially fast convergence to the target distribution. These guarantees are frequently interpreted as evidence that such methods can efficiently sample complex multimodal distributions, often supported by empirical results. In this work, we argue that this interpretation is fundamentally misleading. By invoking the Jordan-Kinderlehrer-Otto (JKO) scheme and Otto calculus, we establish that the canonical WGF sampling dynamics and overdamped forward diffusion share the same density evolution and therefore inherit the same metastability and slow-mixing phenomena long understood in nonequilibrium statistical physics. We analyze this family of samplers using two complementary tools -- spectral analysis and mean first-passage time (MFPT) analysis -- and show that well-separated multimodality can induce exponentially long mixing times associated with small spectral gaps and rare inter-mode transitions. For the commonly adopted log-linear annealing schedule studied here, we find that introducing intermediate distributions does not remove the exponential scaling of the total transport time. The limitation is structural rather than implementation-specific: purely local, gradient-driven transport mechanisms can require exponentially long times to transport probability mass across well-separated modes. We argue that this represents a fundamental limitation of WGF- and FODP-based sampling in their standard forms, and motivates future development of fundamentally nonlocal mechanisms for efficient multimodal sampling.

Daniel McBride, Pratik Khandagale, Cristina Garcia-Cardona +1

Los Alamos National Laboratory, Los Alamos, NM 87545, USA

Wasserstein Gradient Flows Latent Transport Diffusion Models Multimodal Generation

Oct 1, 2026cs.RO

H-SPAR: Hydrodynamic-aware Simulation for Particle Transport and Autonomous Robots

Environmental robotic sampling requires considering the dual influence of water currents on robotic motion and particle transport. Existing marine robotics simulators generally model flow, autonomy, and sampling targets separately, limiting joint evaluation of mission cost and sampling performance. H-SPAR integrates spatially and temporally varying velocity fields, Lagrangian particle transport, probabilistic sampling, and ROS 2/Gazebo-based uncrewed surface vehicle (USV) autonomy. In this work, shared precomputed flow fields drive particle advection and current-induced forces during closed-loop vehicle execution. Path-planning experiments show that the existing current-aware planner SVF-RRT* achieves 69.4% lower upstream cost than conventional RRT* at the planning level, but this reduction falls to 41.7% during execution under time-varying currents, reflecting temporal flow variation, vehicle motion constraints, and path deviation omitted during planning. Coverage experiments show that sweep orientation changes the particle-sampling rate by up to 22.2% under the complete H-SPAR configuration. These findings highlight the importance of evaluating planning, vehicle execution, particle transport, and sampling together under consistent hydrodynamic conditions. The project webpage is available at https://sites.google.com/view/h-spar, and the open-source code is available on GitHub at https://github.com/naviiidz/h-spar-sim.

Navid Zarrabi, Nariman Yousefi, Sajad Saeedi

Department of Mechanical, Industrial, and Mechatronics Engineering, Toronto Metropolitan University, Toronto, Ontario, Canada. · Department of Chemical Engineering, Toronto Metropolitan University, Toronto, Ontario, Canada. · Department of Computer Science, University College London, London, United Kingdom.

Fluid Dynamics Robot Navigation Mobile Robots Latent Transport

Sep 30, 2026cs.AI

PTNO: Training Neural Operators with Noisy Monte Carlo Estimates for Particle Transport Problems

Particle transport under multiple scattering is central to radiative transfer and plasma physics, yet high-fidelity Monte Carlo (MC) simulations must trace prohibitively many particles. Learning-based surrogates can amortize this cost, but typically train on expensive, well-converged MC solutions. We propose the Particle Transport Neural Operator (PTNO), a neural operator that learns particle transport surrogates directly from noisy, low-cost MC labels. Such labels pose two challenges: (1) high variance, which destabilizes standard supervised learning, and (2) a high dynamic range (HDR) spanning many orders of magnitude. For the first, we learn the solution operator from noisy labels of many configurations, amortizing MC cost and generalizing to unseen configurations. Because MC labels are unbiased, we show that the squared loss on them shares its minimizer with the loss on converged solutions, and our budget-allocation study over training scenes

M

, MC samples per render

N

, and independent renders per scene

K

shows that many noisy scenes beat fewer converged ones. For the second, a nonlinear transform such as the logarithm biases noisy supervision. Instead, PTNO keeps labels in physical space and enforces positivity with a softplus output layer that represents small values effectively. We further train with a pointwise relative

L_2

loss (PRelL2), the stop-gradient relative loss of HDR denoising and neural rendering, which normalizes each residual by the stop-gradient prediction instead of the noisy label. We demonstrate PTNO on neutron transport in fusion reactors and radiative transfer in participating media. On the two neutronics tasks, PTNO is

10^4

-

10^5\times

faster than converged MC on the same CPU and

10^3

-

10^5\times

cheaper than MC at matched accuracy; on the two radiative-transfer tasks, MC at matched accuracy costs

0.8

-

11\times

as much as PTNO.

Yubo Cao, Xi Deng, Mengqi Xia +3

California Institute of Technology · Yale University · UK Atomic Energy Authority +1

Neural Operators Latent Transport Monte Carlo Solar Irradiance

Sep 30, 2026cs.LG

Stable Transformers for Graph Generation

Graph generative models increasingly rely on Graph Transformers (GT) to capture complex dependencies among nodes and edges. While deeper architectures should provide greater expressive capacity and a broader receptive field, their effectiveness can decline with depth: repeated self-attention progressively contracts node representations, impeding information flow and gradient propagation. We analyse this phenomenon from a dynamical systems perspective, focusing on how the denoiser's spectral dynamics affect graph generation. We show that standard GT denoisers become increasingly dissipative as depth grows, leading to vanishing gradients and representation collapse. To isolate the effect of these dynamics, we construct a permutation-equivariant GT with inherently stable, non-dissipative transport. We also introduce a damping mechanism that continuously interpolates between non-dissipative and increasingly contractive regimes, enabling a direct assessment of how dissipation influences generation. Experiments on synthetic and molecular graph generation benchmarks show that the gap between these regimes widens with depth: non-dissipative dynamics preserve representation diversity and gradient flow, sustaining strong generative performance, whereas greater contraction progressively impairs it. These findings identify the denoiser's dynamical regime as a key design factor for deep graph generative models.

Luca Miglior, Alessio Gravina, Davide Bacciu

Department of Computer Science, University of Pisa, Italy

Multiplex Graph Transformers Generative Models Transformer Architectures Data Generation Latent Transport

Sep 30, 2026cs.MA

Fast and Scalable Multi-Agent Distribution Matching via Partitioned Optimal Transport

This paper presents a scalable optimal-transport-based framework for terminal distribution matching in multi-agent systems. While optimal transport provides a natural way to measure distributional mismatch and assign agents to a desired spatial distribution, global discrete transport can become computationally expensive for large-scale systems. We address this bottleneck by partitioning agents and target samples into spatially corresponding blocks and solving smaller local transport problems. Under a mass-balance condition, the resulting restricted coupling remains feasible for the global problem and provides an upper bound on the Wasserstein cost. The local assignments generate target locations for finite-horizon agent control, applicable to both linear and nonlinear dynamics. By alternating local assignment and control, we establish a cycle-to-cycle descent guarantee for the resulting transport surrogate. The proposed framework therefore enables scalable terminal distribution matching while retaining a rigorous connection to the Wasserstein objective. The technical soundness of the proposed results is validated through simulations.

Kooktae Lee, Ruchika Singh

Department of Mechanical and Aerospace Engineering, Texas Tech University, Lubbock, TX 79409, USA

Distribution Matching Latent Transport Wasserstein Distance Distributions

Sep 27, 2026cs.LG

PI-NOMT: Physics-Informed Neural Optimal Mass Transport for Brain Fluid Dynamics

Recovering hidden transport mechanisms from sparse spatiotemporal observations is a fundamental inverse problem in scientific machine learning. In brain tracer imaging, dynamic contrast-enhanced MRI (DCE-MRI) provides time-resolved measurements of tracer concentration, while the underlying velocity and source mechanisms governing tracer propagation remain unobserved. We formulate this problem as physics-informed latent-state inference, in which the transport field itself is the primary object of inference rather than an auxiliary variable used only to reconstruct observed densities. We propose Physics-Informed Neural Optimal Mass Transport (PI-NOMT), a framework that represents density, velocity, and source as continuous neural fields and combines a continuous neural density teacher, recursive differentiable advection--diffusion--source rollout, unbalanced optimal-transport regularization, and governing-equation supervision. Physical laws act as structural priors that constrain the space of admissible transport mechanisms, while observed tracer dynamics provide evidence for estimating the latent transport state. We evaluate PI-NOMT on a synthetic benchmark with known ground-truth transport and on DCE-MRI sequences from nine control rats. On the synthetic benchmark, PI-NOMT accurately recovers the prescribed velocity field, including its magnitude, direction, and integrated trajectories, rather than merely reconstructing endpoint densities. Across the nine rat datasets, the framework yields sub-percent local endpoint error, consistent physical speed scales, and low post-training PDE and incompressibility residuals. These results support physics-informed latent-state inference as a general framework for recovering hidden transport mechanisms from observed dynamic scalar fields.

Mehmet Emin Acar, Vahit Bugra Yesilkaynak, Helene Benveniste +1

Istanbul Technical University, Faculty of Computer and Informatics Engineering, AI and Data Engineering Department, Istanbul, Turkiye · Yale University, School of Medicine, New Haven, CT, USA

Latent Transport Bayesian Inverse Problems Latent States

Sep 14, 2026cs.LG

Discrete Beckmann Transport Models for One-Step Language Modeling and Reasoning

Discrete diffusion and flow models are a promising alternative to autoregressive language models, but compressing many-step sampling into fewer steps typically requires distilling a pretrained teacher model. This caps the student at the teacher's quality and requires a costly two-stage training pipeline. We introduce Discrete Beckmann Transport Models (DBTM), built on a time-independent flow whose autonomous transport map provably carries any point in the ambient space to a fixed point on the vertices of the simplex in a single step. We show that this fixed-point property is characterized by a conservation equation whose residual can be minimized directly from data, removing the requirement for a teacher flow and time conditioning. Under this construction, a partially trained map corresponds to the flow truncated at finite time, so generation reduces to iterating one map until it reaches a fixed point. We further extend the map to a partial-context interpolant where additional function evaluations act as refinement steps rather than ODE integration steps. On language modeling and reasoning tasks, DBTM enables one- and few-step generation that improves quality and accuracy over discrete diffusion and continuous flow baselines.

Sophia Tang, Shiyi Wang

University of Pennsylvania · Harvard University · Kempner Institute +1

Diffusion Language Models Autoregressive Language Models Diffusion Models Few-Step Generation Language Modeling Latent Transport+2

Sep 12, 2026physics.plasm-ph

Physics-Informed Neural Networks to Infer the Perpendicular Energy Conductivity in the Scrape-Off Layer of Stellarator Devices

In this work, we develop an inverse Physics-Informed Neural Network (PINN) framework to infer the dependence of the scrape-off layer (SOL) perpendicular heat conductivity on plasma density and temperature,

\kappa_\perp(n,T)

. The method combines radial profile measurements of electron density and temperature with the residual of a reduced one-dimensional SOL transport equation, so that the inferred conductivity is constrained by both the measurements and the underlying transport model. Three neural networks are trained simultaneously: two reconstruct the temperature and density profiles as functions of the radial coordinate and transported power, while a third represents the effective conductivity as a function of the local density and temperature. The framework is first validated using synthetic data generated from a prescribed conductivity function, allowing the inferred

\kappa_\perp(n,T)

to be compared directly with the ground truth. The model recovers the imposed functional dependence with errors below

10~\%

in the data-constrained region. Bootstrap resampling is shown to provide a practical indicator of prediction reliability and consistency. A scan in the number of plasma profiles used for training and the number of radial measurement positions per profile identifies a practical trade-off between reconstruction accuracy and data availability. Finally, the method is applied to an experimental dataset from the TJ-II stellarator obtained with the helium-beam diagnostic. This exploratory application provides an initial estimate of the effective SOL conductivity and illustrates the potential of inverse PINNs for extracting transport information from plasma edge measurements.

J. Gallego (Departamento de Tecnología, CIEMAT, Spain) +23

Departamento de Tecnología, CIEMAT, Spain. · Harvard John A. Paulson School of Engineering and Applied Sciences, USA. · Laboratorio Nacional de Fusión, CIEMAT, Spain.

Parametric Physics-Informed Neural Network Latent Transport Neural Network

Sep 7, 2026cs.LG

ParetoTransport: Generative Optimization by Mass Transport Toward The Pareto Front

Offline multi-objective optimization requires not only moving the objective vectors of candidate designs toward the Pareto front, but also distributing them effectively along it. Generative methods have recently emerged as a natural approach because they learn a distribution over feasible designs while allowing generation to be steered toward promising designs. Existing methods, however, largely retain classical sample-wise guidance strategies, leaving the distribution-level modeling capability of generative methods underused. We propose ParetoTransport, a training-free guidance method for pre-trained flow-matching models that explicitly specifies and refines a population-level distribution in objective space. ParetoTransport guides a flow-matching sampler to iteratively transport the empirical offline distribution toward the Pareto front, with Wasserstein matching to intermediate proxy distributions. This directly controls distributional displacement and mass allocation along the front. We establish a convergence result and demonstrate state-of-the-art performance on standard offline MOO benchmarks, extending recent evaluations beyond hypervolume to generational distance, inverted generational distance, and Wasserstein distance.

Stephanie Holly, Sepp Hochreiter, Werner Zellinger

LIT AI Lab and Institute for Machine Learning JKU Linz, Austria

Multi-Objective Optimization Pareto Frontier Latent Transport Stable Transport Generative Models In-Distribution

Sep 3, 2026cs.CE

Differentiable Hybrid Modelling for Learning and Optimising Chemical Transport Processes from Experimental Data

Reliable transport models are essential when modelling and optimising many chemical engineering processes, yet, most models assume hand-picked constitutive laws which may not reflect reality, and often assume initial conditions are known exactly. Both restrictions can significantly bias model predictions and lead to systematic error when used in predictive and control settings. Black-box neural surrogate alternatives for modelling can better match real example data, but are confined to the task they were trained on and cannot be interrogated for physical consistency. Here we introduce a general-purpose differentiable hybrid modelling framework for transport processes, specifically for the case of population balance equations. Our framework integrates a JAX finite volume population balance solver with learnable neural network components which are trained to both discover constitutive laws and fit initial conditions from real experimental data, allowing us to better model real experimental transport systems. Furthermore, we use our framework for process optimisation, using its differentiability to allow us to direct optimising experimental settings for quantities of interest. This work highlights the huge potential of such differentiable hybrid modelling frameworks for learning and optimising any given chemical separation which involves mass, energy, and/or momentum transport.

Arthur Jessop, Mohammed Alsubeihi, Ben Moseley +1

Department of Chemical Engineering, The University of Manchester, Manchester, M13 9PL, United Kingdom. · Department of Earth Science and Engineering, Imperial College London, South Kensington, SW7 2BX, United Kingdom. · I-X Centre for AI in Science, Imperial College London, South Kensington, SW7 2BX, United Kingdom.

Chemical Process Systems Latent Transport Surrogate Models Prompt Optimization

Sep 2, 2026cs.LG

Mesh-Native Physics-Informed Graph Surrogates for TCAD-in-the-Loop Design Space Exploration

High-fidelity TCAD simulation of drift-diffusion transport remains the workhorse of emerging FinFET device design, but it is computationally expensive, especially for 3D structures where runtime escalates steeply with mesh complexity. This sharply limits multi-objective design space exploration. Existing machine-learning surrogates map a fixed set of design parameters to a few scalar device metrics, discarding the underlying physics and losing transferability across device geometries and families. A physics-informed graph attention network (GAT) surrogate is proposed. It operates directly on the tetrahedral TCAD mesh and predicts, at every mesh node, the electrostatic potential together with the electron and hole quasi-Fermi levels, the fundamental unknowns of the drift-diffusion system. Training combines a data loss with finite-volume current-continuity residuals, embedding carrier-transport physics into the objective. Operating on the mesh as a graph, the surrogate inherits size generalization: a model trained on few-fin meshes applies unchanged to substantially larger arrays, bounded at inference only by GPU memory. Per-node uncertainty from a deep ensemble drives an active-learning loop that screens large candidate pools in seconds and forwards only the most informative designs for full simulation. Benchmarked against Sentaurus Device on multi-fin tri-gate FinFETs, the surrogate reproduces the three drift-diffusion fields with sub-volt per-field RMSE and reaches a per-design throughput orders of magnitude higher than the full simulator. The advantage grows with device size: on large multi-fin arrays that are prohibitively slow to simulate directly, inference still completes in under a second per device, enabling Pareto-front exploration across device scales infeasible for direct TCAD sweeps.

Leonid Popryho, Ayoub Sadeghi, Inna Partin-Vaisband

University of Illinois Chicago · Chicago, IL, USA

Machine Learning Surrogates Latent Transport

Sep 2, 2026cond-mat.mtrl-sci

Physics-Informed Neural Network Surrogate for Oxygen Vacancy Dynamics in epitaxial $\mathrm{SrTiO_3}$ on Si memristors via Dynamic Spectral Optimization

Physics-informed neural networks (PINNs) offer a promising framework for modeling semiconductor devices, yet standard architectures struggle with severe numerical stiffness and multiscale spatial discrepancies inherent to oxide heterostructures. Here, we demonstrate a cascaded PINN architecture coupled with a custom second-order Chebyshev second kind polynomial spectral optimizer (DSO V2 Hybrid) to model ion-electronic drift-diffusion transport in Pt/SrTiO

_3

/Si memristive heterostructures across a 20 nm STO film on a 380

μ

m Si substrate. By isolating potential, carrier density, and vacancy transport into four sequentially trained sub-neural-networks, our model circumvents condition numbers exceeding

10^{16}

without operator splitting. The trained surrogate reproduces experimental conductive-AFM current-voltage hysteresis (

R^2 > 0.96

) while ensuring strict Poisson consistency across continuous space. Compared to conventional finite-element solvers (e.g., COMSOL), the PINN surrogate enables differentiable inverse parameter estimation and linear time inference.

Rodion Podorozhny, Nikoleta Theodoropoulou, Jelena Tešić

Dept. of Computer Science, Texas State University, San Marcos, TX, USA · Dept. of Physics, Texas State University, San Marcos, TX, USA

Reram Crossbar Parametric Physics-Informed Neural Network Porous Media First-Principles Calculation Latent Transport

Sep 1, 2026cs.LG

Generative Diffusion Surrogates with Analytical Variance Schedule

Stochastic transport describes physical systems in which an initially structured distribution spreads under unresolved forcing, scattering, or heterogeneous media. Useful surrogates for such systems should be probabilistic, time-resolved, and able to represent non-Gaussian distributional structure. Generative diffusion models, which corrupt data with Gaussian noise and learn a reverse flow back to structured states, have these properties. Their noise schedules, however, are usually chosen heuristically: image and audio generation---the canonical use cases---provide no physical clock. In transport, by contrast, the variance, or mean-square displacement, is often known from macroscopic theory or empirical scaling even when the full distribution is not. Here we prescribe the forward noising rate as the time derivative of this variance, turning generative time into a calibrated transport clock. The variance path is enforced by construction, while the learned score field represents how non-Gaussian structure inherited from entrance data is smoothed along that path, requiring no intermediate-time physical transport data. For ballistic-to-diffusive transport in turbulent plasmas, the surrogate matches test-particle distributions, reproduces the laboratory-measured variance scale, and tracks the simulated kurtosis evolution without schedule tuning, enabling calibrated emulation and likelihood-based inference.

Patrick Reichherzer, Gianluca Gregori, David N. Hosking +1

Department of Physics, University of Oxford, Oxford OX1 3PU, UK. · Department of Astrophysical Sciences, Princeton University, Princeton NJ 08544, USA. · Max Planck Institute for Security and Privacy, Bochum 44799, Germany. +2

Diffusion Dynamics Diffusion Models Latent Transport Variance Non-Gaussianity

Aug 31, 2026cs.CV

A Lagrangian View of Flow Matching

Modern explicit-time generative models, such as Flow Matching [Lipman et al., 2023] and Rectified Flow [Liu et al., 2023], are typically derived top-down via Optimal Transport and the continuity equation. This standard Eulerian approach focuses on the macroscopic transport of probability mass. In this paper, we present an alternative, bottom-up mechanical derivation grounded in a Lagrangian (particle-centric) perspective. By analyzing the local Taylor expansion of a continuous denoiser, we motivate a strict invariance condition required for optimal, singlestep generation: the conservation of target identity. Enforcing this condition yields a governing quasi-linear advection Partial Differential Equation (PDE). We demonstrate that solving this PDE via the Method of Characteristics analytically yields the straight-line trajectories of Flow Matching. This geometric perspective isolates the Jacobian of the denoiser as the primary source of trajectory curvature, providing a direct mathematical explanation for why straight-line flows enable massive step sizes, and why empirical models require distillation to flatten intersecting characteristics.

Peyman Milanfar

1Google

Latent Transport Generative Models Few-Step Generation Lagrangian Methods Mechanical Systems

Aug 30, 2026physics.flu-dyn

Data-Driven Design Optimization of Streaming-Potential-Mediated Electrokinetic Transport of Viscoelastic Fluids in Microchannels

Streaming-potential-mediated transport of viscoelastic fluids has attracted research attention owing to its applications in electrokinetic energy conversion and microfluidic transport. Existing analytical and semi-analytical models in published literature provide valuable physical insights, but require repeated numerical evaluations for exploring large design spaces and identifying the optimal operating conditions. In this work, a surrogate-assisted framework is developed for rapid design optimization of pressure-driven electrokinetic transport of simplified Phan-Thien-Tanner fluids in a slit microchannel. A high-fidelity numerical database is generated over a broad range of governing dimensionless parameters, which includes the zeta potential, the Debye parameter, the Dukhin number, and the viscoelastic parameter. A Machine Learning surrogate model is subsequently trained to accurately approximate the nonlinear relationship between the governing parameters and the streaming potential, while the volumetric flow rate and hydroelectric energy conversion efficiency were calculated from closed form equation by using the streaming potential predicted by the surrogate. This is coupled with a multi-objective optimization strategy to identify operating conditions that simultaneously maximize energy conversion efficiency and volumetric flow rate. The proposed methodology can significantly accelerate parametric exploration compared with repeated numerical simulations across different parameters and provides practical design guidelines for electrokinetic microfluidic devices. The study demonstrates the potential of combining computational fluid mechanics with data-driven surrogate modeling for efficient engineering design and optimization.

Ankan Basu, Sumanta Banerjee

Department of Computer Science and Engineering, Jadavpur University, Kolkata, India. · 2*Department of Mechanical Engineering, Heritage Institute ofAug Technology, Kolkata, India.

Fluid Controls Latent Transport Surrogate Models Streaming Engineering

Aug 7, 2026cs.LG

Hidden Gauge Controls Feature Specialization in ReLU Networks

Training changes a network's predictions while allocating task-relevant structure across its internal units. In an overparameterized ReLU network, several neurons can begin with exactly the same functional role, yet one may acquire a teacher feature while the others become redundant. We call the identity of that neuron feature ownership and ask whether it can be controlled by a parameter choice invisible to the initial predictor. In a tractable Gaussian teacher--student model, we fix the complete initial function and vary only a positive-homogeneous scaling gauge. Opposite gauges produce distinct feature trajectories and a sharp

Θ(D^2)

separation in specialization time that no global change of clock can explain. Among any fixed number of initially duplicate students, assigning the favorable gauge to one neuron deterministically selects it as the owner and drives the remaining functional contribution to zero. An exact reaction--transport decomposition attributes the effect to different mobilities for changing a feature's coefficient and direction. We prove global selection and functional pruning, extend finite-time selection to visible perturbations and small-step full-batch gradient descent, and verify the predicted loss, alignment, pruning, and dissipation trajectories in population and finite-sample training. The initial predictor therefore determines neither when the feature is learned nor which neuron learns it.

Tongxi Wang

School of Future Technology Southeast University Nanjing, China

Feature Learning Rectified Linear Unit Networks Sparse Structural Specialization Discontinuous Gating Latent Transport

Aug 3, 2026cs.LG

Beckmann Transport Models: From Autonomous Flows to One-Step Maps

We propose an instantiation of flow matching that relies on a time-independent velocity field (an \emph{autonomous flow}) to exactly map between two distributions, so long as the target is singular, i.e.\ supported on a lower-dimensional data manifold. We also show that the one-step generative map associated with this flow is the unique solution of a simple conservation equation, which can be used to learn the map directly from samples. These autonomous flows and maps give a dynamical meaning to the flux constraint of Beckmann's transportation problem. Their construction provides a unifying framework that recovers, for instance, the closed-form Poisson-flow generative model and equilibrium matching with a quadratic flow-matching regression loss. We illustrate how this theory corrects inconsistencies in existing methods and demonstrate the effectiveness of the autonomous flow and the one-step map on ImageNet 256x256.

Lee Cheuk-Kit, Florentin Coeurdoux, Yuyuan Chen +5

1Harvard University · 2Capital Fund Management · University of Pennsylvania +2

Generative Flow Networks Latent Transport Velocity Field Structural Constraints

Jul 31, 2026cs.CV

Dense Temporal Contrast Synthesis via Conditioned Latent Transport

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is essential for breast cancer management, but reliance on gadolinium-based contrast agents (GBCAs) restricts use in contraindicated populations, prolongs scan protocols, and presents environmental toxicity concerns. Contrast synthesis offers a non-invasive alternative; however, existing approaches struggle to balance spatial realism with temporal continuity, suffer from slow iterative sampling, underutilize structural priors, and lack clinical validation. We propose a novel conditioned latent transport framework that predicts contrast enhancement in a single forward pass. By anchoring the latent trajectory to the pre-contrast anatomy and applying continuous time conditioning, the model synthesizes patient-specific contrast evolution at any acquisition time. The proposed approach outperforms baseline and the state-of-the-art models across spatial, perceptual, temporal, and distributional metrics. Evaluated on an independent external cohort, the method demonstrates robustness to domain shifts induced by scanner noise as well as differing acquisition protocol. Furthermore, our synthetic contrast enhancement significantly improved downstream tumor segmentation performance, yielding a 22.4% relative increase in Dice coefficient (0.60 vs. 0.49 baseline pre-contrast, p < 0.01), reducing boundary segmentation error by over 39%, while outperforming all other generative model baselines. Finally, a reader study involving four breast radiologists evaluated the image quality, kinetic fidelity, and diagnostic viability of our synthesized sequences across 40 randomly selected cases. The results demonstrated that in 70% of cases, synthesized images provided sufficient clinical information to support the same management decisions as real DCE-MRI, suggesting a path toward safer and faster contrast-free or contrast-reduced imaging workflows.

Smriti Joshi, Apostolia Tsirikoglou, Daniel M. Lang +15

Departament de Matemàtiques i Informàtica, Universitat de Barcelona, Barcelona, Spain · Department of Oncology-Pathology, Karolinska Institutet, SE-171 77, Stockholm, Sweden · Institute of Machine Learning in Biomedical Imaging, Helmholtz Munich, Munich, Germany +9

Magnetic Resonance Imaging Adaptive Histogram Equalization Latent Transport Contrast Multidisciplinary Tumor Boards Dense

Jul 30, 2026cs.LG

Representations from Pretrained Machine-Learning Interatomic Potentials as Coarse Coordinates for Material Generation and Evaluation

Generative machine learning is increasingly used for inorganic crystal structure generation. Most models and the corresponding evaluation approaches rely on simple forms of crystal structure representation. In this paper, we showcase the power of atom-averaged features from pretrained Machine-Learning Interatomic Potentials (MLIPs), such as MACE, for such tasks. We first introduce a distance measure that assesses the output of material generative models by capturing both quality and novelty in a single distribution-based evaluation framework. In particular, we introduce the Coarse-Fine Transport Distance (CFTD) using two different featurizers, where the quality component is based on coarse MACE features. We showcase CFTD's versatility in capturing crystal-structure quality while also detecting memorization, and compare it with the recently introduced continuous SUN metrics. We further show that coarse MACE features can be used as guidance for a material generative model.

Paul Hagemann, Katharina Ueltzen, Simon Müller +2

Crystal Structure Interatomic Potentials Generative Models Atom-Averaged Features Latent Transport

Jul 29, 2026cs.CC

Field Codes for Distributed Coupling Samplers and Certified Empirical Transport

In this paper, we formulate three communication tasks for empirical optimal transport: distributed coupling sampling, cost-evaluable coupling output, and scalar value-certified sampling. Our main result is a field-code compiler: any communicated transport field approximating an optimal empirical Monge map to error

η

can be completed by sparse target-cell residuals into an exact-marginal value-certified sampler with scalar certificate

W_1(μ,ν)\leq U\leq W_1(μ,ν)+2Δ

, where

Δ

is the public target-partition diameter. The certificate accuracy is controlled by

Δ

alone. The field error

η

controls residual communication under a cell-margin condition; without a margin,

η

alone does not bound residuals. We instantiate the compiler via adaptive local-affine and tensor-product spline codes with

d(m+1)^db

field bits in the spline case, plus residual lists charged separately. For lower bounds, exact Gap-Hamming embeddings prove certified output is hard, including a smooth cell-packing diffeomorphism family requiring

Ω(\varepsilon^{-2d/(d+4)})

communication for any cost-evaluable, cost-certified, or value-certified protocol. The same gadgets admit zero-communication samplers, formally separating the sampler and certificate-bearing output models. These results identify the transport field as the right communicated object whenever a field code is available, primarily as a residual-sparsity tool.

Hung Mai, Hai Nguyen, Luong Doan +4

1B0Labs, N2TP Technology · 3Nanyang Technological University · 4Phenikaa University, Vietnam

Optimal Transport Approach Accelerated Sampling Optimal Sample Complexity Distributional Fidelity Latent Transport Field Evaluation+1

Jul 22, 2026cs.SD

Cumsum-Composable Phase Transport for Low-Cost Streaming Keyword Spotting

State-space sequence models are attractive for streaming speech because they maintain compact recurrent state, but scan-style training kernels can have unfavorable constants for short audio tasks. We study cumsum-composable phase transport, a streaming-native temporal layer for keyword spotting. Each layer projects acoustic frames to complex channels, transports them by learned unitary rotations, accumulates a finite window using prefix differences, and applies a gated residual update. The same prefix representation gives exact batched training with ordinary cumulative sums and exact online inference with one prefix update per frame. Unitary transport is the key constraint: inverse rotations have norm one, keeping prefix terms well conditioned while memory is supplied by windows or block readouts. On Google Speech Commands v2 with 12 labels, mel+cumsum models retain competitive accuracy with compact baselines. The strongest single-seed run reaches 97.3% test accuracy; a 51.6K-parameter tied model also reaches 97.3%, and a 24.8K tied model reaches 96.8% versus 97.1% for a 25.6K MelCNNMaxPool baseline. In a matched cumsum-versus-scan benchmark, cumsum+window gives comparable accuracy, 94.82% versus 94.33%, while training 1.07x faster and reducing single-example latency from 7.09 ms to 5.01 ms on a Tesla T4. These results support cumsum phase transport as a simple low-cost temporal primitive for streaming keyword spotting.

Mahesh Godavarti

A Carrot, Inc

Keyword Spotting Streaming Latent Transport Batch

Jul 13, 2026cs.CV

FlowPET: Physics-Informed Symplectic Flow Matching for Low-Count PET Reconstruction

Low-count Positron Emission Tomography (PET) reconstruction is severely hindered by the dissipative nature of prevailing generative models, where the inherent phase-space contraction leads to the numerical extinction (``wash-out'') of weak but diagnostically critical lesion signals. To overcome this geometric limitation, we propose \textbf{FlowPET}, a physics-informed framework that reformulates reconstruction as volume-preserving transport in a symplectic phase space. By parameterizing the posterior dynamics via a Separable Hamiltonian System, our approach guarantees a divergence-free vector field by construction, theoretically immunizing weak signals against probability mass collapse. To steer this conservative flow, we introduce conjugate boundary conditions based on the Range-Null space decomposition of the PET operator; this strictly enforces data consistency in the range space while confining stochastic uncertainty injection to the unobserved null space. We train the model via symplectic flow matching and perform inference using a symplectic leapfrog integrator. Extensive experiments on BrainWeb, clinical pediatric, and UDPET datasets demonstrate that \textbf{FlowPET} not only surpasses state-of-the-art deterministic and stochastic baselines in SSIM and PSNR but, more crucially, exhibits superior recovery of low-contrast lesions. The results confirm that imposing Hamiltonian structural constraints offers a robust geometric safeguard for medical inverse problems in high-noise regimes.

Zheng Zhang, Hao Tang, Yingying Hu +2

Centre for Smart Health, The Hong Kong Polytechnic University, Hong Kong, China · Department of Nuclear Medicine, Sun Yat-sen University Cancer Center, Guangzhou, China · Research Center for Medical AI, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China

Positron Emission Tomography Riemannian Flow Matching Latent Transport Inverse Dynamics

Jul 8, 2026cs.AI

PHITSBench: an execution-scored benchmark for AI-assisted PHITS radiation-transport input generation using natural language

We introduce PHITSBench, an execution-scored benchmark for the Monte Carlo Particle and Heavy Ion Transport code System (PHITS). PHITSBench comprises 282 transport-scorable tasks spanning three common workflow categories: parameter editing (Edit), syntax repair (Repair ), and complete simulation generation from natural-language descriptions (Reproduce). Each task is evaluated using a Composite Metric Score that combines execution success with agreement between generated and reference transport observables. Using PHITSBench, we evaluate five GPT-5.4-based configurations ranging from zero-shot prompting to knowledge-augmented and agentic workflows. Without domain-specific knowledge, the model performs well on editing and repair tasks (95% and 70% success, respectively) but fails to generate correct simulations from scratch (0% success on the Reproduce track). A structured, machine-readable PHITS knowledge catalog, supplied alongside the user manual, raises single-shot Reproduce-task success to 57%. Agentic execution provides a further improvement to 66-73%, but at increased computational cost. Failure analysis shows that the remaining errors are dominated by incorrect selection and configuration of physical observables rather than syntax generation. These results suggest that future progress in AI-assisted radiation-transport modeling will depend as much on machine-readable knowledge bases, curated domain-training datasets, and execution-grounded evaluation environments as on advances in foundation models themselves.

Xianglin Ji, Svetlana V. Boriskina

Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Data Generation Pipelines Reproducibility Latent Transport Solar Irradiance Natural Language

Jul 8, 2026cs.LG

Physics-guided spatiotemporal neural models for fuel density prediction

This paper presents a physics-guided machine learning (PGML) framework for fuel density prediction, integrating physics constraints and domain knowledge into deep learning models to enhance model accuracy and stability. We explore three deep learning architectures -- ConvLSTM, Adaptive Fourier Neural Operator (AFNONet), and Video Vision Transformer (ViViT) -- to model the spatiotemporal evolution of fuel density. Our approach incorporates differentiable physics-informed terms in the loss function, including a mass-conserving fuel transport term and a rate-of-spread estimation. Experimental results, averaged across multiple independent trials, demonstrate that the proposed PGML framework outperforms purely data-driven baselines without physics constraints in both accuracy and stability. This framework enables computationally efficient, physically plausible fire forecasting to support adaptive prescribed burn management.

Tolga Caglar, Jaynil Jaiswal, Saqib Azim +3

San Diego Supercomputer Center University of California, San Diego

Physics-Guided Machine Learning Wildfire Prediction Combustion Control Dense Prediction Latent Transport

Jun 30, 2026cs.LG

Signed-Permutation Coordinate Transport for RMSNorm Transformers

Modern LLM workflows move coordinate-indexed objects across checkpoints: steering vectors, sparse autoencoders, top-

k

neuron sets, attribution lists, and merge alignments. This is only well posed after fixing the model's residual-stream gauge, which we show is architecture-dependent: LayerNorm residual charts have permutation gauge

S_d

(up to a global sign flip), while RMSNorm charts with generic per-channel gain have signed-permutation gauge

B_d = S_d \ltimes \{\pm 1\}^d

. Permutation-only alignment is therefore symmetry-incomplete for RMSNorm models. We introduce sign-marginalized Hungarian matching and prove a sharp failure mode: with decorrelated coordinates, raw signed-correlation matching has a structural permutation-accuracy ceiling at the positive-sign fraction of the true gauge, which sign-marginalization removes. We then make coordinate-preserving transport, not function-level merging, the primary object: composing saved-checkpoint local

B_d

gauges along same-base fine-tuning trajectories recovers 91.1% of cross-run coordinates at 1500 steps versus 60.3% for endpoint matching, and the gain is not explained by merely routing through the base. The recovered gauge transfers tools that permutation-only alignment breaks: TinyLlama SAE reconstruction has NMSE 0.004 under

B_d

versus 1.08 under

S_d

; Qwen sentiment steering preserves 95.8% of its effect versus 17.2%; refusal steering reverses sign under

S_d

; coordinate-preserving merges behave the same way. The same covariance governs stateful training: signed transport of AdamW state preserves the resumed trajectory, while permutation-only state follows a different one from a functionally identical checkpoint. Finally, gauge-sweep audits show index-level interpretability claims are reproducible only relative to an explicit gauge.

John Sweeney

Sideplane AI

Batch Normalization Transformer Architectures Intermediate Checkpoints Latent Transport Transport Symmetry+1

Jun 30, 2026cs.CV

Do Not Break the Vessels: Structure-Preserving Mean Flow for Vascular Image Translation

Reconstructing anatomically faithful vascular structures from clinically accessible imaging modalities is of substantial clinical significance. However, existing cross-modal translation methods mainly emphasize pixel-level fidelity or visual realism and treat structure preservation as a property of the final output rather than an invariant of the generative process. This limitation often leads to structural discontinuities and artifacts, compromising anatomical coherence and clinical reliability. In this work, we propose a Structure-Preserving Mean Flow (SPMF) framework that formulates vascular image translation as a topology-invariant transport process. Based on a structural invariance principle, we derive an orthogonality constraint on the flow velocity field that formally separates appearance transport from topological distortion. We implement this constraint as a time-weighted surrogate objective within a Brownian bridge diffusion model to preserve topology at every diffusion step. Moreover, we propose a Prototype-Guided Structural Refinement (PGSR) module to align degraded inference-time structures with reliable training-time structures. Experiments on paired NIRII-to-2PF and fundus datasets demonstrate consistent improvements over state-of-the-art methods, achieving peak PSNR values of 24.96 dB and 24.83 dB, respectively.

Changjin Sun, Zhuo Hu, Kaini Wang +6

School of Biological Science and Medical Engineering, Southeast University, Nanjing, China · School of Computer Science and Engineering, Southeast University, Nanjing, China · Department of Computer Science and Engineering, The Chinese University of Hong Kong, Hong Kong, China +2

Latent Transport Meanflow Vessels Cross-Modal

Jun 21, 2026cs.AR

Multi-Level Resistive Synapses for On-Chip Neural Networks: A Physics-Based Design of a Memristive Crossbar Fabric with Quasi-Continuous Conductance States

Building on resistive communication, this paper presents a physics-based design of an on-chip neural network with multi-level memristive synapses supporting a dense spectrum of conductance states. Derived from ionic transport physics, we develop a state-variable model and quantify storable sub-levels under thermal noise, drift, and quantized conductance. We assemble these devices into a 1T1R crossbar fabric, derive the linear algebra of analog vector-matrix multiplication (VMM) under wire resistance, and design a differential synapse for signed weights. A multilayer pipeline executes inference, backpropagation, and weight updates physically in the analog domain. We derive the in-situ outer-product learning rule, its discretization onto the conductance lattice, and the resulting quantization noise. We provide energy, area, capacity, and inter-tile models, showing this substrate is ideally suited for large language models (LLMs). Our design eliminates weight movement, surpassing binary ReRAM and traditional CMOS. We detail the material stack (HfO_2-based), the FEOL/BEOL CMOS foundry-integration flow, a self-contained SPICE model, the complete memristive-FPGA neuromorphic system, and an in-memory self-attention engine with current-mode translinear softmax. Finally, a ternary BitNet datapath shows projected per-token efficiency orders of magnitude better than advanced CPUs or GPUs. The result is a self-contained hardware-native blueprint for a high-density, analog, in-memory neural processor.

David Alejandro Trejo Pizzo

Independent researcher.

Reram Crossbar Neuromorphic Computing Synaptic Plasticity Chip Design Latent Transport

Jun 21, 2026cs.CV

DreamUV: Unwrap Artist-like UV by End-to-End Flow Matching

UV parameterization is a fundamental step in 3D content creation, yet producing production-ready UV layouts remains challenging due to the gap between geometric distortion objectives and the stylistic preferences of professional artists. While classical methods optimize handcrafted energy functions, artist-authored UVs exhibit structural patterns such as straightened seams, axis-aligned islands, and flexible interior deformation, properties that are difficult to explicitly formulate. In this work, we present DreamUV, an end-to-end learning framework that formulates UV unwrapping as a generative Flow Matching problem. Rather than predicting a single optimal parameterization, DreamUV learns a mesh-conditioned transport process that maps noise samples to a distribution of artist-like UV layouts. To reflect real-world authoring practices, we introduce a boundary-aware training strategy that prioritizes seam geometry, and a Model-in-the-Loop Finetuning(MITL) scheme that explicitly accounts for discretization errors during sampling and stabilizes transport dynamics under heterogeneous supervision. We evaluate DreamUV on a large-scale dataset of professionally authored UV layouts. Experiments demonstrate that our method produces significantly straighter boundaries and tighter axis-aligned islands than both classical and learning-based baselines, while maintaining competitive distortion metrics. Qualitative results and a user study with professional artists further confirm that DreamUV generates UV layouts that are not only valid, but aligned with practical production requirements.

Quanyuan Ruan, Jiabao Lei, Xingyi Du +1

South China University of Technology · School of Data Science, The Chinese University of Hong Kong, Shenzhen · Lightspeed

Layouts Deformable Cnn Dream Distortion Latent Transport

Jun 19, 2026cs.LG

Intrinsic Flow Matching on Quantum Pure-State Manifolds with Phase-Aligned Transport

Quantum pure-state ensembles live on complex projective space, making flat Euclidean generative modeling geometrically mismatched. We introduce Intrinsic Flow Matching (IFM), a deterministic transport framework on

\mathbb{CP}^{d-1}

that learns tangent velocity fields using Pancharatnam phase-aligned conditional paths. IFM replaces local score teachers and reverse-time stochastic sampling with manifold probability flow, while horizontal parameterization removes redundant ambient directions. We show that the IFM objective recovers the induced marginal transport field, represents deterministic projective ensemble flows, and yields endpoint and stability guarantees. Empirically, IFM often improves over ambient Euclidean flow matching across higher-qubit, multimodal, spin-coherent, physics-inspired, and amplitude-encoded MNIST image-vector benchmarks, with strongest gains on high-dimensional and coherence-sensitive tasks but not uniformly across every metric.

Jian Xu, Delu Zeng, John Paisley +1

RIKEN iTHEMS · RIKEN AIP · South China University of Technology +1

Conditional Flow Matching Latent Transport Generative Models

Jun 9, 2026cs.LG

First-Order Trajectory Matching: Fast Ensemble Predictions of Chaotic, Turbulent, Stochastic Systems

We introduce First-Order Trajectory Matching (FTM), a surrogate-modeling method that learns the first-order local transport of probability mass from trajectories of stochastic systems. By matching the symmetric first-order motion of trajectories, FTM learns the probability current velocity, whose flow preserves time marginals to match ensemble averages, while also capturing current-like trajectory quantities such as fluxes, circulations, and barrier-crossing currents. FTM learns the current velocity directly from trajectories, avoiding drift, diffusion, and score estimation. Our stability analysis separates discretization error from sampling variance and shows that the one-step simulation-free FTM loss is stable when temporal resolution and sample size are properly balanced. Across stochastic dynamical systems and PDE examples, we empirically demonstrate that FTM provides trajectory-aware ensemble predictions at low, deterministic-rollout cost.

Shreya Jha, Timo Schorlepp, Nicholas Geissler +2

Courant Institute of Mathematical Sciences, New York University

Stochastic Dynamics Single Trajectory Chaos Latent Transport Ensemble

Jun 8, 2026cs.LG

Temporal Sheaf Neural Networks with Dynamic Orthogonal Transport

We introduce Temporal Sheaf Neural Networks (TSNN), a temporal link prediction framework that equips each node with a time-varying orthogonal frame and compares node states only after explicit transport between local coordinate systems. In contrast to existing continuous-time graph models that operate in a shared global embedding space, TSNN models node-specific and evolving interaction semantics through dynamic local frames. The model parameterizes per-node frames via efficient low-rank Householder products, preserves stored hidden states exactly under frame updates, and uses a geometric-residual decoder that anchors predictions on transported distances while learning residual corrections. All computations are strictly causal and use only the pre-event history. We show that the symmetric degree-normalized sheaf Laplacian is orthogonally similar to the symmetric normalized graph Laplacian, with the random-walk normalized form similar in the corresponding degree metric; the full-active, feature-scaled diffusion used by TSNN is exactly a metric-gradient step on the combinatorial sheaf Dirichlet energy, with a degree-free monotone-descent and non-expansiveness guarantee. Frame drift perturbs updates only linearly. Across TGB v2 link-prediction and temporal-heterogeneous leaderboards, together with the DGB benchmark suite, TSNN matches or surpasses the strongest prior methods on most benchmarks, with the largest improvements on graphs exhibiting strong node-role heterogeneity. Ablations confirm the distinct benefit of dynamic frames, orthogonal transport, and geometric-residual decoding.

Md Sadek Hossain Asif, Tanzila Khan, Md. Mosaddek Khan

University of Dhaka

Temporal Graph Neural Networks Sheaf Neural Networks Neural Network Latent Transport

Jun 4, 2026cs.CV

Geodesic Flow Matching on a Riemannian Degradation Manifold for Blind Image Restoration

Blind image restoration requires recovering clean images from observations corrupted by unknown and potentially mixed degradations. While recent deterministic flow-based methods model restoration as transport processes that map degraded images to clean ones, they typically rely on Euclidean interpolation, implicitly assuming linear degradation geometry. In this paper, we explicitly model degradations as points on a low-dimensional Riemannian manifold and formulate restoration as geodesic transport on the joint image-manifold space. Using a geodesic flow matching objective, we learn intrinsic transport dynamics that respect the curvature of degradation space. This framework generalizes linear flow matching, provides a principled treatment of mixed degradations as geodesic compositions, and yields a clean theoretical interpretation for generalization beyond observed degradations.

Akshay Janardan Bankar, Ankita Chatterjee, Sayan Banerjee +3

Samsung Research Institute, Bangalore, India

Riemannian Flow Matching Image Restoration Restoration Riemannian Manifolds Latent Transport

May 31, 2026cs.RO

S2M-Trek: From Single to Multi-Sphere Transport via Per-Frame Deep Sets on a Wheel-Legged Robot

We study the problem of scaling dynamic loco-manipulation from a single free-rolling sphere to multiple spheres transported simultaneously on the back of a wheel-legged quadruped, without fences, grippers, or mechanical stops. Multiple identical free-rolling spheres form an unordered set with no persistent identity: their ordering may change independently at each history frame, creating a \emph{per-frame permutation symmetry} that standard history-concatenation set encoders do not explicitly enforce -- these encoders impose only a shared, diagonal permutation symmetry over the full history. We show that this symmetry mismatch leads to a concrete failure mode in curriculum-based reinforcement learning. Within the same PPO training budget, flat MLPs and branch-wise encoders plateau at or below the two-sphere stage, while a history-concatenation Deep Sets baseline (\HCDS) fails to progress past the two-sphere stage in our runs unless ball-to-slot assignments are randomised during training, suggesting that it exploits slot indices as a curriculum shortcut rather than learning identity-free multi-sphere dynamics. We propose \textbf{Per-Frame Deep Sets (\PFDS)}, which performs permutation-invariant pooling within each history frame before temporal readout; we prove that \PFDS is

\Gframe

-invariant and universally approximates continuous

\Gframe

-invariant policies. A

2{\times}2

ablation over encoder architecture and slot randomisation separates the architectural and data-augmentation pathways, and \PFDS reaches the five-sphere stage with 100% no-drop transport in simulation across all five random seeds. We further distill the \PFDS teacher into \TactSet via DAgger, replacing privileged sphere-state observations with a

16{\times}16

Boolean union contact map, yielding a compact and naturally

\Gframe

-invariant tactile representation.

Zong Chen, Xuebin Li, Jinpeng Xiao +5

School of Mechanical Science and Engineering, Huazhong University of Science and Technology · School of Mathematics, Harbin Institute of Technology

Humanoid Loco-Manipulation Legged Robots Curriculum Reinforcement Learning Latent Transport Symmetry Encoders

May 28, 2026physics.ao-ph

Learning effective Sargassum transport dynamics from limited drifter observations

Floating-material transport is influenced by unresolved processes that are often absent from available circulation products. We develop a data-driven transport-learning framework for learning effective transport corrections from limited Lagrangian observations using physically motivated ocean--atmosphere diagnostics and finite-memory representations motivated in part by inertial-particle memory effects. The diagnostic representation is analyzed through predictive and sparse symbolic-discovery approaches under leave-one-trajectory-out validation. Applications to Sargassum-following drifters in the Puerto Rico region and the Gulf Stream show that the diagnostics contain transport-relevant information beyond the baseline circulation products. Multilayer perceptron (MLP) ensembles provide flexible predictive trajectory corrections, while Sparse Identification of Nonlinear Dynamics (SINDy) tests whether instantaneous or delayed sparse symbolic transport structure can be extracted from the diagnostics. The results differ across flow regimes: (i) in Puerto Rico, delayed sparse symbolic corrections provide modest but systematic improvement; (ii) in the Gulf Stream application, dynamically useful sparse symbolic corrections remain primarily instantaneous even though delayed predictive information persists. These results support finite-memory transport effects in coarse-grained floating-material transport while also illustrating the difficulty of obtaining stable delayed sparse symbolic closures.

F. J. Beron-VEra, M. J. Olascoaga, J. Morell +1

Department of Atmospheric Sciences Rosenstiel School of Marine, Atmospheric, and Earth Science University of Miami Miami, Florida, USA · Department of Ocean Sciences Rosenstiel School of Marine, Atmospheric, and Earth Science University of Miami Miami, Florida, USA · Department of Marine Sciences University of Puerto Rico Mayagüez, Puerto Rico

Latent Transport Lagrangian Methods Transport Inertial

May 21, 2026cs.LG

Open Multimodal Datasets and Open-Source Software for Data-Driven Modeling of Multiphase Transport and Thermal Systems

Data-driven modeling is becoming central to multiphase transport, electronics cooling, acoustic diagnostics, and thermal-fluid digital twins, but progress is limited by fragmented datasets and raw instrument files that are difficult to decode, reuse, or benchmark. This paper presents an open ecosystem of multimodal datasets and open-source software packages developed by the Nano Energy and Data-Driven Discovery (NED3) Laboratory for reproducible AI-enabled thermal-fluid research. We introduce a spatial-plus-temporal dimensionality framework, denoted S+TD, to classify datasets by the dimensionality of measured or simulated fields, including 0+0D point values, 0+1D time series, 1+0D profiles, 2+0D images, 2+1D videos, 3+0D volumetric fields, and multimodal combinations. We organize public NED3 datasets spanning boiling images, acoustic and thermal measurements, high-speed videos, infrared thermography, thermal-resistance measurements, CFD-generated fields, design files, and acoustic-emission data. We also describe complementary software packages, including BubbleID, SeqReg, CFDTwin, IRISApp, decode-wfs, AELab, and FlowLab, which support computer vision, sequence regression, surrogate modeling, infrared analysis, waveform decoding, acoustic-emission analysis, and multimodal diagnostics. Particular emphasis is placed on SeqReg, a general sequence-regression library for 0+1D, 1+1D, and 2+1D data, with applications such as nonintrusive heat-flux estimation. Finally, we discuss future community efforts to build interoperable thermal-fluid databanks and curated AI/ML tool libraries that connect datasets, metadata, decoders, baselines, benchmarks, and physically interpretable models.

Christy Dunlap, Hari Pandey, Stephen Pierson +6

Department of Mechanical Engineering, University of Arkansas, Fayetteville, AR 72701, USA

Multimodal Dataset Data-Driven Heat Diffusion Latent Transport Open-Source Acoustic

May 19, 2026cs.NE

From Mean-Field Limits to Semiclassical Concentration: Global Convergence of the Canonical Evolutionary Strategy

We address the issue of global convergence in stochastic continuous optimization. For that purpose, we formulate the Canonical Evolutionary Strategy (CES) as a controlled mathematical framework to analyze global convergence in evolutionary algorithms via the semiclassical limit of a Schr{ö}dinger-type replicator-mutator equation. We provide a rigorous hierarchy from a discrete individual-based dynamics to a deterministic mean-field limit, demonstrating that global convergence is governed by the principal eigenfunction of the underlying operator. This property, defined as Geometric Selection, naturally prioritizes robust, flat optima over narrow local traps, offering a mathematical justification for the ''survival of the flattest'' phenomenon. Moreover, unlike consensus-driven methods that are prone to premature variance collapse when the global minimizer resides outside the initial support, the replicator-mutator dynamics of CES facilitate intrinsic mass transport. High-dimensional benchmarks (d = 30) confirm this advantage, showing that CES achieves lower residual errors in shifted initialization scenarios where standard consensus-driven and gradient-based methods fail to migrate effectively. By shifting the focus from point-wise consensus to spectral concentration, our framework provides a robust theoretical foundation for global convergence in Evolution Strategies (ES) without the need for additional numerical heuristics.

Matías Neto, Nicolás Garay, Luis Martí +1

Inria Chile Research Center, Av Apoquindo 2827, Las Condes, RM, Chile · Departamento de Ingeniería Matemática, Universidad de Chile, Santiago, Chile

Evolutionary Optimization Convergence Mean-Field Limit Stochastic Optimization Concentration Latent Transport

May 18, 2026q-bio.GN

PACE: Geometry-Aware Bridge Transport for Single-Cell Trajectory Inference

Single-cell trajectory inference from destructive time-course snapshots is fundamentally ill-posed: neither cross-time cell correspondences nor continuous trajectories are observed, so the snapshot distributions alone do not uniquely determine the underlying dynamics. Existing optimal transport and flow-based methods typically couple cells by Euclidean proximity at observed clock times, which can misalign trajectories when development is asynchronous and cells sampled at the same experimental time occupy different latent pseudotime stages. We propose PACE, a trajectory inference framework that recovers geometry-consistent continuous transport dynamics from destructive time-course snapshots through three coupled components. First, PACE constructs a state- and time-dependent anisotropic Riemannian metric that assigns low transport cost along locally supported tangent directions while penalizing normal velocity components. Second, it alternates between refining cross-time couplings under the induced path-action cost and fitting endpoint-preserving neural bridges between adjacent snapshots. Third, it distills the learned bridge dynamics into a global continuous-time velocity field over cellular states. Across seven controlled and biological datasets covering nine held-out reconstruction experiments, PACE achieves the strongest overall reconstruction performance, reducing MMD, Wasserstein-1 distance, and Wasserstein-2 distance by 23.7% on average relative to the strongest competing baseline. PACE also improves RNA-velocity alignment by 15.4% on an embryoid body differentiation benchmark, without requiring explicit cell pairing, lineage tracing, or RNA-velocity supervision during training. Code is available at https://github.com/AI4Science-WestlakeU/PACE.

Chenglei Yu, Chuanrui Wang, Bangyan Liao +1

Zhejiang University · Department of Artificial Intelligence, School of Engineering, Westlake University

Latent Transport Missing Bridge Transport Lineages

May 18, 2026cs.CV

SRC-Flow: Compact Semantic Representations Enable Normalizing Flows for Image Generation

Normalizing flows (NFs) provide exact likelihoods and deterministic invertible sampling, but have historically lagged behind diffusion models for large-scale image generation. We identify a key obstacle: NFs are required to learn a single invertible transport over the full ambient space, making them highly sensitive to high-dimensional representations. This leads to a semantic-capacity mismatch in modern visual representation spaces, where semantic information is compact but encoded in overcomplete features. We propose SRC-Flow, which introduces a Semantic Representation Compressor (SRC) to compact high-dimensional RAE features into a low-dimensional semantic space before flow modeling and preserve reconstruction through the frozen RAE decoder. This compact space reduces the modeling burden of NFs and enables effective likelihood-based generation in semantic representation space. We further adopt constant noise regularization tailored to the fixed unconditional bijection learned by flows. On ImageNet

256 \times 256

and

512 \times 512

, SRC-Flow achieves state-of-the-art generation quality among normalizing flow methods, with gFID scores of 1.65 and 2.07 under classifier-free guidance, while retaining exact likelihood computation in the compact semantic representation space and deterministic invertible sampling at the flow level. Codes and models will be available at https://github.com/longtaojiang/SRC-Flow.

Longtao Jiang, Jianmin Bao, Zhendong Wang +4

University of Science and Technology of China · Kling Team, Kuaishou Technology

Normalizing Flows Multi-Reference Image Generation Image Generation Autoencoder Architectures Latent Transport

May 14, 2026cs.LG

Eradicating Negative Transfer in Multi-Physics Foundation Models via Sparse Mixture-of-Experts Routing

Scaling Scientific Machine Learning (SciML) toward universal foundation models is bottlenecked by negative transfer: the simultaneous co-training of disparate partial differential equation (PDE) regimes can induce gradient conflict, unstable optimization, and plasticity loss in dense neural operators. In particular, broadband open-channel fluid dynamics and boundary-dominated porous media flows impose incompatible spectral and geometric demands on a single dense parameter path. We introduce Shodh-MoE, a sparse-activated latent transformer architecture for multi-physics transport. Shodh-MoE operates on compressed 16^3 physical latents produced by a physics-informed autoencoder with an intra-tokenizer Helmholtz-style velocity parameterization, restricting decoded states to divergence-free velocity manifolds. The model guarantees exact mass conservation, achieving a physically verifiable velocity divergence of ~2.8 x 10^-10 (evaluated post-hoc in FP64) on 128^3 grids. A Top-1 soft-semantic router dynamically assigns localized latent patches to expert subnetworks, enabling specialized parameter paths for distinct physical mechanisms while preserving shared experts for universal symmetries. In a 20,000-step distributed pretraining run over mixed three-dimensional physical tensors, routing telemetry shows autonomous domain bifurcation: held-out validation tokens from the open-channel domain route exclusively to Expert 0, while porous-media tokens route exclusively to Expert 1. The model converges simultaneously across both regimes, achieving latent validation MSEs of 2.46 x 10^-5 and 9.76 x 10^-6, and decoded physical MSEs of 2.48 x 10^-6 and 1.76 x 10^-6. These results support sparse expert routing as a practical architectural mechanism for mitigating multi-physics interference in universal neural operators.

Ellwil Sharma, Arastu Sharma

Shodh AI

Latent Transport Wireless Foundation Models Localized Lora-Moe Foundation Model

May 13, 2026cs.LG

Path-independent Flow Matching for Multi-parameter Generative Dynamics

Flow Matching is a powerful framework for learning transport maps between probability distributions. Yet its standard single-parameter formulation is not designed to capture multi-parameter variations where the resulting transport should be path-independent. Path independence is crucial because it ensures that transformations depend only on the initial and target distributions, not on the specific path. In this work, we introduce Path-independent Flow Matching (PiFM), a method for learning vector fields whose induced flows yield path-independent transport between distributions. We show that PiFM generalizes Flow Matching to higher-dimensional parameter domains while enforcing structural conditions that ensure consistency of composed transformations. In addition, we show that, under suitable assumptions, PiFM approximates the Wasserstein barycenter, linking the framework to a notion of distributional interpolation. To enable practical training, we propose a tractable, simulation-free objective that regresses onto multi-parameter conditional probability paths. We showcase empirically that PiFM outperforms other approaches on both synthetic and real world data in interpolating path-independent trajectories and generating desired out of distribution samples.

Francisco Téllez, AmirHossein Zamani, Philippe Martin +5

Université de Montréal, Mila · Concordia University, Mila · Concordia University +2

Conditional Flow Matching Latent Transport Vector Fields Interpolation

May 13, 2026cs.LG

U-HNO: A U-shaped Hybrid Neural Operator with Sparse-Point Adaptive Routing for Non-stationary PDE Dynamics

Solutions to many partial differential equations (PDEs) display coexisting smooth global transport and localized sharp features within a single trajectory: shock fronts, thin interfaces, and concentrated high-frequency content sit on top of slowly varying backgrounds. This poses a challenge for neural operators: Fourier-based architectures mix nonlocal interactions efficiently but tend to under-resolve localized non-smooth features, whereas spatially local architectures recover fine detail at the cost of long-range propagation and rollout stability. Existing hybrid operators paper over this tension with a fixed, spatially uniform fusion that forces the same trade-off everywhere. We propose U-HNO, a U-shaped hybrid neural operator whose central design is Sparse-Point Adaptive Routing (SPAR): at every spatial location, a per-pixel hard mask selects whether the global Fourier branch or the local multi-scale Gaussian branch should dominate, and the sparsity ratio is a function of the local contrast of the routing signal, so smooth and shock-aligned regions receive different mixtures of global and local computation. SPAR is embedded in a hierarchical encoder-bottleneck-decoder backbone with skip connections so that the dual branches and the gate operate at every resolution. Training combines pointwise supervision with a finite-difference H^1 gradient term and a band-wise spectral consistency regularizer. Across benchmarks spanning 1D Burgers, Kuramoto-Sivashinsky, KdV, 2D advection, Allen-Cahn, Navier-Stokes, Darcy flow, and 3D transonic compressible Navier-Stokes from PDEBench, U-HNO achieves state-of-the-art rollout accuracy on the majority of tasks in both relative L^2 and H^1 metrics, with the largest gains on problems dominated by sharp localized features. Ablations show that removing any single component substantially degrades rollout error.

Yingzhe Ma, Xiao Yang, Yuxin Xie +2

University of Electronic Science and Technology of China · Peking University

Neural Operators Partial Differential Equations Reynolds-Averaged Navier-Stokes Time Discretization Latent Transport Contrastive Learning

May 10, 2026cs.LG

Teaching Molecular Dynamics to a Non-Autoregressive Ionic Transport Predictor

Unlike most static material properties widely studied in the machine learning literature, ionic transport properties are inherently dynamic, making their fast and accurate prediction from static atomic structures challenging. The current standard approach, molecular dynamics (MD) simulations, suffers from prohibitively high computational cost. Recent autoregressive learning-based MD acceleration methods requiring sequential inference remain slow and prone to error accumulation; in contrast, existing non-autoregressive material property prediction models are less accurate because they fail to exploit dynamics. Moreover, existing methods typically benefit from datasets either with or without atomic trajectories, but not both. To overcome these limitations, we propose a non-autoregressive learning framework based on auxiliary modality learning, which treats atomic trajectories as an auxiliary modality during training but does not require them at inference. This enables the predictor to learn dynamics without sequential inference while benefiting from both types of datasets. As a result, our framework achieves over 200 times speedup compared to autoregressive models on the dataset with atomic trajectories while substantially reducing prediction error relative to non-autoregressive benchmarks across both types of datasets. Our code is available at https://github.com/jykim-git/MD.

Jiyeon Kim, Byungju Lee, Won-Yong Shin

School of Mathematics and Computing (Computational Science and Engineering), Yonsei University, Seoul, Republic of Korea · Korea Institute of Science and Technology (KIST), Seoul, Republic of Korea · Nanoscience and Technology, KIST School, University of Science and Technology, Seoul, Republic of Korea

Molecular Dynamics Latent Transport Transport

May 9, 2026cs.LG

Data-driven transport modelling without overfit

Macroscopic transport modelling aims to predict traffic flows after proposed public policy interventions, such as a new road or railway section or a temporary road closure. As such, it is a vital step in infrastructure planning and development. Traditionally, building a transport model has relied on complex understanding of socio-economic characteristics of the population requiring expensive data collection via surveys, which are prone to biases. Previous numerical frameworks to optimize transport models to fit observed traffic flows are not easily-interpretable and can lead to overfit. We present here an alternative: a data-driven modelling protocol with objective function based on traffic counts, which can be nowadays cheaply and reliably obtained; explainable model weights; and a controlled path to increase model complexity and accuracy. We demonstrate our approach on several toy and realistic examples, and suggest ways to generalize to multimodal systems including public transport.

Peter Vanya, Katarína Šimková, Rastislav Farkaš

Sev.en Global Investments, V Celnici 4, 11000 Prague, Czechia · Vrije Universiteit Brussels, Brussels, Belgium · Universit´e Libre de Bruxelles, Brussels, Belgium +1

Transport Data-Driven Latent Transport Overfitting Model Weights

May 5, 2026stat.ML

Entropic Riemannian Neural Optimal Transport

Many machine learning problems involve data supported on curved spaces such as spheres, rotation groups, hyperbolic spaces, and general Riemannian manifolds, where Euclidean geometry can distort distances, averages, and the resulting optimal transport (OT) problem. Existing manifold OT methods have pursued amortized out-of-sample maps, while entropic regularization has made discrete OT more scalable, but these advantages have remained largely disjoint. We propose Entropic Riemannian Neural Optimal Transport (Entropic RNOT), a unified framework that combines intrinsic entropic OT with amortized out-of-sample evaluation on Riemannian manifolds. Our method learns a single target-side Schrödinger potential through a neural pullback parameterization, recovers the induced Gibbs coupling, and uses the resulting conditional laws to construct intrinsic transport surrogates. These include barycentric projections on Cartan-Hadamard manifolds and heat-smoothed conditional surrogates on stochastically complete manifolds, the latter turning possibly atomic target laws into absolutely continuous ones. For fixed regularization

\varepsilon>0

, we prove that the proposed hypothesis class recovers the entropic optimal coupling in strong probabilistic metrics. As consequences, barycentric surrogates converge in

L^2

, while heat-smoothed surrogates are stable at fixed heat time and asymptotically unbiased as the heat time vanishes. The guarantees hold for compactly supported data on possibly noncompact manifolds. Empirically, our method matches or improves over Euclidean, tangent-space, and log-Euclidean baselines on benchmarks over

\mathbb{S}^2

,

\mathrm{SO}(3)

,

\mathrm{SPD}(3)

,

\mathrm{SE}(3)

, and

\mathbb{H}^2

, scales favorably relative to discrete manifold Sinkhorn, and in a protein-ligand docking application, refines poses on

\mathrm{SE}(3)

without retraining or per-instance optimization.

Alessandro Micheli, Silvia Sapora, Anthea Monod +1

Imperial College London London, UK · University of Oxford Oxford, UK · Statens Serum Institut Copenhagen, Denmark +1

Differentiable Optimal Transport Kullback-Leibler Regularization Latent Transport

May 5, 2026cs.LG

A Few-Step Generative Model on Cumulative Flow Maps

We propose a unified, few-step generative modeling framework based on \emph{cumulative flow maps} for long-range transport in probability space, inspired by flow-map techniques for physical transport and dynamics. At its core is a cumulative-flow abstraction that connects local, instantaneous updates with finite-time transport, enabling generative models to reason about global state transitions. This perspective yields a unified few-step framework built on cumulative transport and \revise{cumulative} parameterization that applies broadly to existing diffusion- and flow-based models without being tied to a specific prediction \revise{instantiation}. Our formulation supports few-step and even one-step generation while preserving synthesis quality, requiring only minimal changes to time embeddings and training objectives, and no increase in model capacity. We demonstrate its effectiveness across diverse tasks, including image generation, geometric distribution modeling, joint prediction, and SDF generation, with reduced inference cost.

Zhiqi Li, Duowen Chen, Yuchen Sun +1

Georgia Institute of Technology, Atlanta, United States of America

Flow Map Flow Models Generative Models Latent Transport

Apr 27, 2026cs.LG

Geometry-free prediction of inertial lift forces in microfluidic devices using deep learning

Inertial microfluidic devices (IMDs) offer low-cost, high-throughput alternative techniques for many traditional particle- (or cell-) manipulation tasks, but simulating them requires being able to predict particle migration, and thus particle lift forces, under a variety of possible channel geometries. Recent work has demonstrated that machine learning models can be used to drastically speed up these numerical simulations, but doing so required training individual models for every unique channel cross-section type (e.g., rectangular, triangular) -- shifting the burden from the simulation step to the training step. In this paper, we develop a novel approach for predicting particle lift forces that contains no explicit geometric parameters. We train a neural network model using a new parameter set and show that while it performs comparably to existing models on channel geometries in the training set, it is able to generalize to unseen channel geometries far more effectively. We show that the lift force model developed herein can be easily transferred to particle tracing simulation software, where it is capable of predicting particle migration patterns consistent with the literature across a variety of channel designs.

Jesse Ward-Bond, Ali Mashadian, Timothy C. Y. Chan +1

aDepartment of Mechanical & Industrial Engineering, University of Toronto · bMechanical Engineering, Purdue University · cDepartment of Materials Science & Engineering, University of Toronto +1

Fluid Controls Latent Transport Deep Learning

Apr 22, 2026math.OC

Integrated packing, placement, scheduling, and routing of personalized production: a pharmaceutical Industry 4.0 use-case with a planar transport system

The recent emergence of planar transport systems necessitates re-evaluation of Flexible Manufacturing Systems (FMS) to address the simultaneous scheduling of internal logistics and production operations. By operating on a tile-based planar grid, these systems allow independent movers full two-dimensional freedom, mitigating inefficiencies inherent to traditional sequential lines. This paper applies a planar FMS framework to a real-world use case in the pharmaceutical industry: the automated production of personalized drugs. Implementing this system requires solving optimization problems at both tactical and operational levels. The tactical level involves decisions regarding production line layout and the positioning of drug dispensers. A Mixed-Integer Quadratic Programming model is utilized for the packing problem to exploit drug co-occurrence patterns found in historical patient data. Subsequently, we solve the placement problem - a bi-level problem combining an assignment problem with Shortest Hamiltonian paths with neighborhoods - to arrange dispensers in a layout minimizing expected travel distances. The operational level is encountered daily, scheduling individual movers to process new orders as quickly as possible. This scheduling problem is formulated using Constraint Programming, modeling movers as reservoir resources to ensure order completeness, complemented by a routing phase using an iterative conflict-resolution mechanism and DAG-based reasoning to convert schedules into conflict-free paths. Evaluation using real-world prescription data for 40 drugs shows the framework scales efficiently across several layout topologies for up to 500 orders, with schedules that are highly effective and computationally tractable for daily operations.

Viktor Emil Korladinov, Antonin Novak, Zdeněk Hanzálek +2

Faculty of Electrical Engineering, Czech Technical University in Prague, Karlovo Náměstí 13, 120 00, Prague 2, CZ · Czech Institute of Informatics, Robotics and Cybernetics, Czech Technical University in Prague, Jugoslávských partyzánů 1580/3, 160 00, Prague 6, CZ · Department of Chemical Engineering, University of Chemistry and Technology, Technická 3, 166 28, Prague, CZ

Job Shop Scheduling Logistics Industrial Automation Mixed-Integer Programming Industrial Latent Transport+1

Apr 17, 2026cs.LG

Collective Kernel EFT for Pre-activation ResNets

In finite-width deep neural networks, the empirical kernel

G

evolves stochastically across layers. We develop a collective kernel effective field theory (EFT) for pre-activation ResNets based on a

G

-only closure hierarchy and diagnose its finite validity window. Exploiting the exact conditional Gaussianity of residual increments, we derive an exact stochastic recursion for

G

. Applying Gaussian approximations systematically yields a continuous-depth ODE system for the mean kernel

K_0

, the kernel covariance

V_4

, and the

1/n

mean correction

K_{1,\mathrm{EFT}}

, which emerges diagrammatically as a one-loop tadpole correction. Numerically,

K_0

remains accurate at all depths. However, the

V_4

equation residual accumulates to an

O(1)

error at finite time, primarily driven by approximation errors in the

G

-only transport term. Furthermore,

K_{1,\mathrm{EFT}}

fails due to the breakdown of the source closure, which exhibits a systematic mismatch even at initialization. These findings highlight the limitations of

G

-only state-space reduction and suggest extending the state space to incorporate the sigma-kernel.

Hidetoshi Kawase, Toshihiro Ota

CyberAgent, Inc., Shibuya, Tokyo 150–6121 Japan

Residual Networks Renormalization Group Neural Tangent Kernel Effective Field Theory Gaussian Primitives Latent Transport

Apr 16, 2026stat.ML

One-Shot Generative Flows: Existence and Obstructions

We study dynamic measure transport for generative modeling, focusing on transport maps that connect a source measure

P_0

to a target measure

P_1

by integrating a velocity field of the form

v_t(x) = \mathbb{E}[\dot X_t \mid X_t = x]

, where

X_\bullet = (X_t)_t

is a stochastic process satisfying

(X_0,X_1)\sim{P_0}\otimes{P_1}

and

\dot X_t

is its time derivative. We investigate when

X_\bullet

induces a \emph{straight-line flow}: a flow whose pointwise acceleration vanishes and is therefore exactly integrable by any first-order method. First, we develop multiple characterizations of straight-line flows in terms of PDEs involving the conditional statistics of the process. Then, we prove that straight-line flows under endpoint independence exhibit a sharp dichotomy. On the one hand, we construct explicit, computable straight-line processes for arbitrary Gaussian endpoints. On the other hand, we show that straight-line processes do not exist for targets with sufficiently well-separated modes. We demonstrate this obstruction through a sequence of increasingly general impossibility theorems that uncover a fundamental relationship between the sample-path behavior of a process with independent endpoints and the space-time geometry of this process' flow map. Taken together, these results provide a structural theory of when straight-line generative flows can, and cannot, exist.

Panos Tsimpos, Daniel Sharp, Youssef Marzouk

Operations Research Center · Massachusetts Institute of Technology · Cambridge, MA 02139 +2

Invertible Flows Velocity Field Latent Transport Obstacle Avoidance

Mar 18, 2026cs.LG

SCALE:Scalable Conditional Atlas-Level Endpoint transport for virtual cell perturbation prediction

Virtual-cell models aim to predict how cell populations respond to perturbations, but control and treated cells are measured as unpaired populations, complicating the learning of perturbation-specific effects. We present SCALE, a conditional transport model that represents cells as unordered sets and predicts treated populations without cell-level matching. A shared set-aware encoder and conditional DiT backbone learn latent transport, making endpoint supervision directly delta-aligned without an auxiliary delta objective. Across genetic, chemical, developmental and immune perturbations, SCALE recovered gene-expression changes, response directions and population structure. In CRISPR data with dominant cell-line effects, SCALE outperformed competing methods across seven metrics and maintained separation among gene-target representations rather than collapsing them into a shared region. SCALE further prioritized cytokines predicted to produce distinct immune activation and inflammatory responses. Experiments using matched PBMC samples from three donors confirmed these predicted differences. Together, SCALE enables perturbation-specific prediction from unpaired populations and supports experimental prioritization.

Shuizhou Chen, Lang Yu, Xueqin Lin +12

1Shanghai Artificial Intelligence Laboratory

Single-Cell Perturbation Prediction Cohort Latent Transport