arXiv:2510.21210v1 Announce Type: new 
Abstract: Generative models based on flow matching have demonstrated remarkable success in various domains, yet they suffer from a fundamental limitation: the lack of interpretability in their intermediate generation steps. In fact these models learn to transform noise into data through a series of vector field updates, however the meaning of each step remains opaque. We address this problem by proposing a general framework constraining each flow step to be sampled from a known physical distribution. Flow trajectories are mapped to (and constrained to traverse) the equilibrium states of the simulated physical process. We implement this approach through the 2D Ising model in such a way that flow steps become thermal equilibrium points along a parametric cooling schedule.
  Our proposed architecture includes an encoder that maps discrete Ising configurations into a continuous latent space, a flow-matching network that performs temperature-driven diffusion, and a projector that returns to discrete Ising states while preserving physical constraints.
  We validate this framework across multiple lattice sizes, showing that it preserves physical fidelity while outperforming Monte Carlo generation in speed as the lattice size increases. In contrast with standard flow matching, each vector field represents a meaningful stepwise transition in the 2D Ising model's latent space. This demonstrates that embedding physical semantics into generative flows transforms opaque neural trajectories into interpretable physical processes.

تسلط دراسة جديدة حول نماذج التوليد المعتمدة على مطابقة التدفق الضوء على نجاحها، لكنها تشير إلى مشكلة كبيرة: نقص القابلية للتفسير في خطواتها الوسيطة. تقوم هذه النماذج بتحويل الضوضاء إلى بيانات من خلال تحديثات حقول متجهة، لكن معنى كل خطوة يبقى غامضًا. يقترح الباحثون إطارًا لمعالجة هذه المشكلة، مما قد يعزز فهمنا لهذه النماذج ويحسن تطبيقها عبر مجالات مختلفة.

Un nuevo estudio sobre modelos generativos basados en el emparejamiento de flujo destaca su éxito, pero señala un problema significativo: la falta de interpretabilidad en sus pasos intermedios. Estos modelos transforman ruido en datos a través de actualizaciones de campos vectoriales, pero el significado detrás de cada paso no está claro. Los investigadores proponen un marco para abordar esta limitación, lo que podría mejorar nuestra comprensión de estos modelos y su aplicación en varios campos.

Une nouvelle étude sur les modèles génératifs basés sur le flow matching met en lumière leur succès tout en soulignant un problème majeur : le manque d'interprétabilité dans leurs étapes intermédiaires. Ces modèles transforment le bruit en données à travers des mises à jour de champs vectoriels, mais la signification de chaque étape reste floue. Les chercheurs proposent un cadre pour remédier à cette limitation, ce qui pourrait améliorer notre compréhension de ces modèles et leur application dans divers domaines.

A new study on flow matching generative models highlights their success but points out a significant issue: the lack of interpretability in their intermediate steps. These models transform noise into data through vector field updates, yet the meaning behind each step is unclear. The researchers propose a framework to address this limitation, which could enhance our understanding of these models and improve their application across various fields.

On the flow matching interpretability

arXiv:2512.01172v1 Announce Type: new 
Abstract: Mean-field games (MFGs) study the Nash equilibrium of systems with a continuum of interacting agents, which can be formulated as the fixed-point of optimal control problems. They provide a unified framework for a variety of applications, including optimal transport (OT) and generative models. Despite their broad applicability, solving high-dimensional MFGs remains a significant challenge due to fundamental computational and analytical obstacles. In this work, we propose a particle-based deep Flow Matching (FM) method to tackle high-dimensional MFG computation. In each iteration of our proximal fixed-point scheme, particles are updated using first-order information, and a flow neural network is trained to match the velocity of the sample trajectories in a simulation-free manner. Theoretically, in the optimal control setting, we prove that our scheme converges to a stationary point sublinearly, and upgrade to linear (exponential) convergence under additional convexity assumptions. Our proof uses FM to induce an Eulerian coordinate (density-based) from a Lagrangian one (particle-based), and this also leads to certain equivalence results between the two formulations for MFGs when the Eulerian solution is sufficiently regular. Our method demonstrates promising performance on non-potential MFGs and high-dimensional OT problems cast as MFGs through a relaxed terminal-cost formulation.

تقدم دراسة جديدة طريقة تعتمد على التدفق القائم على الجسيمات لمعالجة التحديات الحسابية للألعاب ذات المجال المتوسط (MFG) عالية الأبعاد، والتي تحلل توازن ناش في أنظمة تحتوي على عدد كبير من الوكلاء المتفاعلين. تقوم هذه الطريقة بتحديث الجسيمات باستخدام معلومات من الدرجة الأولى وتدريب شبكة عصبية للتدفق لمطابقة سرعات المسارات العينة دون محاكاة.

Un nuevo estudio presenta un método de Flow Matching basado en partículas que busca abordar los desafíos computacionales de los Juegos de Campo Medio (MFG) de alta dimensión, que analizan el equilibrio de Nash en sistemas con numerosos agentes interactuantes. Este método actualiza partículas utilizando información de primer orden y entrena una red neuronal de flujo para igualar las velocidades de las trayectorias de muestra sin simulaciones.

Une nouvelle étude présente une méthode de Flow Matching basée sur des particules, visant à relever les défis computationnels des jeux à champ moyen (MFG) de haute dimension, qui analysent l'équilibre de Nash dans des systèmes avec de nombreux agents interagissant. Cette méthode met à jour les particules en utilisant des informations de premier ordre et entraîne un réseau de neurones de flux pour faire correspondre les vitesses des trajectoires d'échantillons sans simulations.

A new study introduces a particle-based deep Flow Matching method aimed at addressing the computational challenges of high-dimensional Mean-Field Games (MFGs), which analyze the Nash equilibrium in systems with numerous interacting agents. This method updates particles using first-order information and trains a flow neural network to match sample trajectory velocities without simulations.

On the flow matching interpretability

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