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Tag: flow

  • Flow Matching is Adaptive to Manifold Structures

    Flow Matching is Adaptive to Manifold Structures arXiv:2602.22486v1 Announce Type: new Abstract: Flow matching has emerged as a simulation-free alternative to diffusion-based generative modeling, producing samples by solving an ODE whose time-dependent velocity field is learned along an interpolation between a simple source distribution (e.g., a standard normal) and a target data distribution. Flow-based methods…

  • TFTF: Training-Free Targeted Flow for Conditional Sampling

    TFTF: Training-Free Targeted Flow for Conditional Sampling arXiv:2602.12932v1 Announce Type: new Abstract: We propose a training-free conditional sampling method for flow matching models based on importance sampling. Because a na”ive application of importance sampling suffers from weight degeneracy in high-dimensional settings, we modify and incorporate a resampling technique in sequential Monte Carlo (SMC) during intermediate…

  • Total Variation Rates for Riemannian Flow Matching

    Total Variation Rates for Riemannian Flow Matching arXiv:2602.05174v1 Announce Type: new Abstract: Riemannian flow matching (RFM) extends flow-based generative modeling to data supported on manifolds by learning a time-dependent tangent vector field whose flow-ODE transports a simple base distribution to the data law. We develop a nonasymptotic Total Variation (TV) convergence analysis for RFM samplers…

  • Alignment of Diffusion Model and Flow Matching for Text-to-Image Generation

    Alignment of Diffusion Model and Flow Matching for Text-to-Image Generation arXiv:2602.00413v1 Announce Type: new Abstract: Diffusion models and flow matching have demonstrated remarkable success in text-to-image generation. While many existing alignment methods primarily focus on fine-tuning pre-trained generative models to maximize a given reward function, these approaches require extensive computational resources and may not generalize…

  • Meta Flow Maps enable scalable reward alignment

    Meta Flow Maps enable scalable reward alignment arXiv:2601.14430v1 Announce Type: new Abstract: Controlling generative models is computationally expensive. This is because optimal alignment with a reward function–whether via inference-time steering or fine-tuning–requires estimating the value function. This task demands access to the conditional posterior $p_{1|t}(x_1|x_t)$, the distribution of clean data $x_1$ consistent with an intermediate…

  • Implicit geometric regularization in flow matching via density weighted Stein operators

    Implicit geometric regularization in flow matching via density weighted Stein operators arXiv:2512.23956v1 Announce Type: new Abstract: Flow Matching (FM) has emerged as a powerful paradigm for continuous normalizing flows, yet standard FM implicitly performs an unweighted $L^2$ regression over the entire ambient space. In high dimensions, this leads to a fundamental inefficiency: the vast majority…

  • On The Hidden Biases of Flow Matching Samplers

    On The Hidden Biases of Flow Matching Samplers arXiv:2512.16768v1 Announce Type: new Abstract: We study the implicit bias of flow matching (FM) samplers via the lens of empirical flow matching. Although population FM may produce gradient-field velocities resembling optimal transport (OT), we show that the empirical FM minimizer is almost never a gradient field, even…

  • Non-Negative Stiefel Approximating Flow: Orthogonalish Matrix Optimization for Interpretable Embeddings

    Non-Negative Stiefel Approximating Flow: Orthogonalish Matrix Optimization for Interpretable Embeddings arXiv:2511.06425v1 Announce Type: new Abstract: Interpretable representation learning is a central challenge in modern machine learning, particularly in high-dimensional settings such as neuroimaging, genomics, and text analysis. Current methods often struggle to balance the competing demands of interpretability and model flexibility, limiting their effectiveness in…

  • Mirror Flow Matching with Heavy-Tailed Priors for Generative Modeling on Convex Domains

    Mirror Flow Matching with Heavy-Tailed Priors for Generative Modeling on Convex Domains arXiv:2510.08929v1 Announce Type: new Abstract: We study generative modeling on convex domains using flow matching and mirror maps, and identify two fundamental challenges. First, standard log-barrier mirror maps induce heavy-tailed dual distributions, leading to ill-posed dynamics. Second, coupling with Gaussian priors performs poorly…

  • Fractal Flow: Hierarchical and Interpretable Normalizing Flow via Topic Modeling and Recursive Strategy

    Fractal Flow: Hierarchical and Interpretable Normalizing Flow via Topic Modeling and Recursive Strategy arXiv:2508.19750v1 Announce Type: new Abstract: Normalizing Flows provide a principled framework for high-dimensional density estimation and generative modeling by constructing invertible transformations with tractable Jacobian determinants. We propose Fractal Flow, a novel normalizing flow architecture that enhances both expressiveness and interpretability through…

  • Flow Matching-Based Generative Modeling for Efficient and Scalable Data Assimilation

    Flow Matching-Based Generative Modeling for Efficient and Scalable Data Assimilation arXiv:2508.13313v1 Announce Type: new Abstract: Data assimilation (DA) is the problem of sequentially estimating the state of a dynamical system from noisy observations. Recent advances in generative modeling have inspired new approaches to DA in high-dimensional nonlinear settings, especially the ensemble score filter (EnSF). However,…

  • Smooth Flow Matching

    Smooth Flow Matching arXiv:2508.13831v1 Announce Type: new Abstract: Functional data, i.e., smooth random functions observed over a continuous domain, are increasingly available in areas such as biomedical research, health informatics, and epidemiology. However, effective statistical analysis for functional data is often hindered by challenges such as privacy constraints, sparse and irregular sampling, infinite dimensionality, and…

  • Flow Stochastic Segmentation Networks

    Flow Stochastic Segmentation Networks arXiv:2507.18838v1 Announce Type: cross Abstract: We introduce the Flow Stochastic Segmentation Network (Flow-SSN), a generative segmentation model family featuring discrete-time autoregressive and modern continuous-time flow variants. We prove fundamental limitations of the low-rank parameterisation of previous methods and show that Flow-SSNs can estimate arbitrarily high-rank pixel-wise covariances without assuming the rank…

  • When Diffusion Models Memorize: Inductive Biases in Probability Flow of Minimum-Norm Shallow Neural Nets

    When Diffusion Models Memorize: Inductive Biases in Probability Flow of Minimum-Norm Shallow Neural Nets arXiv:2506.19031v1 Announce Type: new Abstract: While diffusion models generate high-quality images via probability flow, the theoretical understanding of this process remains incomplete. A key question is when probability flow converges to training samples or more general points on the data manifold.…

  • Liouville PDE-based sliced-Wasserstein flow for fair regression

    Liouville PDE-based sliced-Wasserstein flow for fair regression arXiv:2505.17204v1 Announce Type: new Abstract: The sliced Wasserstein flow (SWF), a nonparametric and implicit generative gradient flow, is applied to fair regression. We have improved the SWF in a few aspects. First, the stochastic diffusive term from the Fokker-Planck equation-based Monte Carlo is transformed to Liouville partial differential…

  • PO-Flow: Flow-based Generative Models for Sampling Potential Outcomes and Counterfactuals

    PO-Flow: Flow-based Generative Models for Sampling Potential Outcomes and Counterfactuals arXiv:2505.16051v1 Announce Type: new Abstract: We propose PO-Flow, a novel continuous normalizing flow (CNF) framework for causal inference that jointly models potential outcomes and counterfactuals. Trained via flow matching, PO-Flow provides a unified framework for individualized potential outcome prediction, counterfactual predictions, and uncertainty-aware density learning.…

  • Path Gradients after Flow Matching

    Path Gradients after Flow Matching arXiv:2505.10139v1 Announce Type: new Abstract: Boltzmann Generators have emerged as a promising machine learning tool for generating samples from equilibrium distributions of molecular systems using Normalizing Flows and importance weighting. Recently, Flow Matching has helped speed up Continuous Normalizing Flows (CNFs), scale them to more complex molecular systems, and minimize…

  • Variational Formulation of the Particle Flow Particle Filter

    Variational Formulation of the Particle Flow Particle Filter arXiv:2505.04007v1 Announce Type: new Abstract: This paper provides a formulation of the particle flow particle filter from the perspective of variational inference. We show that the transient density used to derive the particle flow particle filter follows a time-scaled trajectory of the Fisher-Rao gradient flow in the…

  • On the minimax optimality of Flow Matching through the connection to kernel density estimation

    On the minimax optimality of Flow Matching through the connection to kernel density estimation arXiv:2504.13336v1 Announce Type: new Abstract: Flow Matching has recently gained attention in generative modeling as a simple and flexible alternative to diffusion models, the current state of the art. While existing statistical guarantees adapt tools from the analysis of diffusion models,…

  • Introduction to Minimum Cost Flow Optimization in Python

    Introduction to Minimum Cost Flow Optimization in Python Minimum cost flow optimization minimizes the cost of moving flow through a network of nodes and edges. Nodes include sources (supply) and sinks (demand), with different costs and capacity limits. The aim is to find the least costly way to move volume from sources to sinks while…

  • Adaptivity and Convergence of Probability Flow ODEs in Diffusion Generative Models

    Adaptivity and Convergence of Probability Flow ODEs in Diffusion Generative Models arXiv:2501.18863v1 Announce Type: new Abstract: Score-based generative models, which transform noise into data by learning to reverse a diffusion process, have become a cornerstone of modern generative AI. This paper contributes to establishing theoretical guarantees for the probability flow ODE, a widely used diffusion-based…