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Research · AI field

Flow matching

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

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81papers this week−50.9% vs last week619 this month

Papers

  • arXiv cs.LGOct 19

    Trajectory Replay: Continuous-Time Mixture Transport for Lifelong Generative Models

    Alessandro Palma, Charles Jones, Tristan Cinquin, Fabian J. Theis, Frederik Wenkel

    Adapting pre-trained continuous-time generative models to sequentially incoming data without forgetting earlier tasks is a central challenge in lifelong learning. A leading strategy, generative replay, uses a generative model trained on historical tasks to augment its own continual update with synthetic samples from experience. However, it requires full trajectory simulations at every training step, which accumulate discretization errors and can degrade the replayed historical distribution. Here, we propose trajectory replay, which bypasses sample generation by training an updated velocity field to match both a frozen historical velocity along its trajectories and the incoming task's velocity field, weighted by a stability-plasticity coefficient. Through the lens of continuous-time transport, we show the resulting optimum averages the two task velocities by their respective densities and generates the mixture of their probability paths. Combined with mean velocity distillation, trajectory replay accesses historical trajectories using only a few network evaluations per continual update. Empirically, it outperforms generative replay and distillation baselines on class-incremental…

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  • arXiv cs.LGOct 19

    Cross-Fitting for Neural Posterior Estimation

    Jeffrey Regier

    Neural Posterior Estimation (NPE) fits an amortized conditional density estimator to a simulated training set of complete-data realizations. NPE's training objective, log-likelihood, favors posterior approximations that assign arbitrarily high density to the training points, and typical families of amortized conditional density estimators (e.g., normalizing flows, Gaussian encoders) are flexible enough to oblige. The resulting policy of extreme overconfidence translates poorly to held-out data. Early stopping and other regularizers can prevent this degeneracy, but they are limited to selecting posterior approximations along an unfavorable optimization trajectory set by in-sample residuals, where the posterior mean is underfit while the posterior variance is overfit. To avoid this trade-off, we propose Cross-Fitting NPE (CF-NPE), which uses sample splitting to separate conditional-mean estimation from the estimation of the posterior's higher moments. Using $K$-fold cross-fitting, CF-NPE fits $K$ posterior-mean regressors and then fits a conditional density estimator to the resulting out-of-fold residuals. In experiments with synthetic data and in a cosmological application, CF-NPE…

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  • arXiv cs.CVOct 19

    MRI Reconstruction Risk Estimation from Inference Dynamics

    Tamir Shor, Alex Bronstein

    Iterative MRI reconstructors produce intermediate estimates before returning a final image. We study these inference trajectories as a model-internal representation of realized reconstruction risk, measured by log-NMSE. Model-native states are projected to magnitude images, summarized by a fixed 16-dimensional descriptor, and mapped to risk using a source-trained ridge readout. Across three reconstruction backbones, trajectory features are strongly predictive of reconstruction risk on held-out source data. Under zero-shot target shift, their behavior is backbone-dependent, exhibiting both preserved positive association and readout reversal. Conditional analyses show that trajectory information can remain associated with error beyond an initialization-only predictor. A prefix analysis further shows that useful trajectory information can emerge before reconstruction completes. Repeated-mask and low-shot calibration studies indicate that trajectories primarily encode persistent case difficulty, while their orientation and calibration can change under domain shift.

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  • arXiv math.NAOct 19

    Residual-Based Adaptive Refinement in Hybrid Variational-Collocation PINNs for Singular Elliptic PDEs with Mixed Dirichlet-Neumann Boundary Conditions

    Somnath Giri, Muslim Malik, Rishikesh Yadav

    Solutions of second-order elliptic PDE problems on nonconvex or cracked domains with mixed Dirichlet-Neumann conditions typically lie outside $H^2(Ω)$. Near re-entrant corners, crack tips and points where the boundary condition changes type, the gradient grows like $r^{λ-1}$ with $λ<1$. We study residual-based adaptive refinement in hybrid variational-collocation PINNs. A multiscale Fourier-feature network is trained on a composite loss. The loss combines a variational residual tested against Legendre bubble functions, a strong-form collocation term and penalties for the Dirichlet and Neumann data. The variational term needs only first derivatives of the network, whereas the collocation term requires second derivatives and provides a residual that can be evaluated at any point. After each training stage, candidate points selected by this residual are added to the collocation set. The method is tested on five two dimensional benchmarks, namely a Mode~III crack, a cross-shaped domain with four re-entrant corners with unequal amplitude, a reaction-diffusion problem with four localized peaks, a monotone semilinear problem with a boundary layer and the Motz problem. Compared with…

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  • arXiv stat.MLOct 19

    R2-GP: Variance-Calibrated Priors for Additive Gaussian Processes

    Javier Enrique Aguilar, Soham Mukherjee, David Kohns

    We develop R2-GP, an R2D2-type prior for Gaussian process (GP) generalised additive models (GAMs) that calibrates explained variance ($R^2$) for Matérn covariance kernels. The function variance for standard Matérn kernels depends jointly on the effect magnitude and length-scale. As such, smooth and rough components with identical amplitudes contribute very different amounts of variation. With independent priors on component amplitudes, this variation results in variance overestimation, especially in higher dimensions. We overcome this by taking direct control over each component's expected contribution to prior explained variance. We do this by rescaling each component based on its length scale and observed inputs, and modelling each rescaled variance as a share of the function variance induced by a global $R^2$ prior. This allows R2-GP to scale well to many components. To also scale to large sample sizes, we extend R2-GP to Hilbert space approximation methods, a framework for kernels exploiting their spectral decompositions for fast and efficient inference. Our simulations and real-world case studies demonstrate superior generalisation and parameter recovery over independent…

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  • arXiv cs.LGOct 19

    CIS-Transolver: A Cross-Layer Incremental-State Neural Operator for Fine-Scale Automotive Aerodynamic Flow Prediction

    Jianglong Liu, Zhicheng Zhu, Jia Hao, Liangyue Jia

    Neural operators offer an efficient data-driven approach to rapid prediction of complex automotive aerodynamic flows. However, spectral bias and other factors limit accurate reconstruction of fine-scale flow variations near complex geometries. Existing studies improve the representation and fitting of fine-scale information mainly through information extraction and training objectives. Further study is needed to determine how extracted local details can be used continually in subsequent operator computations and contribute effectively to the overall flow-field representation. We propose CIS-Transolver, a cross-layer incremental-state neural operator that extends fine-scale modeling from local information extraction to its use across layers. The method extracts fine-scale information through local multiscale analysis and encodes it as geometric moment states that are propagated and updated across layers. By combining information from previous layers with feedback to the value representations in Physics-Attention, the method allows local details to contribute continually to subsequent modeling of global physical correlations. We systematically evaluate CIS-Transolver on three…

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  • arXiv cs.LGOct 19

    Learning SOCP Solver Dynamics with Graph Neural Networks

    Adam Ghalem, Lou Salaün, Davide Rinaldi, Fragkiskos D. Malliaros

    Second-order cone programs (SOCPs) are a fundamental class of convex optimization problems widely applied across engineering domains. Classical interior-point methods are robust and accurate, but their iterative nature can be costly in real-time or repeated-solve settings. This has motivated learning-based solvers that approximate optimizer solutions with neural networks. Recent work has increasingly studied graph neural networks (GNNs) for linear, quadratic, and second-order cone optimization, leveraging their ability to model sparse relational structure among variables, constraints, and objective functions. Most existing GNN-based solvers compress the optimization process into a single forward pass, predicting the optimizer directly without using the intermediate trajectory produced by classical solvers. We introduce SOCPNet, a recursive GNN framework that uses solver trajectories to learn an iterative SOCP solution procedure. A shared GNN model is applied repeatedly, refining the current iterate at each step and enabling inference for a variable number of iterations. Rather than predicting the solution in a single pass, SOCPNet learns from intermediate iterates to…

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  • arXiv cs.CVOct 19

    HP-PnP-Flow: Hybrid Time Scheduling and Projection for Plug-and-Play Image Restoration via Flow Matching

    Yong Li, Xiaojie Wang, Xiaoyan Zhang

    Image restoration is a fundamental inverse problem that seeks to recover high-quality images from degraded observations. Plug-and-Play (PnP) methods provide a flexible framework for integrating pretrained denoisers into iterative reconstruction, whereas flow matching offers an efficient generative modeling approach based on continuous-time ODE dynamics. Very recently, Martin et al.\ (ICLR, 2025) developed a PnP-Flow method, which integrates the PnP framework with flow matching through a time-dependent denoiser constructed from a pretrained flow matching model.By incorporating a different time schedule and an additional pixel-space projection operator, this paper proposes a novel efficient PnP-Flow algorithm (HP-PnP-Flow) that enjoys rigorous convergence guarantees under mild assumptions, without imposing restrictive conditions on iterates required by the aforementioned work. Numerical experiments on CelebA and AFHQ-Cat demonstrate that the newly proposed HP-PnP-Flow algorithm significantly outperforms PnP-Flow on several restoration tasks such as denoising, deblurring, super-resolution, random inpainting, and box inpainting. Notably, our algorithm achieves comparable or better…

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  • arXiv cs.LGOct 19

    PnP-CF: A Consensus Flow-Matching Solver for General Inverse Problems

    Dibyanshu Kumar, Magda Gregorova

    Plug-and-Play (PnP) methods using continuous-time deep generative models as learned data distribution priors enable synthesizing high-quality solutions of model-based inverse problems. The quality of the solutions depends critically on the interplay and consensus between the inverse problem solver and the generative model sampler. We revisit a recently introduced flow-based PnP framework, which we refer to as PnP-CF (Consensus Flow), and extend its application to nonlinear inverse problems, including those with learned neural-network forward operators. PnP-CF combines a flow-matching denoiser with (i) ADMM-like dual variable updates and (ii) a time-adaptive pullback onto the intermediate flow probability path that combines a stochastic and a deterministic component. We discuss how these two features stabilize the algorithm and promote consensus, and demonstrate on a set of experiments that PnP-CF not only solves standard linear inverse problems with quality at least comparable to state-of-the-art baselines, but also extends gracefully to nonlinear inverse problems, including forward operators realized by pretrained neural networks, for which existing methods produce…

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  • arXiv cs.CVOct 19

    LEAP: Accelerating ODE-based Diffusion Sampling with Optimal Linear Leaps

    Haowei Zheng, Zhenyu Zhou, Jiawei Chen, Can Wang, Defang Chen

    Diffusion models primarily rely on general-purpose ODE-based numerical methods for training-free accelerated sampling, but performance degrades with coarse time discretization. In this paper, we propose optimal linear leaps (LEAP), a specialized method grounded in theoretical and empirical investigations of sampling trajectory geometry. Built upon low-dimensionality and cross-trajectory consistency, LEAP formulates a supervised least-squares optimization problem within the local trajectory subspace, achieving a precise approximation of future states without model evaluations. Extensive experiments demonstrate that LEAP outperforms previous methods across diverse modalities, including text-to-image (Stable Diffusion 3.5, FLUX.1-dev) and image-to-3D (TRELLIS.2) generation. Furthermore, LEAP can be seamlessly integrated into existing solver-based methods, offering a plug-and-play enhancement for modern diffusion models. Code is available at https://github.com/zju-pi/LEAP.

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  • arXiv q-fin.CPOct 19

    Arbitrage-Free Implied Volatility Surface Reconstruction via Additive Martingales

    Haochen Luo, Sifan Lin, Xiaolong Luo, An Binh Minh, Yuan Zhang +1

    This work focuses on reconstructing a continuous implied volatility (IV) surface from a small number of option quotes, a fundamental task for option pricing and risk management. We propose Additive Martingale (AddMart), a few-shot IV surface reconstruction framework that satisfies static no-arbitrage conditions by construction. Rather than predicting IVs directly, AddMart maps sparse quotes to non-negative increment densities of an exponential additive martingale, from which valid risk-neutral marginals and IVs are recovered. By incorporating the no-arbitrage structure directly into its architecture, rather than enforcing it through regularization in the learning objective, AddMart produces IV surfaces that satisfy static no-arbitrage conditions throughout the domain. Extensive experiments on ten real-option datasets demonstrate that AddMart achieves competitive reconstruction accuracy with no material static arbitrage violations, while directly enabling the estimation of VaR, CVaR, and crash probabilities.

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  • arXiv cs.CVOct 18

    Test-Time Scaling of Text-to-Image Flow Matching Models with Noise-Rejuvenated Sequential Monte Carlo

    Wenyi Lian, Zheng Zhao, Thomas B. Sch{ö}n

    Test-time scaling of diffusion models with sequential Monte Carlo (SMC) has become a promising strategy for sampling under user-specified rewards, such as human preference scores. However, the standard SMC framework typically relies on stochastic proposals and therefore does not directly transfer to flow matching models, in which inference is governed by deterministic ODEs. In this work, we introduce noise-rejuvenated SMC, an inference-time scaling method tailored for text-to-image flow matching models. Our key idea is to perturb each resampled particle by changing its source noise and constructing a new intermediate state using its current endpoint estimate. This moves the particle to another state that remains representable under the flow-matching interpolation form, enabling particle exploration without converting the sampler to an SDE. We further introduce a look-ahead mechanism to refine resampled particles before weighting. Experiments on Stable Diffusion 3, FLUX.1-dev, and Z-Image demonstrate consistent improvements in reward-guided generation, while ablation studies validate the contributions of noise rejuvenation and look-ahead refinement. Code is available at…

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  • arXiv cs.AIOct 18

    LowNet: Looped Wavelet Neural Networks with 24 Learnable Parameters for Solving Poisson Equations

    Yuanhao Gong

    Poisson equations frequently appear in various fields, such as mathematics, physics and informatics. Solving Poisson equation, however, is challenging. Traditional methods are not data-specific, although have high certainty. They require a large number of iterations due to the CFL numerical stability. In contrast, deep learning methods are data-driven and more efficient, but require accurate training data and suffer from heavy computation. To tackle these issues, we propose a wavelet-inspired Poisson solver with 24 trainable scalars. The proposed network has several advantages. First, it is compact. It has four independent $5\times5$ kernels, each represented by six parameters, leading to 24 scalars in total. Such compact format can be deployed on most devices. Second, thanks to the loop design, it achieves higher accuracy than previous methods. A residual loop reuses the wavelet block without increasing its parameters. Numerical experiments confirm that such loop indeed improves the solving accuracy. On 10000 images, one, two, and three loops of the wavelet block lead to PSNRs of $47.27$, $74.14$, and $100.74$ dB, respectively. Third, the proposed method is computationally fast.…

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  • arXiv stat.MLOct 17

    Martingale Posterior Cox Processes

    Joshua Rooijakkers, Edwin Fong

    Cox processes provide a principled Bayesian nonparametric framework for modeling event-based data through an underlying intensity function. However, existing inference methods for estimating the intensity typically rely on computationally expensive Markov chain Monte Carlo sampling or approximate inference techniques. In addition, to ensure tractability, these methods often define priors over indirect latent structures, making them challenging to interpret. In this paper, we introduce the Martingale Posterior Cox Process (MPCP), which recasts Bayesian intensity estimation as inference over unobserved events given the observed event history. This perspective avoids the need to define complex priors while retaining the flexibility of nonparametric modeling. We propose a scalable, GPU-friendly copula-based predictive update, and provide strong theoretical guarantees for the convergence of the predictive resampling algorithm. Empirically, we show that MPCP provides excellent performance in both simulations and real data at a fraction of the computational cost of competing Bayesian approaches.

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  • arXiv physics.plasm-phOct 17

    Reconstruction of Unobserved Core Electron Density in Tokamak Plasmas with a Neural Operator Transport Surrogate and Uncertainty Quantification

    D. Sorokin, A. Granovskiy, M. Stokolesov, E. Adishchev, M. Nurgaliev +1

    Real-time control of tokamak plasmas requires the electron density profile. However, in a reactor-relevant device, diagnostic port access is limited and the profile can be observed only partially. In the present work we reconstruct the density profile by inferring the coefficients of a physics-based one-dimensional particle transport equation, using a Fourier Neural Operator (FNO) surrogate of the transport solver as a fast differentiable forward model. The surrogate enables realtime-compatible gradient-based reconstruction and uncertainty quantification from the reflectometry and interferometry measurements. We compare four uncertainty quantification methods - multi-seed ensembles, the Laplace approximation, Metropolis-Hastings, and a Gaussian method independent of the reconstruction fit. The resulting uncertainty is scored with CRPS and coverage calibration, separately on the observed and unobserved regions. We further demonstrate advantage of our approach over standard analytical function fit on synthetic and experimental DIII-D discharges.

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  • arXiv stat.MLOct 17

    Denoising Implicit Variational Inference

    Zitong Wang, Zekun Wu, Longlin Yu, Cheng Zhang

    Semi-implicit variational inference (SIVI) expands the representational capacity of variational families, but optimizing the Evidence Lower Bound (ELBO) remains challenging because the marginal score of the semi-implicit distribution is generally intractable. Unbiased Implicit Variational Inference (UIVI) and related methods address this difficulty through reparameterized ELBO gradients, but existing approaches estimate the required score indirectly through reverse-conditional sampling or approximation, which can be computationally costly and unstable. We propose Denoising Implicit Variational Inference (DIVI), which learns the marginal score directly via denoising score matching. The learned score is used as a plug-in estimator in the pathwise ELBO gradient, replacing inner reverse-conditional sampling with a score-network evaluation. We analyze DIVI as inexact stochastic gradient ascent and show, under stated assumptions, that the averaged stationarity measure is controlled by the usual optimization term and the average score-matching error. Empirically, we evaluate DIVI on both synthetic distributions and a variety of real-data Bayesian inference tasks. The results show that…

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  • arXiv cs.CVOct 17

    Unifying Amplitude-Phase Coupling and Reliable Endogenous Priors for Low-Light Image Enhancement

    Tongshun Zhang, Zixuan Zhong, Pingping Liu, Jin Kuang, Yubing Lu +2

    Frequency-domain methods have shown strong potential for low-light image enhancement (LLIE) because they can effectively regulate global illumination. However, most existing methods assume that amplitude and phase can be restored independently, while overlooking their inherent spectral coupling. This artificial decoupling often leads to information inconsistency and structural distortions. To address this issue, we propose a frequency-spatial framework that jointly models spectral interaction and reliable prior guidance. We first empirically analyze the coupling between amplitude and phase and develop an Amplitude-Phase Adaptive Compensation Fusion (APACF) module. Instead of enforcing a hard separation between the two components, APACF enables their bidirectional interaction, resulting in spectrally coherent restoration. In addition, directly extracting priors from raw low-light inputs is unreliable, since severe noise and underexposure destroy critical visual content. To alleviate this problem, we introduce an Endogenous Reliability Prior (ERP). Specifically, we treat an intermediate result, preliminarily restored in the frequency domain and already close to the ground-truth…

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  • arXiv cs.LGOct 16

    Latent State Utilization in Probabilistic Circuits

    Zilei Shao, Anji Liu

    Probabilistic circuits (PCs) are generative models that support efficient probabilistic inference. Adding latent states to a PC increases its representational capacity, but yields diminishing gains in likelihood. We use mutual information to examine how the dependence represented by a trained PC changes with latent size. Experiments with Hidden Chow-Liu Trees (HCLTs) on ImageNet32 show that learned dependence grows slowly and remains well below both the latent-state upper bound and estimates of dependence in the data. To understand how learning uses these states, we examine how strongly each sample favors particular latent states and how broadly states are used across the dataset. Tracking these measurements during HCLT training distinguishes rapid early posterior concentration from the more gradual stabilization of sample-dependent state preferences. Early measurements also guide initialization selection in HCLTs and hidden Markov models (HMMs), as well as tree selection in HCLTs. The resulting choices improve the ultimate performance across the tested latent sizes, providing a practical benefit from our study of latent-state utilization.

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  • arXiv cs.LGOct 16

    Torch-DPhys: A Torch-Native, MOOSE-Compatible Framework for Differentiable Physics Simulation and Hybrid Machine Learning Integration

    Akzhol Almukhametov, Yang Liu

    We present Torch-DPhys, a Torch-native framework implemented in PyTorch for differentiable physics simulation and hybrid physics-machine learning. It implements selected thermal-hydraulic modeling concepts and discretizations from MOOSE's Thermal Hydraulics Module and the System Analysis Module (SAM), with a preliminary extension to continuum mechanics. Native tensor residuals support CPU and GPU execution, compilation of selected numerical kernels, and sparse direct linear solves. Sensitivities are obtained by differentiating executed numerical operations or through discrete adjoints of converged residual equations. Verification combines analytical solutions, reference-code comparisons, and derivative checks. Demonstrations cover plane-strain elasticity, one- and two-loop thermal-hydraulic transients, and an axisymmetric molten-salt fast reactor. For the reactor, comparison with SAM-Lite gives a maximum normalized field discrepancy of 1.13 x 10^-5 over 200 adaptive time steps, demonstrating agreement between the tested discrete implementations. Selected transient sensitivities are assessed using tangent-linear calculations and finite differences on fixed time schedules. Two…

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  • arXiv cs.LGOct 16

    Dynamic Neural Optimal Transport for Subset Alignment

    Austin J. Brockmeier, Bilal Riaz

    We study optimal transport between distributions when only a subset of the target population is relevant to the source. The goal is to map the source distribution to a reweighted target distribution whose density ratio with respect to the full target lies in $[0, c]$. This constraint enables the transported distribution to select an appropriate target subpopulation while limiting how strongly any region of the target can be emphasized. We propose a dynamic neural optimal transport framework for this setting using two neural networks. The first parameterizes a time-dependent potential whose spatial gradient defines the velocity field and whose terminal value enforces the density-ratio constraint. The second parameterizes an interpolation between the source distribution and the learned terminal distribution. Unlike prior neural dynamic optimal transport methods, which typically assume a fixed terminal distribution, our formulation learns the terminal distribution within the support of the target. We demonstrate the method on positive-unlabeled learning, unpaired domain translation, and trajectory inference, where meaningful alignments exist between source and target distributions,…

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Open problems in Flow matching

  • Stable and scalable source-target coupling in flow matching1 paper raises it · 1 addresses it

    Independent random pairing introduces high stochasticity, harming training stability and integration accuracy, especially at scale.

    • Scaling Online Optimal Transport Minibatches for Flow Matchingraises · addresses
  • Efficient few-step generation without fixed discretization1 paper raises it · 1 addresses it

    Fixed timestep discretization in few-step flow matching is heuristic, expensive to tune, and may not adapt to sample difficulty.

    • Few-Step Generation via Data-Space Iterationraises · addresses
  • Data-free and simulation-free distillation for flow/diffusion models1 paper raises it · 1 addresses it

    Existing distillation methods rely on curated datasets, costly teacher rollouts, or auxiliary networks, complicating training and scaling.

    • Consistent Distribution Matching for Data-Free Diffusion Distillationraises · addresses
  • Lifelong adaptation without trajectory simulation errors1 paper raises it · 1 addresses it

    Generative replay in continual learning accumulates discretization errors, degrading historical distribution quality.

    • Trajectory Replay: Continuous-Time Mixture Transport for Lifelong Generative Modelsraises · addresses
  • Dynamics-aligned latent spaces for PDE flow matching1 paper raises it · 1 addresses it

    Predictive representations capture physical information but do not guarantee accurate field evolution without explicit alignment.

    • PDE-JEPA: Predictive Representation Learning of Latent Dynamics Modeling for Parametric PDEsraises · addresses

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